The post Pulse Width Modulation first appeared on The Amazing World of Electronics.

The post Pulse Width Modulation appeared first on The Amazing World of Electronics.

]]>Pulse Width Modulation (PWM) is a fancy term for describing a type of digital signal. Pulse width modulation is used in a variety of applications including sophisticated control circuitry. A common way we use them is to control the dimming of RGB LEDs or to control the direction of a servo. We can accomplish a range of results in both applications because pulse width modulation allows us to vary how much time the signal is high in an analog fashion. While the signal can only be high (usually 5V) or low (ground) at any time, we can change the proportion of time the signal is high compared to when it is low over a consistent time interval.

When the signal is high, we call this “on time”. To describe the amount of “on time”, we use the concept of the duty cycle. The duty cycle is measured in percentage. The percentage duty cycle specifically describes the percentage of time a digital signal is on over an interval or period of time. This period is the inverse of the frequency of the waveform.

If a digital signal spends half of the time on and the other half off, we would say the digital signal has a duty cycle of 50% and resembles an ideal square wave. If the percentage is higher than 50%, the digital signal spends more time in the high state than the low state and vice versa if the duty cycle is less than 50%. Here is a graph that illustrates these three scenarios:

A 100% duty cycle would be the same as setting the voltage to 5 Volts (high). A 0% duty cycle would be the same as grounding the signal.

You can control the brightness of an LED by adjusting the duty cycle.

With an RGB (red green blue) LED, you can control how much of each of the three colors you want in the mix of colors by dimming them with various amounts.

If all three are on in equal amounts, the result will be a white light of varying brightness. Blue equally mixed with green will get teal. For a slightly more complex example, try turning red fully on, and green 50% duty cycle, and blue fully off to get an orange color.

The frequency of the square wave does need to be sufficiently high enough when controlling LEDs to get the proper dimming effect. A 20% duty cycle wave at 1 Hz will be obvious that it’s turning on and off to your eyes meanwhile, a 20% duty cycle at 100 Hz or above will just look dimmer than fully on. Essentially, the period can not be too large if you’re aiming for a dimming effect with the LEDs.

You can also use pulse width modulation to control the angle of a servo motor attached to something mechanical like a robot arm. Servos have a shaft that turns to a specific position based on its control line.

Frequency/period is specific to controlling a specific servo. A typical servo motor expects to be updated every 20 ms with a pulse between 1 ms and 2 ms, or in other words, between a 5 and 10% duty cycle on a 50 Hz waveform. With a 1.5 ms pulse, the servo motor will be at the natural 90-degree position. With a 1 ms pulse, the servo will be at the 0-degree position, and with a 2 ms pulse, the servo will be at 180 degrees. You can obtain the full range of motion by updating the servo with a value in between.

Pulse width modulation is used in a variety of applications, particularly for control. You already know it can be used for the dimming of LEDs and controlling the angle of servo motors and now you can begin to explore other possible uses. If you’re ready to jump into coding immediately and have an Arduino, look at the PWM coding example here.

*Source: SparkFun.com*

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]]>The post Touchless capacitive switch first appeared on The Amazing World of Electronics.

The post Touchless capacitive switch appeared first on The Amazing World of Electronics.

]]>At rest, the multivibrator has a frequency of about 15 kHz, after activating the sensor by touching it

two fingers on the plate on the side of the components above the frequency sensor surfaces

drops to about 5 kHz. At a greater distance between the fingers and the sensor, the frequency changes

only slightly.

The rectangular signal alternates approximately 1 : 1 from output 3 IO1

to the integration RC cell with trimmer P1 and capacitor C4. The article changes the shape of the signal from rectangular to exponentially triangular. The task of this cell is to convert a change in the frequency of the signal from IO1 to a change in the amplitude of the signal at the output of the cell. With a set resistance of 200 kQ trimmer P1 and at a frequency of 15 kHz, the triangular signal at the output of the cell has an inter-peak swing of about 4 V. As the frequency decreases, the inter-peak swing of the signal at the cell output increases continuously; at 5kHz is about 8V.

The oscillation of the signal from the output of the integrating element is detected by a high-end rectifier with components D1, C5 and R7. At the output of the rectifier (on capacitor C5) there is a ss voltage which is less than the level of the positive peaks of the signal from the integrator by the voltage drop across D1 (about 0.4 V).

At a multivibrator frequency of 15 (or 5) kHz and at a trimmer resistance of 200 kQ

P1 was measured at C5 ss voltage of 7.4 in the realized switch sample

(or 9.3) V.

The magnitude of the voltage on C5 (and therefore also the frequency of the multivibrator) is evaluated

comparator with operational amplifier (OZ) TL071 (IO2). The OZ is chosen with FETs at the input to have an almost infinite input resistance and not load the peak rectifier. The comparator has no hysteresis. The voltage from C5 is applied to the inverter input OZ, to the non-inverting input OZ, the reference voltage from the runner of the trimmer P2 is fed through the protective resistor R3.

The reference voltage must be set roughly midway between the lowest and highest voltage levels on C5.

At rest, when the multivibrator frequency is 15 kHz, the voltage across C5 is less

than the reference, so the inverting input OZ is more negative than non-inverting input. The OZ output is therefore positive saturation (in high H level). Output PNP transistor T1 excited

from the output OZ is turned off and on its collector, which is brought out to terminal 2 of the terminal board K1, there is a low-level L due to the grounding resistor R6

When activating the capacitive sensor, i.e. after reducing the frequency of the multivibrator to

5 kHz, the voltage at C5 will rise above the reference voltage and the inverting input OZ will thus become more positive than the non-inverting one. The OZ output will therefore go into negative saturation (to a low L level). T1 closes and level H appears on terminal 2 of K1. At the same time, green lights up

LED D2 indicating the closed state of T1.

When testing the function of the switch in the laboratory, it turned out that mains hum is transmitted to the capacitive sensor, which

causing a voltage ripple across C5. Consequently, in a situation where the voltage at C5 is close to the reference, T1 switches intermittently.

Construction and revival The capacitive switch is constructed mainly from terminal components on a single-sided printed circuit board. Only R7, which was additionally added to the capacitive switch, is in SMD design to make the additional modification of printed circuit boards as simple as possible. The pattern of connections is in Fig. 3, and the distribution of components on the board is in Fig. 4. The capacitive sensor with plates KC1 and KC2 can be separated from the board and installed in the required place. The sensor is connected to the board by short connections via soldering points J1A to J2B. The surfaces of the sensor may need to be insulated with plastic film so that it is not possible to touch them directly with your hands. First, we solder R7 to the board in SMD design, which is placed on on the connection side, although it is drawn on the components side in Fig. 4. Then we fit the board with outlet components from the lowest to the highest. There is one wire jumper on the board made from a cut-off resistor terminal. There are sockets on the board for both IO1 and IO2 so that they can be used in other designs as well. When reviving, we first set the trimmer P1 so that when the capacitive sensor is activated, the voltage change on C5 is as large as possible. Then we adjust trimmer P2 so that the reference voltage on its runner is roughly midway between the lowest and highest voltage levels on C5.

Parts list

R1 10 MQ/0.6 W/1%, metal.

R2 33 kQ/0.6 W/1%, metal.

R3, R5 10 kQ/0.6 W/1%, metal.

R4, R6 2.2 kQ/0.6 W/1%, metal.

R7 10 MQ/5%, SMD 1206

P1 1 MQ, horizontal trimmer, 10 mm

P2 50 kQ, horizontal trimmer, 10 mm

C1 1000 pF/25 V, radial

C2 100 nF/J/63 V, foil

C3 2.2 nF/J/100 V, foil

C4 220 pF/NPO, ceramic

05 10 nF/J/100 V, foil

D1 1N4148

D2 LED green, 5 mm

T1 BC557B, TO92

101 NE555 CMOS, DIL8

102 TL071, DIL8

2 precision DIL8 sockets for 101 and 102

K1 ARK210/3, three-pole screw terminal block PCB No. KE02Z5R

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]]>The post White LED Lamp first appeared on The Amazing World of Electronics.

The post White LED Lamp appeared first on The Amazing World of Electronics.

]]>light. They are so bright that you shouldn’t look directly at

them. They are still expensive, but that is bound to change.

You can make a very good solid-state pocket torch using a few

of these white LEDs. The simplest approach is naturally to use

a separate series resistor for each LED, which has an operating

voltage of around 3.5 V at 20 mA. Depending on the value of the

supply voltage, quite a bit of power will be lost in the resistors.

The converter shown here generates a voltage that is high

enough to allow ten LEDs to be connected in series. In addition,

this converter supplies a constant current instead of a constant

voltage. A resistor in series with the LEDs produces a voltage

drop that depends on the current through the LEDs. This volt-

age is compared inside the IC to a 1.25-V reference value, and

the current is held constant at 18.4 mA (1.25 V ÷ 68 Ω).

The IC used here is one of a series of National Semiconductor

‘simple switchers’. The value of the inductor is not critical; it

can vary by plus or minus 50 percent. The black Newport coil,

220 µH at 3.5 A (1422435), is a good choice. Almost any type

of Schottky diode can also be used, as long as it can handle at

least 1 A at 50 V. The zener diodes are not actually necessary,

but they are added to protect the IC. If the LED chain is

opened during experiments, the voltage can rise to a value

that the IC will not appreciate.

The PCB shown here is unfortunately not available ready-

made through the Publishers’ Readers Services.

The post White LED Lamp first appeared on The Amazing World of Electronics.

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]]>The post The Basics of Power Conversion and the New Film Capacitors first appeared on The Amazing World of Electronics.

The post The Basics of Power Conversion and the New Film Capacitors appeared first on The Amazing World of Electronics.

]]>Film capacitors have been around for a long time, but modern technologies and processes have radically expanded the capabilities of these tried and true devices. Now, higher capacitance densities, frequencies, environmental ratings, low losses, and life expectancies are all being realized. Today’s power film capacitors are the ideal solution for power conversion in sustainable energy, energy storage, industrial, or automotive applications.

Power conversion circuitry takes energy from a power source and converts it into an output format usable by end devices. Energy sources could be the traditional power grid, renewable energy generators like solar or wind, or stored energy in batteries or capacitor banks. Those sources provide energy that is not conditioned for end devices, but rather it is conditioned for transmission or the raw output from the source.

Power conversion systems have an input stage, where the power is converted from AC or DC to the desired DC level, and then an output stage where the DC voltage is converted to the AC or DC level required by the end devices. These systems also include an intermediate stage where the DC-link capacitor, or capacitor bank, reside. The DC-link capacitor is responsible for filtering the voltage, and providing energy storage for a clean, consistent, and fast energy source to the output stage.

In each conversion stage, input and output, snubber capacitors (1, in figure above), are used to suppress undesirable voltage and current pulses created by the switching stages of the semiconductor devices. In either the input or output stage, if AC voltage is coming in or going out, AC filter capacitors can be found (2, in figure above). DC filter or DC-link capacitors (3, in figure above) are found in all power conversion circuits, in the input or intermediate stages. DC filter capacitors can also be found in the output stage, if it is a DC/DC converter stage.

Capacitors placed across switching devices and used to suppress the inherent voltage transient noise generated by switching are called snubbers. A snubber circuit is made up of a resistor and a capacitor, and in many cases, the resistance of the traces or wiring and the equivalent series resistance (ESR) of the capacitor can serve as the R part of the RC snubber circuit.

A resonant circuit, tank circuit, or resonant tank circuit, is a resonator made up of an inductor and a capacitor and tuned to resonate at specific frequencies. This resonant circuit can be used to significantly increase the efficiency of certain types of power converters.

Snubbers and resonant tank circuits present special challenges for capacitors. They must withstand high DC voltage pulses, operate at high frequencies, and endure high temperatures. For these types of circuits, the higher the dV/dt, the more efficient. And as circuits get smaller and more space-constrained, capacitance density and power density are becoming increasingly important.

The new R75H series of pulse capacitors are ideal for a variety of applications. With a high capacitance density and high current capability, they can operate at the high frequencies needed for high-efficiency converters. The R75H series has one of the highest dV/dt characteristics in the market, with its single metalized polypropylene construction. These capacitors have a high-temperature rating, up to 125 °C, and are self-healing and extremely reliable.

Capacitors placed on AC voltage lines to filter them are called AC filter capacitors. On three-phase AC power lines, these capacitors can be placed in either a delta or wye configuration. In a delta configuration, the capacitors are connected between the different phases, but in a wye configuration, the capacitors are connected between each phase and a central point. This neutral point is sometimes connected to the ground or sometimes left as a floating neutral, depending on the system design.

These capacitors provide filtering for the AC voltage lines (input or output). Because these are large devices that can be found on high power lines with filter inductors (for instance LCL filters), and connected in banks with several capacitors in series/parallel, one of the most important requirements for these types of devices is safety. They need to be highly reliable and completely safe.

The new C44P-R series AC filter capacitors represent a step forward in technology. They have a high current capability and a long life expectancy. They are metalized polypropylene film capacitors with self-healing capability- in the case of a dielectric breakdown, the arc energy is enough to close the channel, resulting in a self-healed device at the cost of just a small capacitance drop. These capacitors are also constructed with an overpressure safety mechanism. When the internal soft resin in the capacitor expands due to high internal self-heating, the can elongates and disconnects the terminals internally. Once the capacitor is disconnected, the potential for catastrophic failure is avoided, but the capacitor is no longer operational and can be safely replaced.

Capacitors in the DC circuits at the output of either the input or output stages of a converter are called DC-link capacitors. These serve as filters on the DC voltage, as well as energy storage capacitance to provide instantaneous current to all downstream circuits. They can also be used in certain applications to store energy for failsafe power loss operations.

DC-link capacitors must be able to withstand high power, high ripple currents, and many charge/discharge cycles.

They need to do this reliably and safely in extreme conditions, as many of these power converters are found in windmills, solar farms, and other renewable energy source circuits.

The new C44U-M series DC link capacitors are large can capacitors up to 116 mm in diameter, allowing for high capacitance density, high DC voltage load capability, and high ripple current., they have such high-power density and high voltage capability that they actually can be considered as an excellent substitute of screw terminal electrolytic capacitors, reducing the size of the final solutions in which they are needed with better performance in ripple current and lower losses due to their low ESR, and extended operational life. They also have similar self-healing capabilities of the AC filter capacitors, increasing the long-term reliability and lifetime even further.

Together, these innovative and improved devices serve the power converter needs of all kinds of industrial and commercial applications. They are particularly ideal for advanced technologies, in that they support high-frequency converters and harsh conditions, allowing them to work with new silicon and wide bandgap (WBG) semiconductors. These higher efficiency power converters support the latest in energy storage, renewable generators such as wind and solar, and electric vehicles.

The new film capacitors for power conversion meet the needs of today’s most demanding applications. The entire package of R75H pulse snubbers, the C44P-R AC filters, and the C44U-M DC link capacitors provide the full capacitance solution for power converters in any extreme environment.

The post The Basics of Power Conversion and the New Film Capacitors first appeared on The Amazing World of Electronics.

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]]>The post Shutting Down Safely with Capacitors first appeared on The Amazing World of Electronics.

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]]>Ideal capacitors have relatively simple-to-understand energy storage characteristics. Unfortunately, those are complicated considerably by the real world. One common application of energy storage in capacitors is the safe shutdown of electronics when power is lost. Whether power is needed for a period of time long enough to safely shut down or to set the product into a safe condition, the requirements are almost the same.

Ideal capacitors have no loss. They are purely reactive devices, without any resistive component to their impedance. Once fully charged, they hold their charge indefinitely. Unfortunately, ideal capacitors do not exist in the real world. But there is value in understanding the characteristics of ideal capacitors as a foundation for exploring how capacitors store energy.

*Figure 1: A Basic Capacitor Charging Circuit*

Capacitors store energy per the following equation:

E*quation 1: Energy stored by an ideal capacitor*

Where U = Energy (in Joules), Q = Charge (in Coulombs), C = Capacitance (in Farads), and V = Voltage (in Volts).

Once an ideal capacitor is fully charged by current from the supply, it will hold that charge indefinitely. If a resistive load is applied to an ideal capacitor holding a charge, the charge on the capacitor will provide current to the load and the voltage will discharge per the following equation.

*Equation 2: Discharge of an ideal capacitor to a resistive load*

As previously mentioned, however, ideal capacitors do not exist. The equivalent circuit of a real-life capacitor is more like this:

Real capacitors exhibit series resistance (ESR = Equivalent Series Resistance), parallel resistance (IR = Insulation Resistance), and series inductance (ESL = Equivalent Series Inductance), in addition to the ideal capacitance (C). These parasitic elements greatly complicate the energy storage and discharge behavior of capacitors.

The parallel insulation resistance (IR) is very large for most capacitors, on the order of several gigaohms (GΩ). But its very existence causes a non-ideal capacitor to self-discharge over time. Per Equation 2, the voltage on the capacitor will discharge to zero with IR as the load.

*Figure 2: Discharge behavior of an ideal and real capacitor*

Because of self-discharge, long-term energy storage in capacitors is not technologically realistic. Batteries, of course, experience a similar self-discharge of their stored energy due to internal resistance. But batteries can store thousands of times more energy chemically than capacitors of the same volume can in electric fields, making batteries preferred for longer term energy storage. Immediately upon power loss, however, there is still an opportunity for energy stored in capacitors to be discharged usefully, in a controlled fashion, to supply electronics for a short time.

Different capacitor construction and material technologies cause capacitors to react differently to the application of a DC voltage. Multilayer ceramic (MLCC) class 2 capacitors, for example, use a ferroelectric dielectric which causes a reduction in capacitance as applied DC voltage increases. MLCC class 1 capacitors, however, use a paraelectric dielectric that remains stable over DC voltage. Polymer capacitors are similarly stable.

The practical effect of this is that some capacitors will experience a saturation of stored charge at a voltage lower than their maximum rated voltage. These capacitors are still able to operate up to their rated voltage, they just will not be storing the maximum possible charge – instead, the capacitance will drop and the charge will plateau.

*Figure 3: Stored charge as DC voltage approaches maximum rated voltage for various capacitors*

For power fail scenarios, this means selecting the proper capacitors is of critical importance. The designer has two options: select capacitors that are stable across DC voltage (i.e., using Cap 1 in the figure above) or understand the characteristics of the capacitor and derate the voltage accordingly (i.e., using Cap 2 in the figure above at <50% of its voltage rating).

Because of the effect of DC voltage on the capacitance of certain types of capacitors, the discharge of the example capacitors would vary depending on the amount of energy actually stored, rather than the labeled capacitance.

*Figure 4: Discharge behavior is worse for capacitors storing less energy because of DC voltage*

Applied DC voltage is not the only factor in energy storage. Operating temperature and internal temperature also affect capacitance and lifetime.

Capacitors have temperature coefficients (T_{C}), which indicate how much capacitance changes over temperature. Some capacitors have positive coefficients, meaning their capacitance increases as temperature increases, while most have negative coefficients, meaning their capacitance decreases as temperature increases.

Internal temperature, or self-heating, occurs primarily due to ESR and varies depending on the amount of ripple current or charge/discharge cycles in a given application.

Capacitors can be an excellent solution for the energy storage needed to safely shut down electronics. Energy storage capacitors should be selected to have stable capacitance over the application’s desired temperature range, a derated voltage rating, and a very low ESR. Supercapacitors and electrolytics are often used for these types of applications.

For example application of energy storage calculations, is used the SSD Hold-Up Capacitor Calculator. SSDs require a certain amount of hold-up time upon power loss to flush the volatile cache and reach a safe shutdown state. This example uses T545 polymer electrolytic capacitors, which are designed for high energy applications.

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]]>The post Decibels first appeared on The Amazing World of Electronics.

The post Decibels appeared first on The Amazing World of Electronics.

]]>When designing or working with amplifier and filter circuits, some of the numbers used in the calculations can be very large or very small. For example, if we cascade two amplifier stages together with power or voltage gains of say 20 and 36, respectively, then the total gain would be 720 (20*36).

Likewise, if we cascaded together to first-order RC filter circuits with attenuations of 0.7071 each, the total attenuation would be 0.5 (0.7071*0.7071). Remembering of course that if a circuit’s output is positive, then it produces amplification or gain, and if its output is negative, then it produces attenuation or loss.

When analyzing circuits in the *frequency domain*, it is more convenient to compare the amplitude ratio of the output to input values on a logarithmic scale rather than on a linear scale. So if we use the logarithmic ratio of two quantities, P_{1} and P_{2} we end up with a new quantity or level which can be presented using *Decibels*.

Unlike voltage or current which is measured in volts and amperes respectively, the **decibel**, or simple **dB** for short, is just a ratio of two values, well actually the ratio of one value against another known or fixed value, so, therefore, the decibel is a dimensionless quantity, but does have the “Bel” as its units after the telephone inventor, Alexander Graham Bell.

The ratio of any two values, where one is fixed or known and of the same quantity of units, whether power, voltage or current, can be represented using decibels (dB) where “deci” means one-tenth (1/10th) of a Bel. Clearly then there are 10 decibels (10dB) per Bel or 1 Bel = 10 decibels.

The decibel is commonly used to show the ratio of power change (increasing or decreasing) and is commonly defined as the value which is ten times the Base-10 logarithm of two power levels. So for example, 1 watts to 10 watts is the same power ratio as 10 watts to 100 watts, that is 10:1, so while there is a large difference in the number of watts, 9 compared to 90, the decibel ratio would be exactly the same.

Hopefully, then we can see that the decibel (dB) value is a ratio used for comparing and calculating levels of change in power and is not the power itself. So if we have two quantities of power, for example: P_{1} and P_{2}, the ratio of these two values is represented by the equation:

Where, P_{1} represents the input power and P_{2} represents the output power, (P_{OUT}/P_{IN}).

As the decibel represents the Base-10 logarithmic change of two power levels, we can expand this equation further by using anti logarithms to show by how much change one decibel (1dB) really is.

dB = 10log_{10}[P_{2}/P_{1}]

If P_{2}/P_{1} is equal to 1, that is P_{1} = P_{2} then:

dB = 10log_{10}[1] = log_{10}[1/10] = log_{10}[0.1] = antilog[0.1]

Thus a dB change in value equals: 10^{0.1} = 1.259

Clearly then the logarithmic change of two powers has a ratio of 1.259, meaning that a 1dB change represents an increase (or decrease) in the power of 25.9% (or 26% rounded-off).

So if a circuit or system has a gain of say 5 (7dB), and it is increased by 26%, then the new power ratio of the circuit will be: 5*1.26 = 6.3, so 10log_{10}(6.3) = 8dB. An increase in gain of +1dB, proving again that a +1dB change represents a logarithmic increase in power of 26% and not a linear change.

An audio amplifier delivers 100 watts into an 8 ohm speaker load when fed by a 100mW input signal. Calculate the power gain of the amplifier in decibels.

We can express the power gain of the amplifier in units of decibels regardless of its input or output values, as an amplifier delivering 40 watts output for 40mW input will also have a power gain of 30 dB, and so on.

We could also, if we so wished, convert this amplifiers decibels value back into a linear value by first converting from decibels (dB) to a Bel remembering that a decibel is 1/10th of a Bel. For example:

A 100 watt audio amplifier has a power gain ratio of 30dB. What will be its maximum input value.

So the result is 100mW as declared in example No1.

One of the advantages of using the base 10 logarithm ratio of two powers is that when dealing with multiple amplifier, filter or attenuator stages cascaded together, we can simply add or subtract their decibel values instead of multiplying or dividing their linear values. In other words, a circuit’s overall gain (+dB), or attenuation (-dB) is the sum of the individual gains and attenuations for all stages connected between the input and output.

For example, if a single stage amplifier has a power gain of 20dB and it supplies a passive resistive network that has an attenuation of 2, before the signal is amplified again using a second amplifier stage with a gain of 200. Then the total power gain of the circuit between the input and output in decibels would be:

For the passive circuit, an attenuation of 2 is the same as saying the circuit has a positive gain of 1/2 = 0.5, thus the power gain of the passive section is:

dB Gain = 10log_{10}[0.5] = -3dB (note a negative value)

The second stage amplifier has a gain of 200, thus the power gain of this section is:

dB Gain = 10log_{10}[200] = +23dB

Then the overall gain of the circuit will be:

20 – 3 + 23 = +40dB

We can double check our answer of 40dB by multiplying the individual gains of each stage in the usual way as follows:

A power gain of 20dB in decibels is equal to a gain of 100, as 10^{(20/10)} = 100. So:

100 x 0.5 x 200 = 10,000 (or 10,000 times greater)

Converting this back to a decibel value gives:

dB Gain = 10log_{10}[10,000] = 40dB

Then clearly we can see that a gain of 10,000 is equal to a power gain ratio of +40dB as shown above and that we can use the decibel value to express large ratios of powers with much smaller numbers as 40dB is a power ratio of 10,000, whereas -40dB is a power ratio of 0.0001. So using decibels makes maths a little easier.

Any power level can be expressed as a voltage or current if we know the resistance. According to Ohms Law, P = V^{2}/R and P = I^{2}R. As V and I relate to the current through and the voltage across the same resistance, if (and only if) we make R = R = 1, then the dB values for the ratios of voltage (V_{1}, and V_{2}) as well as for current (I_{1}, and I_{2}) will be given as:

that is 20log(voltage gain), and for the current gain would be:

Thus the only difference between defining the power, voltage, and current decibel (dB) calculations is the constant of 10 and 20, and that for the dB ratio to be correct in all instances the two quantities must both have the same units, either watts, milli-watts, volts, milli-volts, amperes or milli-amperes, or any other unit.

A passive-resistive network is used to provide an attenuation (loss) of 10dB, with an input voltage is 12V. What will be the network’s output voltage value?

As *decibels* represent a logarithmic change in terms of power, voltage or current, we can construct a table to show the specific gains and their equivalent decibel values below.

Decibel Table of Gains

We can see from the above decibel table that at 0dB the ratio gain for power, voltage and current is equal to “1” (unity). This means that the circuit (or system) produces no gain or loss between the input and output signals. So zero dB corresponds to a unity gain i.e. A = 1 and not zero gain.

We can also see that at +3dB the output of the circuit (or system) has doubled its input value, meaning a positive dB gain (amplification) so A > 1. Likewise, at -3dB the output the circuit is at half its input value, meaning a negative dB gain (attenuation) so A < 1. This -3dB value is commonly called the “half-power” point and defines the corner frequency in filter networks.

It is all well and good tabulating the power gains against decibels in a reference table, but when dealing with amplifier and filters, Electrical Engineers prefer to use Bode Plots, charts or graphs as a visual display of the circuits (or systems) frequency response characteristics. Then using the data values in the table above we can create the following “decibel” Bode plot showing the various positions of the power points.

**Decibel Power Bode Plot**

Then we can clearly see that the power curve is not linear but follows the logarithmic ratio of 1.259.

We have seen in this tutorial about the **Decibel** (dB) that it is a Base-10 logarithmic unit of power change and that the decibel unit is a 1/10th dimensionless value of a Bel (1 Bel = 10 decibels or 1dB = 0.1B). The decibel allows us to present large ratios of powers using small numbers and we have seen above that 30dB is equivalent to a power ratio of 1000 with the most commonly used decibel values being: 3dB, 6dB, 10dB and 20dB (and their negative equivalents). However, 20dB is not double the power of 10dB.

The decibel also shows us that any change in power by the same ratio will have the same decibel ratio. For example, doubling the power from 1 watt to 2 watts is the same ratio as 10 watts to 20 watts, that is a +3dB change, while a -3dB change means that the power ratio will be halved.

If the dB ratio is positive in value, then it means amplification or gain is present as the output power is greater than the input power (P_{OUT} > P_{IN}). If however the dB power ratio is of a negative value, then this means an attenuation or loss is affecting the circuit as the output power will be less than the circuits input power (P_{OUT} < P_{IN}). Clearly then 0dB means the power ratio is one with no reduction or gain of the signal.

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]]>The post Speed checker first appeared on The Amazing World of Electronics.

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]]>permitted for their vehicles. However, accidents keep occurring due to speed violations since the drivers tend to ignore their speedometers.

This speed checker will come in handy for the highway traffic police as it will not only provide a digital

display in accordance with a vehicle’s speed but also sound an alarm if the vehicle exceeds the permissible speed for the highway.

The system basically comprises two laser transmitter-LDR sensor pairs, which are installed on the highway 100 meters apart, with the transmitter and the LDR sensor of each pair on the oppo-

site sides of the road. The installation of lasers and LDRs is shown in Fig. 1. The system displays the time taken by the vehicle in crossing this 100m distance from one pair to the other with a resolution of 0.01 seconds, from which the speed of the vehicle can be calculated as follows:

As per the above equation, for a speed of 40 kmph the display will read 900 (or 9 seconds), and for a speed of

60 kmph the display will read 600 (or 6 seconds). Note that the LSB of the display equals 0.01 seconds and each succeeding digit is ten times the preceding digit. You can similarly calculate the other readings (or time).

**Circuit description**

Fig. 2 shows the circuit of the speed checker. It has been designed assuming that the maximum permissible speed for highways is either 40 kmph or 60 kmph as per the traffic rule.

The circuit is built around five NE555 timer ICs (IC1 through IC5), four CD4026 counter ICs (IC6

through IC9) and four 7-segment displays (DIS1 through DIS4). IC1 through IC3 function as monostables, with IC1 serving as count-start mono, IC2 as count-stop mono and IC3 as speed-limit detector mono, controlled by IC1 and IC2 outputs. Bistable set-reset IC4 is also controlled by the outputs of IC1 and IC2 and it (IC4), in turn, controls switching on/off of the 100Hz (period = 0.01 second) astable timer IC5.

The time period of timer NE555 (IC1) count-start monostable multivibrator is adjusted using preset VR1 or VR2 and capacitor C1. For 40kmph limit, the time period is set for 9 seconds using preset

VR1, while for 60kmph limit the time period is set for 6 seconds using preset VR2. Slide switch S1 is used to select the time period as per the speed limit (40 kmph and 60 kmph, respectively).

The junction of LDR1 and resistor R1 is coupled to pin 2 of IC1. Normally, light from the laser keeps falling on the LDR sensor continuously and thus the LDR offers a low resistance and pin 2 of IC1 is high. Whenever light falling on the LDR is interrupted by any vehicle, the LDR

resistance goes high and hence pin 2 of IC1 goes low to trigger the monostable. As a result, output pin 3 goes high for the preset period (9 or 6 seconds) and LED1 glows to indicate it. Reset pin 4

is controlled by the output of NAND gate N3 at power-on or whenever reset switch S2 is pushed.

For IC2, the monostable is triggered in the same way as IC1 when the vehicle intersects the laser beam incident on LDR2 to generate a small pulse for stopping the count and for use in the speed detection. LED2 glows for the duration for which pin 3 of IC2 is high.

The outputs of IC1 and IC2 are fed to input pins 2 and 1 of NAND gate N1, respectively. When the outputs of IC1 and IC2 go high simultaneously (meaning that the vehicle has crossed the preset speed limit), output pin 3 of gate N1 goes low to trigger monostable timer IC3. The output of IC3 is used for driving piezobuzzer PZ1, which alerts the operator of speed-limit violation.

Resistor R9 and capacitor C5 decide the time period for which the piezo buzzer sounds.

The output of IC1 triggers the bistable (IC4) through gate N2 at the leading edge of the count-start pulse. When pin 2 of IC4 goes low, the high output at its pin 3 enables astable clock generator IC5. Since the count-stop pulse output of IC2 is connected to pin 6 of IC4 via diode D1, it resets clock

generator IC5. IC5 can also be reset via diode D2 at power-on as well as when reset switch S2 is pressed. IC5 is configured as a stable multivibrator whose time period is decided by preset VR3, resistor R12, and capacitor C10. Using preset VR1, the frequency of the astable multivibrator is set as 100 Hz. The output of IC5 is fed to clock pin 1 of decade counter/7-segment decoder IC6 CD4026. IC CD4026 is a 5-stage Johnson decade counter and an output decoder that converts the Johnson code into a 7-segment decoded output for driving

DIS1 display. The counter advances by one count at the positive clock signal transition.

The carry-out (Cout) signal from CD4026 provides one clock after every ten clock inputs to clock the succeeding decade counter in a multidecade counting chain. This is achieved by connecting pin 5 of each CD4026 to pin 1 of the next CD4026. A high reset signal clears the decade counter to its zero count. Pressing switch S2 provides a reset signal to pin 15 of all CD4026 ICs and also IC1 and IC4. Capacitor C12 and resistor R14

generate the power-on-reset signal. The seven decoded outputs ‘a’ through ‘g’ of CD4026s illuminate

the proper segment of the 7-segment displays (DIS1 through DIS4) used for representing the decimal digits ‘0’ through ‘9.’ Resistors R16 through R19 limit the current across DIS1 through DIS4, respectively.

Fig. 3 shows the circuit of the power supply. The AC mains is stepped down by transformer X1 to deliver the secondary output of 15 volts, 500 mA. The transformer output is rectified by a bridge rectifier comprising diodes D3 through D6, filtered by capacitor C14, and regulated by IC11 to provide a regulated 12V supply. Capacitor C15 bypasses any ripple in the regulated output. Switch S3 is used as the ‘on’/‘off’ switch. In mobile application of the circuit, where mains 230V AC is not available, it is advisable to use an external 12V battery. For activating the lasers used in conjunction with LDR1 and LDR2, separate batteries may be used.

Co**nstruction and working**

Assemble the circuit on a PCB. An actual-size, single-side PCB layout for the speed checker is shown in Fig. 4 and its component layout in Fig. 5. Before the operation, using a multimeter check whether the power supply output is correct. If yes, apply power supply to the circuit by flipping switch S3 to ‘on.’ In the circuit, use long wires for connecting the two LDRs, so that you can take them out of the PCB and install them on one side of the highway, 100 meters apart. Install the two laser transmitters (such as laser torches) on the other side of the highway exactly opposite to the LDRs such that laser light falls directly on the LDRs. Reset the circuit by pressing switch S2, so the display shows ‘0000.’ Using switch S1, select the speed limit (say, 60 kmph) for the highway. When any vehicle crosses the first laser light, LDR1 will trigger IC1. The output of IC1 goes high for the time set to cross 100 meters with the selected speed (60 kmph) and LED1 glows during for period. When the vehicle crosses the second laser light, the output of IC2 goes high and LED2 glows for this period. Piezo buzzer PZ1 sounds an alarm if the vehicle crosses the distance between

the laser set-ups at more than the selected speed (lesser period than preset period). The counter starts counting when the first laser beam is intercepted and stops when the second laser beam

is intercepted. The time taken by the vehicle to cross both the laser beams is displayed on the 7-segment display. For 60kmph speed setting, with timer frequency set at 100 Hz, if the display

count is less than ‘600,’ it means that the vehicle has crossed the speed limit (and simultaneously the buzzer sounds). Reset the circuit for monitoring the speed of the next vehicle.

** Note. **This speed checker can check the speed of only one vehicle at a time.

The post Speed checker first appeared on The Amazing World of Electronics.

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]]>The post Band Stop Filter first appeared on The Amazing World of Electronics.

The post Band Stop Filter appeared first on The Amazing World of Electronics.

]]>By combining a basic RC low-pass filter with a RC high-pass filter we can form a simple band-pass filter that will pass a range or band of frequencies either side of two cut-off frequency points. But we can also combine these low and high pass filter sections to produce another kind of RC filter network called a band stop filter that can block or at least severely attenuate a band of frequencies within these two cut-off frequency points.

The **Band Stop Filter**, (BSF) is another type of frequency selective circuit that functions in exactly the opposite way to the Band Pass Filter we looked at before. The band stop filter, also known as a *band reject filter*, passes all frequencies with the exception of those within a specified stop band which are greatly attenuated.

If this stop band is very narrow and highly attenuated over a few hertz, then the band stop filter is more commonly referred to as a *notch filter*, as its frequency response shows that of a deep notch with high selectivity (a steep-side curve) rather than a flattened wider band.

Also, just like the band pass filter, the band stop (band reject or notch) filter is a second-order (two-pole) filter having two cut-off frequencies, commonly known as the -3dB or half-power points producing a wide stop band bandwidth between these two -3dB points.

Then the function of a band stop filter is too pass all those frequencies from zero (DC) up to its first (lower) cut-off frequency point ƒ_{L}, and pass all those frequencies above its second (upper) cut-off frequency ƒ_{H}, but block or reject all those frequencies in-between. Then the filters bandwidth, BW is defined as: (ƒ_{H} – ƒ_{L}).

So for a wide-band band stop filter, the filters actual stop band lies between its lower and upper -3dB points as it attenuates, or rejects any frequency between these two cut-off frequencies. The frequency response curve of an ideal band stop filter is therefore given as:

We can see from the amplitude and phase curves above for the band pass circuit, that the quantities ƒ_{L}, ƒ_{H} and ƒ_{C} are the same as those used to describe the behaviour of the band-pass filter. This is because the band stop filter is simply an inverted or complimented form of the standard band-pass filter. In fact the definitions used for bandwidth, pass band, stop band and center frequency are the same as before, and we can use the same formulas to calculate bandwidth, BW, center frequency, ƒ_{C}, and quality factor, Q.

The ideal band stop filter would have infinite attenuation in its stop band and zero attenuation in either pass band. The transition between the two pass bands and the stop band would be vertical (brick wall). There are several ways we can design a “Band Stop Filter”, and they all accomplish the same purpose.

Generally band-pass filters are constructed by combining a low pass filter (LPF) in series with a high pass filter (HPF). Band stop filters are created by combining together the low pass and high pass filter sections in a “parallel” type configuration as shown.

The summing of the high pass and low pass filters means that their frequency responses do not overlap, unlike the band-pass filter. This is due to the fact that their start and ending frequencies are at different frequency points. For example, suppose we have a first-order low-pass filter with a cut-off frequency, ƒ_{L} of 200Hz connected in parallel with a first-order high-pass filter with a cut-off frequency, ƒ_{H} of 800Hz. As the two filters are effectively connected in parallel, the input signal is applied to both filters simultaneously as shown above.

All of the input frequencies below 200Hz would be passed unattenuated to the output by the low-pass filter. Likewise, all input frequencies above 800Hz would be passed unattenuated to the output by the high-pass filter. However, and input signal frequencies in-between these two frequency cut-off points of 200Hz and 800Hz, that is ƒ_{L} to ƒ_{H} would be rejected by either filter forming a notch in the filters output response.

In other words a signal with a frequency of 200Hz or less and 800Hz and above would pass unaffected but a signal frequency of say 500Hz would be rejected as it is too high to be passed by the low-pass filter and too low to be passed by the high-pass filter. We can show the effect of this frequency characteristic below.

The transformation of this filter characteristic can be easily implemented using a single low pass and high pass filter circuits isolated from each other by non-inverting voltage follower, (Av = 1). The output from these two filter circuits is then summed using a third operational amplifier connected as a voltage summer (adder) as shown.

The use of operational amplifiers within the band stop filter design also allows us to introduce voltage gain into the basic filter circuit. The two non-inverting voltage followers can easily be converted into a basic non-inverting amplifier with a gain of Av = 1 + Rƒ/Rin by the addition of input and feedback resistors, as seen in our non-inverting op-amp tutorial.

Also if we require a band stop filter to have its -3dB cut-off points at say, 1kHz and 10kHz and a stop band gain of -10dB in between, we can easily design a low-pass filter and a high-pass filter with these requirements and simply cascade them together to form our wide-band band-pass filter design.

Now we understand the principle behind a **Band Stop Filter**, let us design one using the previous cut-off frequency values.

Design a basic wide-band, RC band stop filter with a lower cut-off frequency of 200Hz and a higher cut-off frequency of 800Hz. Find the geometric center frequency, -3dB bandwidth and Q of the circuit.

The upper and lower cut-off frequency points for a band stop filter can be found using the same formula as that for both the low and high pass filters as shown.

Assuming a capacitor, C value for both filter sections of 0.1uF, the values of the two frequency determining resistors, R_{L} and R_{H} are calculated as follows.

From this we can calculate the geometric center frequency, ƒ_{C} as:

Now that we know the component values for the two filter stages, we can combine them into a single voltage adder circuit to complete our filter design. The magnitude and polarity of the adders output will be at any given time, the algebraic sum of its two inputs.

If we make the op-amps feedback resistor and its two input resistors the same values, say 10kΩ, then the inverting summing circuit will provide a mathematically correct sum of the two input signals with zero voltage gain.

Then the final circuit for our band stop (band-reject) filter example will be:

We have seen above that simple band stop filters can be made using first or second order low and high pass filters along with a non-inverting summing op-amp circuit to reject a wide band of frequencies. But we can also design and construct band stop filters to produce a much narrower frequency response to eliminate specific frequencies by increasing the selectivity of the filter. This type of filter design is called a “Notch Filter”.

**Notch filters** are a highly selective, high-Q, form of the band stop filter which can be used to reject a single or very small band of frequencies rather than a whole bandwidth of different frequencies. For example, it may be necessary to reject or attenuate a specific frequency generating electrical noise (such as mains hum) which has been induced into a circuit from inductive loads such as motors or ballast lighting, or the removal of harmonics, etc.

But as well as filtering, variable notch filters are also used by musicians in sound equipment such as graphic equalizers, synthesizers and electronic crossovers to deal with narrow peaks in the acoustic response of the music. Then we can see that notch filters are widely used in much the same way as low-pass and high-pass filters.

Notch filters by design have a very narrow and very deep stop band around their center frequency with the width of the notch being described by its selectivity Q in exactly the same way as resonance frequency peaks in RLC circuits.

The most common notch filter design is the twin-T notch filter network. In its basic form, the twin-T, also called a parallel-tee, configuration consists of two RC branches in the form of two tee sections, that use three resistors and three capacitors with opposite and opposing R and C elements in the tee part of its design as shown, creating a deeper notch.

The upper T-pad configuration of resistors 2R and capacitor 2C form the low-pass filter section of the design, while the lower T-pad configuration of capacitors C and resistor R form the high-pass filter section. The frequency at which this basic twin-T notch filter design offers maximum attenuation is called the “notch frequency”, ƒ_{N} and is given as:

Being a passive RC network, one of the disadvantages of this basic twin-T notch filter design is that the maximum value of the output (Vout) below the notch frequency is generally less than the maximum value of output above the notch frequency due in part to the two series resistances (2R) in the low-pass filter section having greater losses than the reactances of the two series capacitors (C) in the high-pass section.

As well as uneven gains either side of the notch frequency, another disadvantage of this basic design is that it has a fixed Q value of **0.25**, in the order of -12dB. This is because at the notch frequency, the reactances of the two series capacitors equals the resistances of the two series resistors, resulting in the currents flowing in each branch being out-of-phase by 180^{o}.

We can improve on this by making the notch filter more selective with the application of positive feedback connected to the center of the two reference legs. Instead of connecting the junction of R and 2C to ground, (0v) but instead connect it to the central pin of a voltage divider network powered by the output signal, the amount of the signal feedback, set by the voltage divider ratio, determines the value of Q, which in turn, determines to some extent, the depth of the notch.

Here the output from the twin-T notch filter section is isolated from the voltage divider by a single non-inverting op-amp buffer. The output from the voltage divider is fed back to “ground” point of R and 2C. The amount of signal feedback, known as the feedback fraction k, is set by the resistor ratio and is given as:

The value of Q is determined by the R3 and R4 resistor ratio, but if we wanted to make Q fully adjustable, we could replace these two feedback resistors with a single potentiometer and feed it into another op-amp buffer for increased negative gain. Also, to obtain the maximum notch depth at the given frequency, resistors R3 and R4 could be eliminated and the junction of R and 2C connected directly to the output.

Design a two op-amp narrow-band, RC notch filter with a center notch frequency, ƒ_{N} of 1kHz and a -3dB bandwidth of 100 Hz. Use 0.1uF capacitors in your design and calculate the expected notch depth in decibels.

Data given: ƒ_{N} = 1000Hz, BW = 100Hz and C = 0.1uF.

1. Calculate value of R for the given capacitance of 0.1uF

2. Calculate value of Q

3. Calculate value of feedback fraction k

4. Calculate the values of resistors R3 and R4

5. Calculate expected notch depth in decibels, dB

We have seen here that an ideal **band stop filter** has a frequency response which is the inverse of the band-pass filter. Band stop filters block or “reject” frequencies that lie between its two cut-off frequency points ( ƒ_{L} and ƒ_{H} ) but passes all those frequencies either side of this range. The range of frequencies above ƒ_{L} and below ƒ_{H} is called the stop band.

Band stop filters accomplish this by summing the outputs of a high pass with that of a low pass filter (especially for the wide band design) with the filters output being the difference. A band stop filter design with a wide stop band is also referred to as a *band reject filter* and a band stop filter design with a narrow stop band is referred to as a *notch filter*. Either way, band stop filters are second-order filters.

Notch filters are designed to provide high attenuation at and near a single frequency with little or no attenuation at all other frequencies. Notch filters use a twin-T parallel resistance-capacitance (RC) network to obtain a deep notch. Higher values of Q can be obtained by feeding back some of the output to the junction of the two tees.

To make the notch filter more selective and with adjustable values of Q, we can connect the junction of the resistance and the capacitance in the two tees to the central point of a voltage divider network connected to the filters output signal. A properly designed notch filter can produce attenuation of more than -60dB at the notch frequency.

**Band Stop Filters** have many uses in electronics and communication circuits and as we have seen here, they can be used to remove a band of unwanted frequencies from a system, allowing other frequencies to pass with minimum loss. Notch filters can be highly selective and can be designed to reject or attenuate a specific frequency or harmonic content generating electrical noise, such as mains hum within a circuit.

The post Band Stop Filter first appeared on The Amazing World of Electronics.

The post Band Stop Filter appeared first on The Amazing World of Electronics.

]]>The post State Variable Filter first appeared on The Amazing World of Electronics.

The post State Variable Filter appeared first on The Amazing World of Electronics.

]]>State variable filters use three (or more) operational amplifier circuits (the active element) cascaded together to produce the individual filter outputs but if required an additional summing amplifier can also be added to produce a fourth *Notch filter* output response as well.

*State variable filters* are second-order RC active filters consisting of two identical op-amp integrators with each one acting as a first-order, single-pole low pass filter, a summing amplifier around which we can set the filters gain and its damping feedback network. The output signals from all three op-amp stages are fed back to the input allowing us to define the state of the circuit.

One of the main advantages of a state variable filter design is that all three of the filters main parameters, Gain (A), corner frequency, ƒ_{C} and the filters Q can be adjusted or set independently without affecting the filters performance.

In fact if designed correctly, the -3dB corner frequency, ( ƒc ) point for both the low pass amplitude response and the high pass amplitude response should be identical to the center frequency point of the band pass stage. That is ƒ_{LP(-3dB)} equals ƒ_{HP(-3dB)} which equals ƒ_{BP(center)}. Also the damping factor, ( ζ ) for the band pass filter response should be equal to 1/Q as Q will be set at -3dB, (0.7071).

Although the filter provides low pass (LP), high pass (HP) and band pass (BP) outputs the main application of this type of filter circuit is as a state variable band pass filter design with the center frequency set by the two RC integers.

While we have seen before that a band pass filters characteristics can be obtained by simply cascading together a low pass filter with a high pass filter, state variable band pass filters have the advantage that they can be tuned to be highly selective (high Q) offering high gains at the center frequency point.

There are several state variable filter designs available all based on the standard filter design with both inverting and non-inverting variations available. However, the basic filter design will be the same for both variations as shown in the following block diagram representation.

Then we can see from the basic block diagram above that the state variable filter has three possible outputs, V_{HP}, V_{BP} and V_{LP} with one each from the three op-amps. A notch filter response can also be realized by the addition of a fourth op-amp.

With a constant input voltage, V_{IN} the output from the summing amplifier produces a high pass response which also becomes the input of the first RC Integrator. The output from this integrator produces a band pass response which becomes the input of the second RC Integrator producing a low pass response at its output. As a result, separate transfer functions for each individual output with respect to the input voltage can be found.

The basic non-inverting state variable filter design is therefore given as:

and the amplitude response of the three outputs from the state variable filter will look like:

One of the main design elements of a state variable filter is its use of two op-amp integrators. As we saw in the Integrator tutorial, op-amp integrators use a frequency dependant impedance in the form of a capacitor within their feedback loop. As a capacitor is used the output voltage is proportional to the integral of the input voltage as shown.

To simplify the math’s a little, this can also be re-written in the frequency domain as:

The output voltage Vout is a constant 1/RC times the integral of the input voltage Vin with respect to time. Integrators produce a phase lag with the minus sign ( – ) indicating a 180^{o} phase shift because the input signal is connected directly to the inverting input terminal of the op-amp.

In the case of op-amp A2 above, its input signal is connected to the output of the proceeding op-amp, A1 so its input is given as V_{HP} and its output as V_{BP}. Then from above, the expression for op-amp, A2 can be written as:

Then by rearranging this formula we can find the transfer function of the inverting integrator, A2

Exactly the same assumption can be made as above to find the transfer function for the other op-amp integrator, A3

So the two op-amp integrators, A2 and A3 are connected together in cascade, so the output from the first (V_{BP}) becomes the input of the second. So we can see that the band pass response is created by integrating the high pass response and the low pass response is created by integrating the band pass response. Therefore the transfer function between V_{HP} and V_{LP} is given as:

Note that each integrator stage provides an inverted output but the summed output will be positive since they are inverting integrators. If exactly the same values for R and C are used so that the two circuits have the same integrator time constant, the two amplifier circuits can be regarded with one single integrator circuit having a corner frequency, ƒ_{C}.

As well as the two integrator circuits, the filter also has a differential summing amplifier providing a weighted summation of its inputs. The advantage here is that the inputs to the summing amplifier, A1 combines oscillatory feedback, damping and input signals to the filter as all three outputs are fed back to the summing inputs.

Operational amplifier, A1 is connected as an adder–subtracter circuit. That is it sums the input signal, V_{IN} with the V_{BP} output of op-amp A2 and the subtracts from it the V_{LP} output of op-amp A3, thus:

and

As the differential inputs, +V and -V of an operational amplifier are the same, that is: +V – -V, we can rearrange the two expressions above to find the transfer function for the output of A1, the high pass output.

We know from above, that V_{BP} and V_{LP} are the outputs from the two integrators, A2 and A3 respectively. By substituting the integrator equations for A2 and A3 into the above equation, we get the transfer function of the state variable filter to be:

We said previously that a **State Variable Filter** produces three filter responses, *Low Pass*, *High Pass* and *Band Pass* and that the band pass response is that of a very narrow high Q filter and this is evident in the SVF’s transfer function above as it resembles that of a standard second-order response.

If we make both the integrators input resistors and feedback capacitors the same, then the state variable filters corner frequency can be easily tuned without affective its overall Q. Likewise, the value of Q can be varied without altering the corner frequency. Then the corner frequency is given as:

If we make feedback resistors R3 and R4 the same values, then the corner frequency of each filter output from the state variable filter simply becomes:

Then tuning of the state variable corner frequency is accomplished simply by varying either the tuning resistor, R or the capacitor, C.

State variable filters are characterised not only by their individual output responses, but also by the filters “Q”, Quality factor. Q relates to the “sharpness” of the band pass filters amplitude response curve and the higher the Q, the higher or sharper the output response resulting in a filter that is highly selective.

For a band pass filter, Q is defined as the center frequency divided by the filters -3dB bandwidth, that is Q = ƒc/BW. But Q can also be found from the denominator of the above transfer function as it is the reciprocal of the damping factor ( ζ ). Then Q is given as:

Again, if resistors R3 and R4 are equal and both integrator components R and C are equal, then the final square root expression would reduce to: √1 or simply 1 as the numerator and denominator cancel each other out.

Design a *State Variable Filter* which has a corner (natural undamped) frequency, ƒ_{C} of 1kHz and a quality factor, Q of 10. Assume both the frequency determining resistors and capacitors are equal. Determine the filters DC gain and draw the resulting circuit and Bode plot.

We said above that if both the resistor, R and the feedback capacitor, C of the two integrator circuits are the same values, that is R = R and C = C, the cut-off or corner frequency point for the filter is given simply as:

We can choose a value for either the resistor, or the capacitor to find the value of the other. If we assume a suitable value of 10nF for the capacitor then the value of the resistor will be:

Giving C = 10nF and R = 15.9kΩ, or 16kΩ to the nearest preferred value.

The value of Q is given as **10**. This relates to the filters damping coefficient as:

In the state variable transfer function above, the 2ζ part is replaced by the resistor combination giving:

We know from above that R = 16kΩ and C = 10nF, but if we assume that the two feedback resistors, R3 and R4 are the same and equal to 10kΩ, then the above equation reduces down to:

Assuming a suitable value for the input resistor, R1 of say 1kΩ, then we can find the value of R2 as follows:

From the normalised transfer function above, the DC passband gain is defined as A_{o} and from the equivalent state variable filter transfer function this equates to:

Therefore the DC voltage gain of the filter is calculated at 1.9, which basically equates to R2/R3. Also the maximum gain of the filter at ƒ_{C} can be calculated as: A_{o} x Q as follows.

Then the design of the state variable filter circuit will be: R = 16kΩ, C = 10nF, R1 = 1kΩ, R2 = 19kΩ and R3 = R4 = 10kΩ as shown.

We can now plot the individual output response curves for the state variable filter circuit over a range of frequencies from 1Hz to 1MHz onto a Bode Plot as shown.

Then we can see from the filters response curves above, that the DC gain of the filter circuit is at 5.57dB which equates to an open loop voltage gain, A_{o} or 1.9 as calculated above. The response also shows that the output curves peaks at a maximum voltage gain of 25.6dB at the corner frequency due to the value of **Q**. As Q also relates the band pass filters center frequency to its bandwidth, the bandwidth of the filter will therefore be: ƒ_{o}/10 = 100Hz.

We have seen in this *state variable filter* tutorial that instead of an active filter producing one type of frequency response, we can use multiple-feedback techniques to produce all three filter responses, *Low Pass*, *High Pass* and *Band Pass* simultaneously from the same single active filter design.

But as well as the three basic filter responses, we can add an additional op-amp circuit onto the basic state variable filter design above to produce a fourth output response resembling that of a standard *Notch Filter*.

A **notch filter** filter is basically the opposite of a band pass filter, in that it rejects or stops a specific band of frequencies. Then a notch filter is also known as a “band stop filter”. To obtain the response of a notch filter from the basic state variable filter design, we have to sum together the high pass and low pass output responses using another op-amp summing amplifier, A4 as shown.

Here to keep things simple we have assumed that the two input resistors, R5 and R6 as well as the feedback resistor, R7 all have the same value of 10kΩ the same as for R3 and R4. This therefore gives the notch filter a gain of 1, unity.

The output response of the notch filter and bandpass filter are related with the center frequency of the bandpass response being equal to the point of zero response of the notch filter, and in this example will be 1kHz.

Also the bandwidth of the notch is determined by the circuits Q, exactly the same as for the pass band response. The downward peak is therefore equal to the center frequency divided by the -3dB bandwidth, that is the frequency difference between the -3dB points either side of the notch. Note that the quality factor Q has nothing to do with the actual depth of the notch.

This basic notch filter (band-stop) design has only two inputs applied to its summing amplifier, the low pass output, V_{LP} and the high pass output, V_{HP}. However, there are two more signals available for us to use from the basic state variable filter circuit, the band pass output, V_{BP} and the input signal itself, V_{IN}.

If one of these two signals is also used as an input to the notch filter summing amplifier along with the low pass and high pass signals, then the depth of the notch can be controlled.

Depending upon how you wanted to control the output from the notch filter section would depend upon which one of the two available signals you would use. If it was required that the output notch changes from a negative response to a positive response at the undamped natural frequency ƒ_{o} then the band pass output signal V_{BP} would be used.

Likewise, if it was required that the output notch only varies in its downward negative depth, then the input signal, V_{IN} would be used. If either one of these two additional signals was connected to the op-amp summing amplifier through a variable resistor then the depth and direction of the notch could be fully controlled. Consider the modified notch filter circuit below.

The **State Variable Filter**, (**SVF**) circuit is a second-order active RC filter design that use multiple feedback techniques to produce three different frequency response outputs, namely: *Low Pass*, *High Pass* and *Band Pass* from the same single filter. The advantage of the state variable filter over other basic filter designs is that the three main filter parameters, Gain, Q and ƒc can be adjusted independently.

We have also seen here that the filter is also easy to tune as the corner frequency, ƒc can be set and adjusted by varying either R or C without affecting the filters damping factor. However, at higher corner frequencies and larger damping factors the filter can become unstable so is best used with low Q, less than 10, and at low corner frequencies.

The basic state variable filter design uses three op-amp sections to produce its outputs, but we have also seen that with the addition of a fourth op-amp section summing the low pass and high pass sections together, a notch (band-stop) filter output response can also be achieved at the desired center frequency.

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]]>**Second Order Filters** which are also referred to as VCVS filters, because the op-amp is used as a Voltage Controlled Voltage Source amplifier, are another important type of active filter design because along with the active first order RC filters we looked at previously, higher order filter circuits can be designed using them.

In this analogue filters section tutorials we have looked at both passive and active filter designs and have seen that first order filters can be easily converted into second order filters simply by using an additional RC network within the input or feedback path. Then we can define second order filters as simply being: “two 1st-order filters cascaded together with amplification”.

Most designs of second order filters are generally named after their inventor with the most common filter types being: *Butterworth*, *Chebyshev*, *Bessel* and *Sallen-Key*. All these types of filter designs are available as either: low pass filter, high pass filter, band pass filter and band stop (notch) filter configurations, and being second order filters, all have a 40-dB-per-decade roll-off.

The Sallen-Key filter design is one of the most widely known and popular 2nd order filter designs, requiring only a single operational amplifier for the gain control and four passive RC components to accomplish the tuning.

Most active filters consist of only op-amps, resistors, and capacitors with the cut-off point being achieved by the use of feedback eliminating the need for inductors as used in passive 1st-order filter circuits.

Second order (two-pole) active filters whether low pass or high pass, are important in Electronics because we can use them to design much higher order filters with very steep roll-off’s and by cascading together first and second order filters, analogue filters with an n^{th} order value, either odd or even can be constructed up to any value, within reason.

Second order low pass filters are easy to design and are used extensively in many applications. The basic configuration for a Sallen-Key second order (two-pole) low pass filter is given as:

This second order low pass filter circuit has two RC networks, R1 – C1 and R2 – C2 which give the filter its frequency response properties. The filter design is based around a non-inverting op-amp configuration so the filters gain, A will always be greater than 1. Also the op-amp has a high input impedance which means that it can be easily cascaded with other active filter circuits to give more complex filter designs.

The normalised frequency response of the second order low pass filter is fixed by the RC network and is generally identical to that of the first order type. The main difference between a 1st and 2nd order low pass filter is that the stop band roll-off will be twice the 1st order filters at 40dB/decade (12dB/octave) as the operating frequency increases above the cut-off frequency ƒc, point as shown.

The frequency response bode plot above, is basically the same as that for a 1st-order filter. The difference this time is the steepness of the roll-off which is -40dB/decade in the stop band. However, second order filters can exhibit a variety of responses depending upon the circuits voltage magnification factor, Q at the the cut-off frequency point.

In active second order filters, the damping factor, ζ (zeta), which is the inverse of Q is normally used. Both Q and ζ are independently determined by the gain of the amplifier, A so as Q decreases the damping factor increases. In simple terms, a low pass filter will always be low pass in its nature but can exhibit a resonant peak in the vicinity of the cut-off frequency, that is the gain can increases rapidly due to resonance effects of the amplifiers gain.

Then Q, the quality factor, represents the “peakiness” of this resonance peak, that is its height and narrowness around the cut-off frequency point, ƒ_{C}. But a filters gain also determines the amount of its feedback and therefore has a significant effect on the frequency response of the filter.

Generally to maintain stability, an active filters gain must not be more than 3 and is best expressed as:

Then we can see that the filters gain, A for a non-inverting amplifier configuration must lie somewhere between 1 and 3 (the damping factor, ζ between zero an 2). Therefore, higher values of Q, or lower values of ζ gives a greater peak to the response and a faster initial roll-off rate as shown.

The amplitude response of the second order low pass filter varies for different values of damping factor, ζ. When ζ = 1.0 or more (2 is the maximum) the filter becomes what is called “overdamped” with the frequency response showing a long flat curve. When ζ = 0, the filters output peaks sharply at the cut-off point resembling a sharp point at which the filter is said to be “underdamped”.

Then somewhere in between, ζ = 0 and ζ = 2.0, there must be a point where the frequency response is of the correct value, and there is. This is when the filter is “critically damped” and occurs when ζ = 0.7071.

One final note, when the amount of feedback reaches 4 or more, the filter begins to oscillate by itself at the cut-off frequency point due to the resonance effects, changing the filter into an oscillator. This effect is called self oscillation. Then for a low pass second order filter, both Q and ζ play a critical role.

We can see from the normalised frequency response curves above for a 1st order filter (red line) that the pass band gain stays flat and level (called maximally flat) until the frequency response reaches the cut-off frequency point when: ƒ = ƒr and the gain of the filter reduces past its corner frequency at 1/√2, or 0.7071 of its maximum value. This point is generally referred to as the filters -3dB point and for a first order low pass filter the damping factor will be equal to one, ( ζ = 1 ).

However, this -3dB cut-off point will be at a different frequency position for second order filters because of the steeper -40dB/decade roll-off rate (blue line). In other words, the corner frequency, ƒr changes position as the order of the filter increases. Then to bring the second order filters -3dB point back to the same position as the 1st order filter’s, we need to add a small amount of gain to the filter.

So for a Butterworth second order low pass filter design the amount of gain would be: **1.586**, for a Bessel second order filter design: **1.268**, and for a Chebyshev low pass design: **1.234**.

A **Second Order Low Pass Filter** is to be design around a non-inverting op-amp with equal resistor and capacitor values in its cut-off frequency determining circuit. If the filters characteristics are given as: **Q = 5**, and **ƒc = 159Hz**, design a suitable low pass filter and draw its frequency response.

Characteristics given: R1 = R2, C1 = C2, Q = 5 and ƒc = 159Hz

From the circuit above we know that for equal resistances and capacitances, the cut-off frequency point, ƒc is given as:

Choosing a suitable value of say, 10kΩ’s for the resistors, the resulting capacitor value is calculated as:

Then for a cut-off corner frequency of **159Hz**, R = 10kΩ and C = 0.1uF.

with a value of **Q = 5**, the filters gain, A is calculated as:

We know from above that the gain of a non-inverting op-amp is given as:

Therefore the final circuit for the second order low pass filter is given as:

We can see that the peakiness of the frequency response curve is quite sharp at the cut-off frequency due to the high quality factor value, Q = 5. At this point the gain of the filter is given as: Q × A = 14, or about **+23dB**, a big difference from the calculated value of 2.8, (+8.9dB).

But many books, like the one on the right, tell us that the gain of the filter at the normalised cut-off frequency point, etc, etc, should be at the -3dB point. By lowering the value of Q significantly down to a value of **0.7071**, results in a gain of, A = 1.586 and a frequency response which is maximally flat in the passband having an attenuation of -3dB at the cut-off point the same as for a second order butterworth filter response.

So far we have seen that **second order filters** can have their cut-off frequency point set at any desired value but can be varied away from this desired value by the damping factor, ζ. Active filter designs enable the order of the filter to range up to any value, within reason, by cascading together filter sections.

In practice when designing n^{th}-order low pass filters it is desirable to set the cut-off frequency for the first-order section (if the order of the filter is odd), and set the damping factor and corresponding gain for each of the second order sections so that the correct overall response is obtained. To make the design of low pass filters easier to achieve, values of ζ, Q and A are available in tabulated form for active filters as we will see in the Butterworth Filter tutorial. Let’s look at another example.

Design a non-inverting second order Low Pass filter which will have the following filter characteristics: Q = 1, and ƒc = 79.5Hz.

From above, the corner frequency, ƒc of the filter is given as:

Choosing a suitable value of 1kΩ for the filters resistors, then the resulting capacitor values are calculated as:

Therefore, for a corner frequency of **79.5Hz**, or 500 rads/s, R = 1kΩ and C = 2.0uF.

With a value of **Q = 1** given, the filters gain A is calculated as follows:

The voltage gain for a non-inverting op-amp circuit was given previously as:

Therefore the second order low pass filter circuit which has a Q of 1, and a corner frequency of 79.5Hz is given as:

There is very little difference between the second order low pass filter configuration and the second order high pass filter configuration, the only thing that has changed is the position of the resistors and capacitors as shown.

Since second order high pass and low pass filters are the same circuits except that the positions of the resistors and capacitors are interchanged, the design and frequency scaling procedures for the high pass filter are exactly the same as those for the previous low pass filter. Then the bode plot for a 2nd order high pass filter is therefore given as:

As with the previous low pass filter, the steepness of the roll-off in the stop band is -40dB/decade.

In the above two circuits, the value of the op-amp voltage gain, ( Av ) is set by the amplifiers feedback network. This only sets the gain for frequencies well within the pass band of the filter. We can choose to amplify the output and set this gain value by whatever amount is suitable for our purpose and define this gain as a constant, K.

2nd order Sallen-Key filters are also referred to as positive feedback filters since the output feeds back into the positive terminal of the op-amp. This type of active filter design is popular because it requires only a single op-amp, thus making it relatively inexpensive.

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]]>The post Butterworth Filter Design first appeared on The Amazing World of Electronics.

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]]>In applications that use filters to shape the frequency spectrum of a signal such as in communications or control systems, the shape or width of the roll-off also called the “transition band”, for a simple first-order filter may be too long or wide and so active filters designed with more than one “order” are required. These types of filters are commonly known as “High-order” or “n^{th}-order” filters.

The complexity or filter type is defined by the filters “order”, and which is dependant upon the number of reactive components such as capacitors or inductors within its design. We also know that the rate of roll-off and therefore the width of the transition band, depends upon the order number of the filter and that for a simple first-order filter it has a standard roll-off rate of 20dB/decade or 6dB/octave.

Then, for a filter that has an n^{th} number order, it will have a subsequent roll-off rate of 20n dB/decade or 6n dB/octave. So a first-order filter has a roll-off rate of 20dB/decade (6dB/octave), a second-order filter has a roll-off rate of 40dB/decade (12dB/octave), and a fourth-order filter has a roll-off rate of 80dB/decade (24dB/octave), etc, etc.

High-order filters, such as third, fourth, and fifth-order are usually formed by cascading together single first-order and second-order filters.

For example, two second-order low pass filters can be cascaded together to produce a fourth-order low pass filter, and so on. Although there is no limit to the order of the filter that can be formed, as the order increases so does its size and cost, also its accuracy declines.

One final comment about *Decades* and *Octaves*. On the frequency scale, a **Decade** is a tenfold increase (multiply by 10) or tenfold decrease (divide by 10). For example, 2 to 20Hz represents one decade, whereas 50 to 5000Hz represents two decades (50 to 500Hz and then 500 to 5000Hz).

An **Octave** is a doubling (multiply by 2) or halving (divide by 2) of the frequency scale. For example, 10 to 20Hz represents one octave, while 2 to 16Hz is three octaves (2 to 4, 4 to 8 and finally 8 to 16Hz) doubling the frequency each time. Either way, *Logarithmic* scales are used extensively in the frequency domain to denote a frequency value when working with amplifiers and filters so it is important to understand them.

Since the frequency determining resistors are all equal, and as are the frequency determining capacitors, the cut-off or corner frequency ( ƒ_{C} ) for either a first, second, third or even a fourth-order filter must also be equal and is found by using our now old familiar equation:

As with the first and second-order filters, the third and fourth-order high pass filters are formed by simply interchanging the positions of the frequency determining components (resistors and capacitors) in the equivalent low pass filter. High-order filters can be designed by following the procedures we saw previously in the Low Pass filter and High Pass filter tutorials. However, the overall gain of high-order filters is **fixed** because all the frequency determining components are equal.

So far we have looked at a low and high pass first-order filter circuits, their resultant frequency and phase responses. An ideal filter would give us specifications of maximum pass band gain and flatness, minimum stop band attenuation and also a very steep pass band to stop band roll-off (the transition band) and it is therefore apparent that a large number of network responses would satisfy these requirements.

Not surprisingly then that there are a number of “approximation functions” in linear analogue filter design that use a mathematical approach to best approximate the transfer function we require for the filters design.

Such designs are known as **Elliptical**, **Butterworth**, **Chebyshev**, **Bessel**, **Cauer** as well as many others. Of these five “classic” linear analogue filter approximation functions only the **Butterworth Filter** and especially the *low pass Butterworth filter* design will be considered here as its the most commonly used function.

The frequency response of the **Butterworth Filter** approximation function is also often referred to as “maximally flat” (no ripples) response because the pass band is designed to have a frequency response which is as flat as mathematically possible from 0Hz (DC) until the cut-off frequency at -3dB with no ripples. Higher frequencies beyond the cut-off point rolls-off down to zero in the stop band at 20dB/decade or 6dB/octave. This is because it has a “quality factor”, “Q” of just 0.707.

However, one main disadvantage of the Butterworth filter is that it achieves this pass band flatness at the expense of a wide transition band as the filter changes from the pass band to the stop band. It also has poor phase characteristics as well. The ideal frequency response, referred to as a “brick wall” filter, and the standard Butterworth approximations, for different filter orders are given below.

Note that the higher the Butterworth filter order, the higher the number of cascaded stages there are within the filter design, and the closer the filter becomes to the ideal “brick wall” response.

In practice however, Butterworth’s ideal frequency response is unattainable as it produces excessive passband ripple.

Where the generalised equation representing a “nth” Order Butterworth filter, the frequency response is given as:

Where: n represents the filter order, Omega ω is equal to 2πƒ and Epsilon ε is the maximum pass band gain, (A_{max}). If A_{max} is defined at a frequency equal to the cut-off -3dB corner point (ƒc), ε will then be equal to one and therefore ε^{2} will also be one. However, if you now wish to define A_{max} at a different voltage gain value, for example 1dB, or 1.1220 (1dB = 20*logA_{max}) then the new value of epsilon, ε is found by:

Transpose the equation to give:

The **Frequency Response** of a filter can be defined mathematically by its **Transfer Function** with the standard Voltage Transfer Function H(jω) written as:

Note: ( jω ) can also be written as ( s ) to denote the **S-domain.** and the resultant transfer function for a second-order low pass filter is given as:

To help in the design of his low pass filters, Butterworth produced standard tables of normalized second-order low pass polynomials given the values of coefficient that correspond to a cut-off corner frequency of 1 radian/sec.

Find the order of an active low pass Butterworth filter whose specifications are given as: A_{max} = 0.5dB at a pass band frequency (ωp) of 200 radian/sec (31.8Hz), and A_{min} = -20dB at a stop band frequency (ωs) of 800 radian/sec. Also design a suitable Butterworth filter circuit to match these requirements.

Firstly, the maximum pass band gain A_{max} = 0.5dB which is equal to a gain of **1.0593**, remember that: 0.5dB = 20*log(A) at a frequency (ωp) of 200 rads/s, so the value of epsilon ε is found by:

Secondly, the minimum stop band gain A_{min} = -20dB which is equal to a gain of **10** (-20dB = 20*log(A)) at a stop band frequency (ωs) of 800 rads/s or 127.3Hz.

Substituting the values into the general equation for a Butterworth filters frequency response gives us the following:

Since n must always be an integer ( whole number ) then the next highest value to 2.42 is n = 3, therefore a **“a third-order filter is required”** and to produce a third-order **Butterworth filter**, a second-order filter stage cascaded together with a first-order filter stage is required.

From the normalised low pass Butterworth Polynomials table above, the coefficient for a third-order filter is given as (1+s)(1+s+s^{2}) and this gives us a gain of 3-A = 1, or A = 2. As A = 1 + (Rf/R1), choosing a value for both the feedback resistor Rf and resistor R1 gives us values of 1kΩ and 1kΩ respectively as: ( 1kΩ/1kΩ ) + 1 = 2.

We know that the cut-off corner frequency, the -3dB point (ω_{o}) can be found using the formula 1/CR, but we need to find ω_{o} from the pass band frequency ω_{p} then,

So, the cut-off corner frequency is given as 284 rads/s or 45.2Hz, (284/2π) and using the familiar formula 1/CR we can find the values of the resistors and capacitors for our third-order circuit.

Note that the nearest preferred value to 0.352uF would be 0.36uF, or 360nF.

and finally our circuit of the third-order low pass **Butterworth Filter** with a cut-off corner frequency of 284 rads/s or 45.2Hz, a maximum pass band gain of 0.5dB and a minimum stop band gain of 20dB is constructed as follows.

So for our 3rd-order Butterworth Low Pass Filter with a corner frequency of 45.2Hz, C = 360nF and R = 10kΩ

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]]>The post Active Band Pass Filter first appeared on The Amazing World of Electronics.

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]]>For a low pass filter, this passband starts from 0Hz or DC and continues up to the specified cut-off frequency point at -3dB down from the maximum passband gain. Equally, for a high pass filter the passband starts from this -3dB cut-off frequency and continues up to infinity or the maximum open-loop gain for an active filter.

However, the **Active Band Pass Filter** is slightly different in that it is a frequency selective filter circuit used in electronic systems to separate a signal at one particular frequency, or a range of signals that lie within a certain “band” of frequencies from signals at all other frequencies. This band or range of frequencies is set between two cut-off or corner frequency points labelled the “lower frequency” ( ƒ_{L} ) and the “higher frequency” ( ƒ_{H} ) while attenuating any signals outside of these two points.

Simple **Active Band Pass Filter** can be easily made by cascading together a single Low Pass Filter with a single High Pass Filter as shown.

The cut-off or corner frequency of the low pass filter (LPF) is higher than the cut-off frequency of the high pass filter (HPF) and the difference between the frequencies at the -3dB point will determine the “bandwidth” of the band pass filter while attenuating any signals outside of these points. One way of making a very simple **Active Band Pass Filter** is to connect the basic passive high and low pass filters we look at previously to an amplifying op-amp circuit as shown.

This cascading together of the individual low and high pass passive filters produces a low “Q-factor” type filter circuit which has a wide passband. The first stage of the filter will be the high pass stage that uses the capacitor to block any DC biasing from the source. This design has the advantage of producing a relatively flat asymmetrical passband frequency response with one half representing the low pass response and the other half representing high pass response as shown.

The higher corner point ( ƒ_{H} ), as well as the lower corner frequency cut-off point ( ƒL ), are calculated the same as before in the standard first-order low and high pass filter circuits. Obviously, a reasonable separation is required between the two cut-off points to prevent any interaction between the low pass and high pass stages. The amplifier also provides isolation between the two stages and defines the overall voltage gain of the circuit.

The bandwidth of the filter is therefore the difference between these upper and lower -3dB points. For example, suppose we have a band pass filter whose -3dB cut-off points are set at 200Hz and 600Hz. Then the bandwidth of the filter would be given as: Bandwidth (BW) = 600 – 200 = 400Hz.

The normalised frequency response and phase shift for an active band pass filter will be as follows.

While the above passive tuned filter circuit will work as a bandpass filter, the passband (bandwidth) can be quite wide and this may be a problem if we want to isolate a small band of frequencies. An active bandpass filter can also be made using an inverting operational amplifier.

So by rearranging the positions of the resistors and capacitors within the filter we can produce a much better filter circuit as shown below. For an active band pass filter, the lower cut-off -3dB point is given by ƒ_{C1} while the upper cut-off -3dB point is given by ƒ_{C2}.

This type of band pass filter is designed to have a much narrower pass band. The centre frequency and bandwidth of the filter is related to the values of R1, R2, C1 and C2. The output of the filter is again taken from the output of the op-amp.

We can improve the band pass response of the above circuit by rearranging the components again to produce an infinite-gain multiple-feedback (IGMF) band pass filter. This type of active band pass design produces a “tuned” circuit based around a negative feedback active filter giving it a high “Q-factor” (up to 25) amplitude response and steep roll-off on either side of its centre frequency. Because the frequency response of the circuit is similar to a resonance circuit, this center frequency is referred to as the resonant frequency, ( ƒr ). Consider the circuit below.

This active band pass filter circuit uses the full gain of the operational amplifier, with multiple negative feedback applied via resistor, R_{2} and capacitor C_{2}. Then we can define the characteristics of the IGMF filter as follows:

We can see then that the relationship between resistors, R_{1} and R_{2} determines the band pass “Q-factor” and the frequency at which the maximum amplitude occurs, the gain of the circuit will be equal to -2Q^{2}. Then as the gain increases so to does the selectivity. In other words, high gain – high selectivity.

An active band pass filter that has a voltage gain Av of one (1) and a resonant frequency, ƒr of 1kHz is constructed using an infinite gain multiple feedback filter circuit. Calculate the values of the components required to implement the circuit.

Firstly, we can determine the values of the two resistors, R_{1} and R_{2} required for the active filter using the gain of the circuit to find Q as follows.

Then we can see that a value of Q = 0.7071 gives a relationship of resistor, R_{2} being twice the value of resistor R_{1}. Then we can choose any suitable value of resistances to give the required ratio of two. Then resistor R_{1} = 10kΩ and R_{2} = 20kΩ.

The center or resonant frequency is given as 1kHz. Using the new resistor values obtained, we can determine the value of the capacitors required assuming that C = C_{1} = C_{2}.

The closest standard value is 10nF.

The actual shape of the frequency response curve for any passive or active band pass filter will depend upon the characteristics of the filter circuit with the curve above being defined as an “ideal” band pass response. An active band pass filter is a **2nd Order** type filter because it has “two” reactive components (two capacitors) within its circuit design.

As a result of these two reactive components, the filter will have a peak response or **Resonant Frequency** ( ƒr ) at its “center frequency”, ƒc. The center frequency is generally calculated as being the geometric mean of the two -3dB frequencies between the upper and the lower cut-off points with the resonant frequency (point of oscillation) being given as:

Where:

- ƒ
_{r}is the resonant or Center Frequency - ƒ
_{L}is the lower -3dB cut-off frequency point - ƒ
_{H}is the upper -3db cut-off frequency point

and in our simple example in the text above of a filters lower and upper -3dB cut-off points being at 200Hz and 600Hz respectively, then the resonant center frequency of the active band pass filter would be:

In a **Band Pass Filter** circuit, the overall width of the actual passband between the upper and lower -3dB corner points of the filter determines the **Quality Factor** or **Q-point** of the circuit. This **Q Factor** is a measure of how “Selective” or “Un-selective” the bandpass filter is towards a given spread of frequencies. The lower the value of the Q factor the wider is the bandwidth of the filter and consequently the higher the Q factor the narrower and more “selective” is the filter.

The **Quality Factor, Q** of the filter is sometimes given the Greek symbol of **Alpha**, ( α ) and is known as the **alpha-peak frequency** where:

As the quality factor of an active bandpass filter (Second-order System) relates to the “sharpness” of the filter’s response around its center resonant frequency ( ƒr ) it can also be thought of as the “Damping Factor” or “Damping Coefficient” because the more damping the filter has the flatter is its response and likewise, the less damping the filter has the sharper is its response. The damping ratio is given the Greek symbol of **Xi**, ( ξ ) where:

The “Q” of a bandpass filter is the ratio of the **Resonant Frequency**, ( ƒr ) to the **Bandwidth**, ( BW ) between the upper and lower -3dB frequencies and is given as:

So for our simple example above, if the bandwidth (BW) is 400Hz, that is ƒ_{H} – ƒ_{L}, and the center resonant frequency, ƒ_{r} is 346Hz. Then the quality factor “**Q**” of the band pass filter will be given as:

346Hz / 400Hz = **0.865**. Note that **Q** is a ratio, it has no units.

When analyzing active filters, generally a normalized circuit is considered which produces an “ideal” frequency response having a rectangular shape and a transition between the passband and the stopband that has an abrupt or very steep roll-off slope. However, these ideal responses are not possible in the real world so we use approximations to give us the best frequency response possible for the type of filter we are trying to design.

Probably the best-known filter approximation for doing this is the Butterworth or maximally-flat response filter. In the next tutorial, we will look at higher-order filters and use Butterworth approximations to produce filters that have a frequency response that is as flat as mathematically possible in the passband and a smooth transition or roll-off rate.

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]]>The post Active High Pass Filter first appeared on The Amazing World of Electronics.

The post Active High Pass Filter appeared first on The Amazing World of Electronics.

]]>The basic operation of an **Active High Pass Filter** (HPF) is the same as for its equivalent RC passive high pass filter circuit, except this time the circuit has an operational amplifier or included within its design providing amplification and gain control.

Like the previous active low pass filter circuit, the simplest form of an *active high pass filter* is to connect a standard inverting or non-inverting operational amplifier to the basic RC high pass passive filter circuit as shown.

Technically, there is no such thing as an **active high pass filter**. Unlike Passive High Pass Filters which have an “infinite” frequency response, the maximum pass band frequency response of an active high pass filter is limited by the open-loop characteristics or bandwidth of the operational amplifier being used, making them appear as if they are band pass filters with a high frequency cut-off determined by the selection of op-amp and gain.

In the Operational Amplifier tutorial we saw that the maximum frequency response of an op-amp is limited to the Gain/Bandwidth product or open loop voltage gain ( A_{ V} ) of the operational amplifier being used giving it a bandwidth limitation, where the closed loop response of the op amp intersects the open loop response.

A commonly available operational amplifier such as the uA741 has a typical “open-loop” (without any feedback) DC voltage gain of about 100dB maximum reducing at a roll off rate of -20dB/Decade (-6db/Octave) as the input frequency increases. The gain of the uA741 reduces until it reaches unity gain, (0dB) or its “transition frequency” ( ƒt ) which is about 1MHz. This causes the op-amp to have a frequency response curve very similar to that of a first-order low pass filter and this is shown below.

Then the performance of a “high pass filter” at high frequencies is limited by this unity gain crossover frequency which determines the overall bandwidth of the open-loop amplifier. The gain-bandwidth product of the op-amp starts from around 100kHz for small signal amplifiers up to about 1GHz for high-speed digital video amplifiers and op-amp based active filters can achieve very good accuracy and performance provided that low tolerance resistors and capacitors are used.

Under normal circumstances the maximum pass band required for a closed loop active high pass or band pass filter is well below that of the maximum open-loop transition frequency. However, when designing active filter circuits it is important to choose the correct op-amp for the circuit as the loss of high frequency signals may result in signal distortion.

A first-order (single-pole) **Active High Pass Filter** as its name implies, attenuates low frequencies and passes high frequency signals. It consists simply of a passive filter section followed by a non-inverting operational amplifier. The frequency response of the circuit is the same as that of the passive filter, except that the amplitude of the signal is increased by the gain of the amplifier and for a non-inverting amplifier the value of the pass band voltage gain is given as 1 + R2/R1, the same as for the low pass filter circuit.

This *first-order high pass filter*, consists simply of a passive filter followed by a non-inverting amplifier. The frequency response of the circuit is the same as that of the passive filter, except that the amplitude of the signal is increased by the gain of the amplifier.

For a non-inverting amplifier circuit, the magnitude of the voltage gain for the filter is given as a function of the feedback resistor ( R2 ) divided by its corresponding input resistor ( R1 ) value and is given as:

Where:

- A
_{F}= the Pass band Gain of the filter, ( 1 + R2/R1 ) - ƒ = the Frequency of the Input Signal in Hertz, (Hz)
- ƒc = the Cut-off Frequency in Hertz, (Hz)

Just like the low pass filter, the operation of a high pass active filter can be verified from the frequency gain equation above as:

Then, the **Active High Pass Filter** has a gain A_{F} that increases from 0Hz to the low frequency cut-off point, ƒ_{C} at 20dB/decade as the frequency increases. At ƒ_{C} the gain is 0.707*A_{F,} and after ƒ_{C} all frequencies are pass band frequencies so the filter has a constant gain A_{F} with the highest frequency being determined by the closed loop bandwidth of the op-amp.

When dealing with filter circuits the magnitude of the pass band gain of the circuit is generally expressed in *decibels* or *dB* as a function of the voltage gain, and this is defined as:

For a first-order filter the frequency response curve of the filter increases by 20dB/decade or 6dB/octave up to the determined cut-off frequency point which is always at -3dB below the maximum gain value. As with the previous filter circuits, the lower cut-off or corner frequency ( ƒc ) can be found by using the same formula:

The corresponding phase angle or phase shift of the output signal is the same as that given for the passive RC filter and **leads** that of the input signal. It is equal to **+45 ^{o}** at the cut-off frequency ƒc value and is given as:

A simple first-order active high pass filter can also be made using an inverting operational amplifier configuration as well, and an example of this circuit design is given along with its corresponding frequency response curve. A gain of 40dB has been assumed for the circuit.

A first order active high pass filter has a pass band gain of two and a cut-off corner frequency of 1kHz. If the input capacitor has a value of 10nF, calculate the value of the cut-off frequency determining resistor and the gain resistors in the feedback network. Also, plot the expected frequency response of the filter.

With a cut-off corner frequency given as 1kHz and a capacitor of 10nF, the value of R will therefore be:

or 16kΩ to the nearest preferred value.

Thus the pass band gain of the filter, A_{F} is therefore given as being: 2.

As the value of resistor, R_{2} divided by resistor, R_{1} gives a value of one. Then, resistor R_{1} must be equal to resistor R_{2}, since the pass band gain, A_{F} = 2. We can therefore select a suitable value for the two resistors of say, 10kΩ each for both feedback resistors.

So for a high pass filter with a cut-off corner frequency of 1kHz, the values of R and C will be, 10kΩ and 10nF respectively. The values of the two feedback resistors to produce a pass band gain of two are given as: R_{1} = R_{2} = 10kΩ

The data for the frequency response bode plot can be obtained by substituting the values obtained above over a frequency range from 100Hz to 100kHz into the equation for voltage gain:

This then will give us the following table of data.

he frequency response data from the table above can now be plotted as shown below. In the stop band (from 100Hz to 1kHz), the gain increases at a rate of 20dB/decade. However, in the pass band after the cut-off frequency, ƒ_{C} = 1kHz, the gain remains constant at 6.02dB. The upper-frequency limit of the pass band is determined by the open loop bandwidth of the operational amplifier used as we discussed earlier. Then the bode plot of the filter circuit will look like this.

Applications of **Active High Pass Filters** are in audio amplifiers, equalizers or speaker systems to direct the high frequency signals to the smaller tweeter speakers or to reduce any low frequency noise or “rumble” type distortion. When used like this in audio applications the active high pass filter is sometimes called a “Treble Boost” filter.

As with the passive filter, a first-order high pass active filter can be converted into a second-order high pass filter simply by using an additional RC network in the input path. The frequency response of the second-order high pass filter is identical to that of the first-order type except that the stop band roll-off will be twice the first-order filters at 40dB/decade (12dB/octave). Therefore, the design steps required of the second-order active high pass filter are the same.

Higher-order high pass active filters, such as third, fourth, fifth, etc are formed simply by cascading together first and second-order filters. For example, a third order high pass filter is formed by cascading in series first and second order filters, a fourth-order high pass filter by cascading two second-order filters together and so on.

Then an **Active High Pass Filter** with an even order number will consist of only second-order filters, while an odd order number will start with a first-order filter at the beginning as shown.

Although there is no limit to the order of a filter that can be formed, as the order of the filter increases so to does its size. Also, its accuracy declines, that is the difference between the actual stop band response and the theoretical stop band response also increases.

If the frequency determining resistors are all equal, R1 = R2 = R3 etc, and the frequency determining capacitors are all equal, C1 = C2 = C3 etc, then the cut-off frequency for any order of filter will be exactly the same. However, the overall gain of the higher-order filter is fixed because all the frequency determining components are equal.

In the next tutorial about filters, we will see that Active Band Pass Filters, can be constructed by cascading together a high pass and a low pass filter.

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]]>The post Active Low Pass Filter first appeared on The Amazing World of Electronics.

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]]>In the RC Passive Filter tutorials, we saw how a basic first-order filter circuits, such as the low pass and the high pass filters can be made using just a single resistor in series with a non-polarized capacitor connected across a sinusoidal input signal.

We also noticed that the main disadvantage of passive filters is that the amplitude of the output signal is less than that of the input signal, ie, the gain is never greater than unity and that the load impedance affects the filters characteristics.

With passive filter circuits containing multiple stages, this loss in signal amplitude called “Attenuation” can become quiet severe. One way of restoring or controlling this loss of signal is by using amplification through the use of **Active Filters**.

As their name implies, **Active Filters** contain active components such as operational amplifiers, transistors or FET’s within their circuit design. They draw their power from an external power source and use it to boost or amplify the output signal.

Filter amplification can also be used to either shape or alter the frequency response of the filter circuit by producing a more selective output response, making the output bandwidth of the filter more narrower or even wider. Then the main difference between a “passive filter” and an “active filter” is amplification.

An active filter generally uses an operational amplifier (op-amp) within its design and in the Operational Amplifier tutorial we saw that an Op-amp has a high input impedance, a low output impedance and a voltage gain determined by the resistor network within its feedback loop.

Unlike a passive high pass filter which has in theory an infinite high frequency response, the maximum frequency response of an active filter is limited to the Gain/Bandwidth product (or open loop gain) of the operational amplifier being used. Still, active filters are generally much easier to design than passive filters, they produce good performance characteristics, very good accuracy with a steep roll-off and low noise when used with a good circuit design.

The most common and easily understood active filter is the **Active Low Pass Filter**. Its principle of operation and frequency response is exactly the same as those for the previously seen passive filter, the only difference this time is that it uses an op-amp for amplification and gain control. The simplest form of a low pass active filter is to connect an inverting or non-inverting amplifier, the same as those discussed in the Op-amp tutorial, to the basic RC low pass filter circuit as shown.

This first-order low pass active filter, consists simply of a passive RC filter stage providing a low frequency path to the input of a non-inverting operational amplifier. The amplifier is configured as a voltage-follower (Buffer) giving it a DC gain of one, Av = +1 or unity gain as opposed to the previous passive RC filter which has a DC gain of less than unity.

The advantage of this configuration is that the op-amps high input impedance prevents excessive loading on the filters output while its low output impedance prevents the filters cut-off frequency point from being affected by changes in the impedance of the load.

While this configuration provides good stability to the filter, its main disadvantage is that it has no voltage gain above one. However, although the voltage gain is unity the power gain is very high as its output impedance is much lower than its input impedance. If a voltage gain greater than one is required we can use the following filter circuit.

The frequency response of the circuit will be the same as that for the passive RC filter, except that the amplitude of the output is increased by the pass band gain, A_{F} of the amplifier. For a non-inverting amplifier circuit, the magnitude of the voltage gain for the filter is given as a function of the feedback resistor ( R_{2} ) divided by its corresponding input resistor ( R_{1} ) value and is given as:

Therefore, the gain of an active low pass filter as a function of frequency will be:

- Where:
- A
_{F}= the pass band gain of the filter, (1 + R2/R1) - ƒ = the frequency of the input signal in Hertz, (Hz)
- ƒc = the cut-off frequency in Hertz, (Hz)

Thus, the operation of a low pass active filter can be verified from the frequency gain equation above as:

hus, the **Active Low Pass Filter** has a constant gain A_{F} from 0Hz to the high frequency cut-off point, ƒ_{C}. At ƒ_{C} the gain is 0.707A_{F,} and after ƒ_{C} it decreases at a constant rate as the frequency increases. That is, when the frequency is increased tenfold (one decade), the voltage gain is divided by 10.

In other words, the gain decreases 20dB (= 20*log(10)) each time the frequency is increased by 10. When dealing with filter circuits the magnitude of the pass band gain of the circuit is generally expressed in *decibels* or *dB* as a function of the voltage gain, and this is defined as:

Design a non-inverting active low pass filter circuit that has a gain of ten at low frequencies, a high frequency cut-off or corner frequency of 159Hz and an input impedance of 10KΩ.

The voltage gain of a non-inverting operational amplifier is given as:

Assume a value for resistor R1 of 1kΩ rearranging the formula above gives a value for R2 of:

So for a voltage gain of 10, R1 = 1kΩ and R2 = 9kΩ. However, a 9kΩ resistor does not exist so the next preferred value of 9k1Ω is used instead. Converting this voltage gain to an equivalent decibel dB value gives:

The cut-off or corner frequency (ƒc) is given as being 159Hz with an input impedance of 10kΩ. This cut-off frequency can be found by using the formula:

By rearranging the above standard formula we can find the value of the filter capacitor C as:

Thus the final low pass filter circuit along with its frequency response is given below as:

If the external impedance connected to the input of the filter circuit changes, this impedance change would also affect the corner frequency of the filter (components connected together in series or parallel). One way of avoiding any external influence is to place the capacitor in parallel with the feedback resistor R2 effectively removing it from the input but still maintaining the filters characteristics.

However, the value of the capacitor will change slightly from being 100nF to 110nF to take account of the 9k1Ω resistor, but the formula used to calculate the cut-off corner frequency is the same as that used for the RC passive low pass filter.

Examples of different first-order *active low pass filter circuit* configurations are given as:

Here the capacitor has been moved from the op-amps input to its feedback circuit in parallel with R2. This parallel combination of C and R2 sets the -3dB point as before, but allows the amplifiers gain to roll-off indefinitely beyond the corner frequency.

At low frequencies the capacitors reactance is much higher than R2, so the dc gain is set by the standard inverting formula of: -R2/R1 = 10, for this example. As the frequency increases the capacitors reactance decreases reducing the impedance of the parallel combination of Xc||R2, until eventually at a high enough frequency, Xc reduces to zero.

The advantage here is that the circuits input impedance is now just R1 and the output signal is inverted. With the corner frequency determining components in the feedback circuit, the RC set-point is unaffected by variations in source impedance and the dc gain can be adjusted independently of the corner frequency.

Here due to the position of the capacitor in parallel with the feedback resistor R2, the low pass corner frequency is set as before but at high frequencies the reactance of the capacitor dominates shorting out R2 reducing the amplifiers gain. At a high enough frequency the gain bottoms out at unity (0dB) as the amplifier effectively becomes a voltage follower so the gain equation becomes 1 + 0/R1 which equals 1 (unity).

Applications of **Active Low Pass Filters** are in audio amplifiers, equalizers or speaker systems to direct the lower frequency bass signals to the larger bass speakers or to reduce any high frequency noise or “hiss” type distortion. When used like this in audio applications the active low pass filter is sometimes called a “Bass Boost” filter.

As with the passive filter, a first-order low-pass active filter can be converted into a second-order low pass filter simply by using an additional RC network in the input path. The frequency response of the second-order low pass filter is identical to that of the first-order type except that the stop band roll-off will be twice the first-order filters at 40dB/decade (12dB/octave). Therefore, the design steps required of the second-order active low pass filter are the same.

When cascading together filter circuits to form higher-order filters, the overall gain of the filter is equal to the product of each stage. For example, the gain of one stage may be 10 and the gain of the second stage may be 32 and the gain of a third stage may be 100. Then the overall gain will be 32,000, (10 x 32 x 100) as shown below.

Second-order (two-pole) active filters are important because higher-order filters can be designed using them. By cascading together first and second-order filters, filters with an order value, either odd or even up to any value can be constructed. In the next tutorial about *filters*, we will see that Active High Pass Filters, can be constructed by reversing the positions of the resistor and capacitor in the circuit.

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]]>The post Passive Band Pass Filter first appeared on The Amazing World of Electronics.

The post Passive Band Pass Filter appeared first on The Amazing World of Electronics.

]]>Band Pass Filters can be used to isolate or filter out certain frequencies that lie within a particular band or range of frequencies. The cut-off frequency or ƒc point in a simple RC passive filter can be accurately controlled using just a single resistor in series with a non-polarized capacitor, and depending upon which way around they are connected, we have seen that either a Low Pass or a High Pass filter is obtained.

One simple use for these types of passive filters is in audio amplifier applications or circuits such as in loudspeaker crossover filters or pre-amplifier tone controls. Sometimes it is necessary to only pass a certain range of frequencies that do not begin at 0Hz, (DC) or end at some upper high frequency point but are within a certain range or band of frequencies, either narrow or wide.

By connecting or “cascading” together with a single **Low Pass Filter** circuit with a **High Pass Filter** circuit, we can produce another type of passive RC filter that passes a selected range or “band” of frequencies that can be either narrow or wide while attenuating all those outside of this range. This new type of passive filter arrangement produces a frequency selective filter known commonly as a **Band Pass Filter** or **BPF** for short.

Unlike the low pass filter which only pass signals of a low frequency range or the high pass filter which pass signals of a higher frequency range, a **Band Pass Filters** passes signals within a certain “band” or “spread” of frequencies without distorting the input signal or introducing extra noise. This band of frequencies can be any width and is commonly known as the filters **Bandwidth**.

Bandwidth is commonly defined as the frequency range that exists between two specified frequency cut-off points ( ƒc ), that are 3dB below the maximum centre or resonant peak while attenuating or weakening the others outside of these two points.

Then for widely spread frequencies, we can simply define the term “bandwidth”, BW as being the difference between the lower cut-off frequency ( ƒc_{LOWER} ) and the higher cut-off frequency ( ƒc_{HIGHER} ) points. In other words, BW = ƒ_{H} – ƒ_{L}. Clearly for a pass band filter to function correctly, the cut-off frequency of the low pass filter must be higher than the cut-off frequency for the high pass filter.

The “ideal” **Band Pass Filter** can also be used to isolate or filter out certain frequencies that lie within a particular band of frequencies, for example, noise cancellation. Band pass filters are known generally as second-order filters, (two-pole) because they have “two” reactive component, the capacitors, within their circuit design. One capacitor in the low pass circuit and another capacitor in the high pass circuit.

The **Bode Plot** or frequency response curve above shows the characteristics of the band pass filter. Here the signal is attenuated at low frequencies with the output increasing at a slope of +20dB/Decade (6dB/Octave) until the frequency reaches the “lower cut-off” point ƒ_{L}. At this frequency the output voltage is again 1/√2 = 70.7% of the input signal value or **-3dB** (20*log(V_{OUT}/V_{IN})) of the input.

The output continues at maximum gain until it reaches the “upper cut-off” point ƒ_{H} where the output decreases at a rate of -20dB/Decade (6dB/Octave) attenuating any high frequency signals. The point of maximum output gain is generally the geometric mean of the two -3dB value between the lower and upper cut-off points and is called the “Centre Frequency” or “Resonant Peak” value ƒr. This geometric mean value is calculated as being ƒr^{ 2} = ƒ_{(UPPER)} x ƒ_{(LOWER)}.

A band pass filter is regarded as a second-order (two-pole) type filter because it has “two” reactive components within its circuit structure, then the phase angle will be twice that of the previously seen first-order filters, ie, **180 ^{o}**. The phase angle of the output signal

The upper and lower cut-off frequency points for a band pass filter can be found using the same formula as that for both the low and high pass filters, For example.

Then clearly, the width of the pass band of the filter can be controlled by the positioning of the two cut-off frequency points of the two filters.

A second-order **band pass filter** is to be constructed using RC components that will only allow a range of frequencies to pass above 1kHz (1,000Hz) and below 30kHz (30,000Hz). Assuming that both the resistors have values of 10kΩ, calculate the values of the two capacitors required.

The value of the capacitor C1 required to give a cut-off frequency ƒ_{L} of 1kHz with a resistor value of 10kΩ is calculated as:

Then, the values of R1 and C1 required for the high pass stage to give a cut-off frequency of 1.0kHz are: R1 = 10kΩ and to the nearest preferred value, C1 = 15nF.

The value of the capacitor C2 required to give a cut-off frequency ƒ_{H} of 30kHz with a resistor value of 10kΩ is calculated as:

Then, the values of R2 and C2 required for the low pass stage to give a cut-off frequency of 30kHz are, R = 10kΩ and C = 530pF. However, the nearest preferred value of the calculated capacitor value of 530pF is 560pF, so this is used instead.

With the values of both the resistances R1 and R2 given as 10kΩ, and the two values of the capacitors C1 and C2 found for both the high pass and low pass filters as 15nF and 560pF respectively, then the circuit for our simple passive **Band Pass Filter** is given as.

We can also calculate the “Resonant” or “Centre Frequency” (ƒr) point of the band pass filter were the output gain is at its maximum or peak value. This peak value is not the arithmetic average of the upper and lower -3dB cut-off points as you might expect but is in fact the “geometric” or mean value. This geometric mean value is calculated as being ƒr^{ 2} = ƒc_{(UPPER)} x ƒc_{(LOWER)} for example:

- Where, ƒ
_{r}is the resonant or centre frequency - ƒ
_{L}is the lower -3dB cut-off frequency point - ƒ
_{H}is the upper -3db cut-off frequency point

and in our simple example above, the calculated cut-off frequencies were found to be ƒ_{L} = 1,060 Hz and ƒ_{H} = 28,420 Hz using the filter values.

Then by substituting these values into the above equation gives a central resonant frequency of:

A simple passive **Band Pass Filter** can be made by cascading together a single **Low Pass Filter** with a **High Pass Filter**. The frequency range, in Hertz, between the lower and upper -3dB cut-off points of the RC combination is know as the filters “Bandwidth”.

The width or frequency range of the filters bandwidth can be very small and selective, or very wide and non-selective depending upon the values of R and C used.

The centre or resonant frequency point is the geometric mean of the lower and upper cut-off points. At this centre frequency the output signal is at its maximum and the phase shift of the output signal is the same as the input signal.

The amplitude of the output signal from a band pass filter or any passive RC filter for that matter, will always be less than that of the input signal. In other words a passive filter is also an attenuator giving a voltage gain of less than 1 (Unity). To provide an output signal with a voltage gain greater than unity, some form of amplification is required within the design of the circuit.

A **Passive Band Pass Filter** is classed as a second-order type filter because it has two reactive components within its design, the capacitors. It is made up from two single RC filter circuits that are each first-order filters themselves.

If more filters are cascaded together the resulting circuit will be known as an “n^{th}-order” filter where the “n” stands for the number of individual reactive components and therefore poles within the filter circuit. For example, filters can be a 2^{nd}-order, 4^{th}-order, 10^{th}-order, etc.

The higher the filters order the steeper will be the slope at n times -20dB/decade. However, a single capacitor value made by combining together two or more individual capacitors is still one capacitor.

Our example above shows the output frequency response curve for an “ideal” band pass filter with constant gain in the pass band and zero gain in the stop bands. In practice the frequency response of this Band Pass Filter circuit would not be the same as the input reactance of the high pass circuit would affect the frequency response of the low pass circuit (components connected in series or parallel) and vice versa. One way of overcoming this would be to provide some form of electrical isolation between the two filter circuits as shown below.

One way of combining amplification and filtering into the same circuit would be to use an Operational Amplifier or Op-amp, and examples of these are given in the Operational Amplifier section. In the next tutorial, we will look at filter circuits that use an operational amplifier within their design to not only to introduce gain but provide isolation between stages. These types of filter arrangements are generally known as **Active Filters**.

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]]>The post Passive High Pass Filter first appeared on The Amazing World of Electronics.

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]]>Whereas the low pass filter only allowed signals to pass below its cut-off frequency point, ƒc, the passive high pass filter circuit as its name implies, only passes signals above the selected cut-off point, ƒc eliminating any low-frequency signals from the waveform. Consider the circuit below.

In this circuit arrangement, the reactance of the capacitor is very high at low frequencies so the capacitor acts like an open circuit and blocks any input signals at V_{IN} until the cut-off frequency point ( ƒ_{C} ) is reached. Above this cut-off frequency point the reactance of the capacitor has reduced sufficiently as to now act more like a short circuit allowing all of the input signal to pass directly to the output as shown below in the filters response curve.

The **Bode Plot** or Frequency Response Curve above for a passive high pass filter is the exact opposite to that of a low pass filter. Here the signal is attenuated or damped at low frequencies with the output increasing at +20dB/Decade (6dB/Octave) until the frequency reaches the cut-off point ( ƒc ) where again R = Xc. It has a response curve that extends down from infinity to the cut-off frequency, where the output voltage amplitude is 1/√2 = 70.7% of the input signal value or -3dB (20 log (Vout/Vin)) of the input value.

Also we can see that the phase angle ( Φ ) of the output signal **LEADS** that of the input and is equal to **+45 ^{o}** at frequency ƒc. The frequency response curve for this filter implies that the filter can pass all signals out to infinity. However in practice, the filter response does not extend to infinity but is limited by the electrical characteristics of the components used.

The cut-off frequency point for a first order high pass filter can be found using the same equation as that of the low pass filter, but the equation for the phase shift is modified slightly to account for the positive phase angle as shown below.

The circuit gain, Av which is given as Vout/Vin (magnitude) and is calculated as:

Calculate the cut-off or “breakpoint” frequency ( ƒc ) for a simple passive high pass filter consisting of an 82pF capacitor connected in series with a 240kΩ resistor.

Again as with low pass filters, high pass filter stages can be cascaded together to form a second order (two-pole) filter as shown.

The above circuit uses two first-order filters connected or cascaded together to form a second-order or two-pole high pass network. Then a first-order filter stage can be converted into a second-order type by simply using an additional RC network, the same as for the 2^{nd}-order low pass filter. The resulting second-order high pass filter circuit will have a slope of 40dB/decade (12dB/octave).

As with the low pass filter, the cut-off frequency, ƒc is determined by both the resistors and capacitors as follows.

In practice, cascading passive filters together to produce larger-order filters is difficult to implement accurately as the dynamic impedance of each filter order affects its neighbouring network. However, to reduce the loading effect we can make the impedance of each following stage 10x the previous stage, so R_{2} = 10*R_{1} and C_{2} = 1/10th of C_{1}.

We have seen that the **Passive High Pass Filter** is the exact opposite to the low pass filter. This filter has no output voltage from DC (0Hz), up to a specified cut-off frequency ( ƒc ) point. This lower cut-off frequency point is 70.7% or **-3dB** (dB = -20log V_{OUT}/V_{IN}) of the voltage gain allowed to pass.

The frequency range “below” this cut-off point ƒc is generally known as the **Stop Band** while the frequency range “above” this cut-off point is generally known as the **Pass Band**.

The cut-off frequency, corner frequency or -3dB point of a high pass filter can be found using the standard formula of: ƒc = 1/(2πRC). The phase angle of the resulting output signal at ƒc is **+45 ^{o}**. Generally, the high pass filter is less distorting than its equivalent low pass filter due to the higher operating frequencies.

A very common application of this type of passive filter, is in audio amplifiers as a coupling capacitor between two audio amplifier stages and in speaker systems to direct the higher frequency signals to the smaller “tweeter” type speakers while blocking the lower bass signals or are also used as filters to reduce any low frequency noise or “rumble” type distortion. When used like this in audio applications the high pass filter is sometimes called a “low-cut”, or “bass cut” filter.

The output voltage Vout depends upon the time constant and the frequency of the input signal as seen previously. With an AC sinusoidal signal applied to the circuit it behaves as a simple 1st Order high pass filter. But if we change the input signal to that of a “square wave” shaped signal that has an almost vertical step input, the response of the circuit changes dramatically and produces a circuit known commonly as an **Differentiator**.

Up until now the input waveform to the filter has been assumed to be sinusoidal or that of a sine wave consisting of a fundamental signal and some harmonics operating in the frequency domain giving us a frequency domain response for the filter. However, if we feed the **High Pass Filter** with a **Square Wave** signal operating in the time domain giving an impulse or step response input, the output waveform will consist of short duration pulse or spikes as shown.

Each cycle of the square wave input waveform produces two spikes at the output, one positive and one negative and whose amplitude is equal to that of the input. The rate of decay of the spikes depends upon the time constant, ( RC ) value of both components, ( t = R x C ) and the value of the input frequency. The output pulses resemble more and more the shape of the input signal as the frequency increases.

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]]>The post Passive Low Pass Filter first appeared on The Amazing World of Electronics.

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]]>In other words they “filter-out” unwanted signals and an ideal filter will separate and pass sinusoidal input signals based upon their frequency. In low frequency applications (up to 100kHz), passive filters are generally constructed using simple RC (Resistor-Capacitor) networks, while higher frequency filters (above 100kHz) are usually made from RLC (Resistor-Inductor-Capacitor) components.

Passive filters are made up of passive components such as resistors, capacitors and inductors and have no amplifying elements (transistors, op-amps, etc) so have no signal gain, therefore their output level is always less than the input.

Filters are so named according to the frequency range of signals that they allow to pass through them, while blocking or “attenuating” the rest. The most commonly used filter designs are the:

- The Low Pass Filter – the low pass filter only allows low frequency signals from 0Hz to its cut-off frequency, ƒc point to pass while blocking those any higher.
- The High Pass Filter – the high pass filter only allows high frequency signals from its cut-off frequency, ƒc point and higher to infinity to pass through while blocking those any lower.
- The Band Pass Filter – the band pass filter allows signals falling within a certain frequency band setup between two points to pass through while blocking both the lower and higher frequencies either side of this frequency band.

Simple First-order passive filters (1st order) can be made by connecting together a single resistor and a single capacitor in series across an input signal, ( V_{IN} ) with the output of the filter, ( V_{OUT} ) taken from the junction of these two components.

Depending on which way around we connect the resistor and the capacitor with regards to the output signal determines the type of filter construction resulting in either a **Low Pass Filter** or a **High Pass Filter**.

As the function of any filter is to allow signals of a given band of frequencies to pass unaltered while attenuating or weakening all others that are not wanted, we can define the amplitude response characteristics of an ideal filter by using an ideal frequency response curve of the four basic filter types as shown.

Filters can be divided into two distinct types: active filters and passive filters. Active filters contain amplifying devices to increase signal strength while passive do not contain amplifying devices to strengthen the signal. As there are two passive components within a passive filter design the output signal has a smaller amplitude than its corresponding input signal, therefore passive RC filters attenuate the signal and have a gain of less than one, (unity).

A Low Pass Filter can be a combination of capacitance, inductance or resistance intended to produce high attenuation above a specified frequency and little or no attenuation below that frequency. The frequency at which the transition occurs is called the “cut-off” or “corner” frequency.

The simplest low pass filters consist of a resistor and capacitor but more sophisticated low pass filters have a combination of series inductors and parallel capacitors. In this tutorial we will look at the simplest type, a passive two component RC low pass filter.

A simple passive **RC Low Pass Filter** or **LPF** can be easily made by connecting together in series a single Resistor with a single Capacitor as shown below. In this type of filter arrangement, the input signal ( V_{IN} ) is applied to the series combination (both the Resistor and Capacitor together) but the output signal ( V_{OUT} ) is taken across the capacitor only.

This type of filter is known generally as a “first-order filter” or “one-pole filter”, why first-order or single-pole?, because it has only “one” reactive component, the capacitor, in the circuit.

As mentioned previously in the Capacitive Reactance tutorial, the reactance of a capacitor varies inversely with frequency, while the value of the resistor remains constant as the frequency changes. At low frequencies the capacitive reactance, ( X_{C} ) of the capacitor will be very large compared to the resistive value of the resistor, R.

This means that the voltage potential, V_{C} across the capacitor will be much larger than the voltage drop, V_{R} developed across the resistor. At high frequencies the reverse is true with V_{C} being small and V_{R} being large due to the change in the capacitive reactance value.

While the circuit above is that of an RC Low Pass Filter circuit, it can also be thought of as a frequency dependant variable potential divider circuit similar to the one we looked at in the Resistors tutorial. In that tutorial we used the following equation to calculate the output voltage for two single resistors connected in series.

We also know that the capacitive reactance of a capacitor in an AC circuit is given as:

Opposition to current flow in an AC circuit is called **impedance**, symbol Z and for a series circuit consisting of a single resistor in series with a single capacitor, the circuit impedance is calculated as:

Then by substituting our equation for impedance above into the resistive potential divider equation gives us:

So, by using the potential divider equation of two resistors in series and substituting for impedance we can calculate the output voltage of an RC Filter for any given frequency.

A **Low Pass Filter** circuit consisting of a resistor of 4k7Ω in series with a capacitor of 47nF is connected across a 10v sinusoidal supply. Calculate the output voltage ( V_{OUT} ) at a frequency of 100Hz and again at frequency of 10,000Hz or 10kHz.

We can see from the results above, that as the frequency applied to the RC network increases from 100Hz to 10kHz, the voltage dropped across the capacitor and therefore the output voltage ( V_{OUT} ) from the circuit decreases from 9.9v to 0.718v.

By plotting the networks output voltage against different values of input frequency, the **Frequency Response Curve** or **Bode Plot** function of the low pass filter circuit can be found, as shown below.

The Bode Plot shows the **Frequency Response** of the filter to be nearly flat for low frequencies and all of the input signal is passed directly to the output, resulting in a gain of nearly 1, called unity, until it reaches its **Cut-off Frequency** point ( ƒc ). This is because the reactance of the capacitor is high at low frequencies and blocks any current flow through the capacitor.

After this cut-off frequency point the response of the circuit decreases to zero at a slope of -20dB/ Decade or (-6dB/Octave) “roll-off”. Note that the angle of the slope, this -20dB/ Decade roll-off will always be the same for any RC combination.

Any high frequency signals applied to the low pass filter circuit above this cut-off frequency point will become greatly attenuated, that is they rapidly decrease. This happens because at very high frequencies the reactance of the capacitor becomes so low that it gives the effect of a short circuit condition on the output terminals resulting in zero output.

Then by carefully selecting the correct resistor-capacitor combination, we can create a RC circuit that allows a range of frequencies below a certain value to pass through the circuit unaffected while any frequencies applied to the circuit above this cut-off point to be attenuated, creating what is commonly called a **Low Pass Filter**.

For this type of “Low Pass Filter” circuit, all the frequencies below this cut-off, ƒc point that are unaltered with little or no attenuation and are said to be in the filters **Pass band** zone. This pass band zone also represents the **Bandwidth** of the filter. Any signal frequencies above this point cut-off point are generally said to be in the filters **Stop band** zone and they will be greatly attenuated.

This “Cut-off”, “Corner” or “Breakpoint” frequency is defined as being the frequency point where the capacitive reactance and resistance are equal, R = Xc = 4k7Ω. When this occurs the output signal is attenuated to 70.7% of the input signal value or **-3dB** (20 log (Vout/Vin)) of the input. Although R = Xc, the output is **not** half of the input signal. This is because it is equal to the vector sum of the two and is therefore 0.707 of the input.

As the filter contains a capacitor, the Phase Angle ( Φ ) of the output signal **LAGS** behind that of the input and at the -3dB cut-off frequency ( ƒc ) is -45^{o} out of phase. This is due to the time taken to charge the plates of the capacitor as the input voltage changes, resulting in the output voltage (the voltage across the capacitor) “lagging” behind that of the input signal. The higher the input frequency applied to the filter the more the capacitor lags and the circuit becomes more and more “out of phase”.

The cut-off frequency point and phase shift angle can be found by using the following equation:

Then for our simple example of a “**Low Pass Filter**” circuit above, the cut-off frequency (ƒc) is given as 720Hz with an output voltage of 70.7% of the input voltage value and a phase shift angle of -45^{o}.

Thus far we have seen that simple first-order RC low pass filters can be made by connecting a single resistor in series with a single capacitor. This single-pole arrangement gives us a roll-off slope of -20dB/decade attenuation of frequencies above the cut-off point at ƒ_{-3dB} . However, sometimes in filter circuits this -20dB/decade (-6dB/octave) angle of the slope may not be enough to remove an unwanted signal then two stages of filtering can be used as shown.

The above circuit uses two passive first-order low pass filters connected or “cascaded” together to form a second-order or two-pole filter network. Therefore we can see that a first-order low pass filter can be converted into a second-order type by simply adding an additional RC network to it and the more RC stages we add the higher becomes the order of the filter.

If a number ( n ) of such RC stages are cascaded together, the resulting RC filter circuit would be known as an “n^{th}-order” filter with a roll-off slope of “n x -20dB/decade”.

So for example, a second-order filter would have a slope of -40dB/decade (-12dB/octave), a fourth-order filter would have a slope of -80dB/decade (-24dB/octave) and so on. This means that, as the order of the filter is increased, the roll-off slope becomes steeper and the actual stop band response of the filter approaches its ideal stop band characteristics.

Second-order filters are important and widely used in filter designs because when combined with first-order filters any higher-order n^{th}-value filters can be designed using them. For example, a third order low-pass filter is formed by connecting in series or cascading together a first and a second-order low pass filter.

But there is a downside too cascading together RC filter stages. Although there is no limit to the order of the filter that can be formed, as the order increases, the gain and accuracy of the final filter declines.

When identical RC filter stages are cascaded together, the output gain at the required cut-off frequency ( ƒc ) is reduced (attenuated) by an amount in relation to the number of filter stages used as the roll-off slope increases. We can define the amount of attenuation at the selected cut-off frequency using the following formula.

where “n” is the number of filter stages.

So for a second-order passive low pass filter the gain at the corner frequency ƒc will be equal to 0.7071 x 0.7071 = 0.5Vin (-6dB), a third-order passive low pass filter will be equal to 0.353Vin (-9dB), fourth-order will be 0.25Vin (-12dB) and so on. The corner frequency, ƒc for a second-order passive low pass filter is determined by the resistor/capacitor (RC) combination and is given as.

In reality as the filter stage and therefore its roll-off slope increases, the low pass filters -3dB corner frequency point and therefore its pass band frequency changes from its original calculated value above by an amount determined by the following equation.

where ƒc is the calculated cut-off frequency, n is the filter order and ƒ_{-3dB} is the new -3dB pass band frequency as a result in the increase of the filters order.

Then the frequency response (bode plot) for a second-order low pass filter assuming the same -3dB cut-off point would look like:

In practice, cascading passive filters together to produce larger-order filters is difficult to implement accurately as the dynamic impedance of each filter order affects its neighbouring network. However, to reduce the loading effect we can make the impedance of each following stage 10x the previous stage, so R2 = 10 x R1 and C2 = 1/10th C1. Second-order and above filter networks are generally used in the feedback circuits of op-amps, making what are commonly known as Active Filters or as a phase-shift network in RC Oscillator circuits.

So to summarize, the **Low Pass Filter** has a constant output voltage from D.C. (0Hz), up to a specified Cut-off frequency, ( ƒ_{C} ) point. This cut-off frequency point is 0.707 or **-3dB** ( dB = –20log*V_{OUT/IN} ) of the voltage gain allowed to pass.

The frequency range “below” this cut-off point ƒ_{C} is generally known as the **Pass Band** as the input signal is allowed to pass through the filter. The frequency range “above” this cut-off point is generally known as the **Stop Band** as the input signal is blocked or stopped from passing through.

A simple 1st order low pass filter can be made using a single resistor in series with a single non-polarized capacitor (or any single reactive component) across an input signal Vin, whilst the output signal Vout is taken from across the capacitor.

The cut-off frequency or -3dB point, can be found using the standard formula, ƒc = 1/(2πRC). The phase angle of the output signal at ƒc and is -45^{o} for a Low Pass Filter.

The gain of the filter or any filter for that matter, is generally expressed in **Decibels** and is a function of the output value divided by its corresponding input value and is given as:

Applications of passive Low Pass Filters are in audio amplifiers and speaker systems to direct the lower frequency bass signals to the larger bass speakers or to reduce any high frequency noise or “hiss” type distortion. When used like this in audio applications the low pass filter is sometimes called a “high-cut”, or “treble cut” filter.

If we were to reverse the positions of the resistor and capacitor in the circuit so that the output voltage is now taken from across the resistor, we would have a circuit that produces an output frequency response curve similar to that of a High Pass Filter, and this is discussed in the next tutorial.

Until now we have been interested in the frequency response of a low pass filter when subjected to sinusoidal waveform. We have also seen that the filters cut-off frequency ( ƒc ) is the product of the resistance ( R ) and the capacitance ( C ) in the circuit with respect to some specified frequency point and that by altering any one of the two components alters this cut-off frequency point by either increasing it or decreasing it.

We also know that the phase shift of the circuit lags behind that of the input signal due to the time required to charge and then discharge the capacitor as the sine wave changes. This combination of R and C produces a charging and discharging effect on the capacitor known as its **Time Constant** ( τ ) of the circuit as seen in the RC Circuit tutorials giving the filter a response in the time domain.

The time constant, **tau** ( τ ), is related to the cut-off frequency ƒc as:

or expressed in terms of the cut-off frequency, ƒc as:

The output voltage, V_{OUT} depends upon the time constant and the frequency of the input signal. With a sinusoidal signal that changes smoothly over time, the circuit behaves as a simple 1st order low pass filter as we have seen above.

But what if we were to change the input signal to that of a “square wave” shaped “ON/OFF” type signal that has an almost vertical step input, what would happen to our filter circuit now. The output response of the circuit would change dramatically and produce another type of circuit known commonly as an **Integrator**.

The **Integrator** is basically a low pass filter circuit operating in the time domain that converts a square wave “step” response input signal into a triangular shaped waveform output as the capacitor charges and discharges. A **Triangular** waveform consists of alternate but equal, positive and negative ramps.

As seen below, if the RC time constant is long compared to the time period of the input waveform the resultant output waveform will be triangular in shape and the higher the input frequency the lower will be the output amplitude compared to that of the input.

This then makes this type of circuit ideal for converting one type of electronic signal to another for use in wave-generating or wave-shaping circuits.

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]]>In the RC Network tutorial we saw that when a DC voltage is applied to a capacitor, the capacitor itself draws a charging current from the supply and charges up to a value equal to the applied voltage.

Likewise, when the supply voltage is reduced the charge stored in the capacitor also reduces and the capacitor discharges. But in an AC circuit in which the applied voltage signal is continually changing from a positive to a negative polarity at a rate determined by the frequency of the supply, as in the case of a sine wave voltage, for example, the capacitor is either being charged or discharged on a continuous basis at a rate determined by the supply frequency.

As the capacitor charges or discharges, a current flows through it which is restricted by the internal impedance of the capacitor. This internal impedance is commonly known as **Capacitive Reactance** and is given the symbol X_{C} in Ohms.

Unlike resistance which has a fixed value, for example, 100Ω, 1kΩ, 10kΩ etc, (this is because resistance obeys Ohms Law), **Capacitive Reactance** varies with the applied frequency so any variation in supply frequency will have a big effect on the capacitor’s, “capacitive reactance” value.

As the frequency applied to the capacitor increases, its effect is to decrease its reactance (measured in ohms). Likewise as the frequency across the capacitor decreases its reactance value increases. This variation is called the capacitor’s *complex impedance*.

Complex impedance exists because the electrons in the form of an electrical charge on the capacitor plates, appear to pass from one plate to the other more rapidly with respect to the varying frequency.

As the frequency increases, the capacitor passes more charge across the plates in a given time resulting in a greater current flow through the capacitor appearing as if the internal impedance of the capacitor has decreased. Therefore, a capacitor connected to a circuit that changes over a given range of frequencies can be said to be “Frequency Dependant”.

**Capacitive Reactance** has the electrical symbol “X_{C}” and has units measured in Ohms the same as resistance, ( R ). It is calculated using the following formula:

Where:

- Xc = Capacitive Reactance in Ohms, (Ω)
- π (pi) = 3.142 (decimal) or as 22÷7 (fraction)
- ƒ = Frequency in Hertz, (Hz)
- C = Capacitance in Farads, (F)

Calculate the capacitive reactance value of a 220nF capacitor at a frequency of 1kHz and again at a frequency of 20kHz.

At a frequency of 1kHz:

Again at a frequency of 20kHz:

where: ƒ = frequency in Hertz and C = capacitance in Farads

Therefore, it can be seen from above that as the frequency applied across the 220nF capacitor increases, from 1kHz to 20kHz, its reactance value, X_{C} decreases, from approx 723Ω to just 36Ω and this is always true as capacitive reactance, X_{C} is inversely proportional to frequency with the current passed by the capacitor for a given voltage being proportional to the frequency.

For any given value of capacitance, the reactance of a capacitor, X_{C} expressed in ohms can be plotted against the frequency as shown below.

By re-arranging the reactance formula above, we can also find at what frequency a capacitor will have a particular capacitive reactance ( X_{C} ) value.

At which frequency would a 2.2uF Capacitor have a reactance value of 200Ωs?

Or we can find the value of the capacitor in Farads by knowing the applied frequency and its reactance value at that frequency.

What will be the value of a capacitor in farads when it has a capacitive reactance of 200Ω and is connected to a 50Hz supply.

We can see from the above examples that a capacitor when connected to a variable frequency supply, acts a bit like a “frequency controlled variable resistor” as its reactance (X) is directly proportional to frequency. At very low frequencies, such as 1Hz our 220nF capacitor has a high capacitive reactance value of approx 723.3KΩ (giving the effect of an open circuit).

At very high frequencies such as 1Mhz the capacitor has a low capacitive reactance value of just 0.72Ω (giving the effect of a short circuit). So at zero frequency or steady state DC our 220nF capacitor has infinite reactance looking more like an “open-circuit” between the plates and blocking any flow of current through it.

We remember from our tutorial about Resistors in Series that different voltages can appear across each resistor depending upon the value of the resistance and that a voltage divider circuit has the ability to divide its supply voltage by the ratio of R2/(R1+R2). Therefore, when R1 = R2 the output voltage will be half the value of the input voltage. Likewise, any value of R2 greater or less than R1 will result in a proportional change to the output voltage. Consider the circuit below.

We now know that a capacitor’s reactance, X_{c} (its complex impedance) value changes with respect to the applied frequency. If we now changed resistor R2 above for a capacitor, the voltage drop across the two components would change as the frequency changed because the reactance of the capacitor affects its impedance.

The impedance of resistor R1 does not change with frequency. Resistors are of fixed values and are unaffected by frequency change. Then the voltage across resistor R1 and therefore the output voltage is determined by the capacitive reactance of the capacitor at a given frequency. This then results in a frequency-dependent RC voltage divider circuit. With this idea in mind, passive **Low Pass Filters** and **High Pass Filters** can be constructed by replacing one of the voltage divider resistors with a suitable capacitor as shown.

The property of **Capacitive Reactance**, makes the capacitor ideal for use in AC filter circuits or in DC power supply smoothing circuits to reduce the effects of any unwanted Ripple Voltage as the capacitor applies an short circuit signal path to any unwanted frequency signals on the output terminals.

So, we can summarize the behavior of a capacitor in a variable frequency circuit as being a sort of frequency-controlled resistor that has a high capacitive reactance value (open circuit condition) at very low frequencies and low capacitive reactance value (short circuit condition) at very high frequencies as shown in the graph above.

It is important to remember these two conditions and in our next tutorial about the Passive Low Pass Filter, we will look at the use of **Capacitive Reactance** to block any unwanted high-frequency signals while allowing only low-frequency signals to pass.

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]]>The post Capacitor Characteristics first appeared on The Amazing World of Electronics.

The post Capacitor Characteristics appeared first on The Amazing World of Electronics.

]]>There are a bewildering array of capacitor characteristics and specifications associated with the humble capacitor and reading the information printed onto the body of a capacitor can sometimes be difficult to understand especially when colours or numeric codes are used.

Each family or type of capacitor uses its own unique set of capacitor characteristics and identification system with some systems being easy to understand, and others that use misleading letters, colours or symbols.

The best way to figure out which capacitor characteristics the label means is to first figure out what type of family the capacitor belongs to whether it is ceramic, film, plastic or electrolytic and from that it may be easier to identify the particular capacitor characteristics.

Even though two capacitors may have exactly the same capacitance value, they may have different voltage ratings. If a smaller rated voltage capacitor is substituted in place of a higher rated voltage capacitor, the increased voltage may damage the smaller capacitor.

Also we remember from the last tutorial that with a polarised electrolytic capacitor, the positive lead must go to the positive connection and the negative lead to the negative connection otherwise it may again become damaged. So it is always better to substitute an old or damaged capacitor with the same type as the specified one. An example of capacitor markings is given below.

Capacitor Characteristics

The capacitor, as with any other electronic component, comes defined by a series of characteristics. These **Capacitor Characteristics** can always be found in the data sheets that the capacitor manufacturer provides to us so here are just a few of the more important ones.

The nominal value of the **Capacitance**, C of a capacitor is the most important of all capacitor characteristics. This value measured in pico-Farads (pF), nano-Farads (nF) or micro-Farads (μF) and is marked onto the body of the capacitor as numbers, letters or coloured bands.

The capacitance of a capacitor can change value with the circuit frequency (Hz) y with the ambient temperature. Smaller ceramic capacitors can have a nominal value as low as one pico-Farad, ( 1pF ) while larger electrolytic’s can have a nominal capacitance value of up to one Farad, ( 1F ).

All capacitors have a tolerance rating that can range from -20% to as high as +80% for aluminium electrolytic’s affecting its actual or real value. The choice of capacitance is determined by the circuit configuration but the value read on the side of a capacitor may not necessarily be its actual value.

The **Working Voltage** is another important capacitor characteristic that defines the maximum continuous voltage either DC or AC that can be applied to the capacitor without failure during its working life. Generally, the working voltage printed onto the side of a capacitors body refers to its DC working voltage, (WVDC).

DC and AC voltage values are usually not the same for a capacitor as the AC voltage value refers to the r.m.s. value and NOT the maximum or peak value which is 1.414 times greater. Also, the specified DC working voltage is valid within a certain temperature range, normally -30°C to +70°C.

Any DC voltage in excess of its working voltage or an excessive AC ripple current may cause failure. It follows therefore, that a capacitor will have a longer working life if operated in a cool environment and within its rated voltage. Common working DC voltages are 10V, 16V, 25V, 35V, 50V, 63V, 100V, 160V, 250V, 400V and 1000V and are printed onto the body of the capacitor.

As with resistors, capacitors also have a **Tolerance** rating expressed as a plus-or-minus value either in picofarad’s (±pF) for low value capacitors generally less than 100pF or as a percentage (±%) for higher value capacitors generally higher than 100pF.

The tolerance value is the extent to which the actual capacitance is allowed to vary from its nominal value and can range anywhere from -20% to +80%. Thus a 100µF capacitor with a ±20% tolerance could legitimately vary from 80μF to 120μF and still remain within tolerance.

Capacitors are rated according to how near to their actual values they are compared to the rated nominal capacitance with coloured bands or letters used to indicated their actual tolerance. The most common tolerance variation for capacitors is 5% or 10% but some plastic capacitors are rated as low as ±1%.

The dielectric used inside the capacitor to separate the conductive plates is not a perfect insulator resulting in a very small current flowing or “leaking” through the dielectric due to the influence of the powerful electric fields built up by the charge on the plates when applied to a constant supply voltage.

This small DC current flow in the region of nano-amps (nA) is called the capacitors **Leakage Current**. Leakage current is a result of electrons physically making their way through the dielectric medium, around its edges or across its leads and which will over time fully discharging the capacitor if the supply voltage is removed.

When the leakage is very low such as in film or foil type capacitors it is generally referred to as “insulation resistance” ( R_{p} ) and can be expressed as a high value resistance in parallel with the capacitor as shown. When the leakage current is high as in electrolytic’s it is referred to as a “leakage current” as electrons flow directly through the electrolyte.

Capacitor leakage current is an important parameter in amplifier coupling circuits or in power supply circuits, with the best choices for coupling and/or storage applications being Teflon and the other plastic capacitor types (polypropylene, polystyrene, etc) because the lower the dielectric constant, the higher the insulation resistance.

Electrolytic-type capacitors (tantalum and aluminium) on the other hand may have very high capacitances, but they also have very high leakage currents (typically of the order of about 5-20 μA per μF) due to their poor isolation resistance, and are therefore not suited for storage or coupling applications. Also, the flow of leakage current for aluminium electrolytic’s increases with temperature.

Changes in temperature around the capacitor affect the value of the capacitance because of changes in the dielectric properties. If the air or surrounding temperature becomes to hot or to cold the capacitance value of the capacitor may change so much as to affect the correct operation of the circuit. The normal working range for most capacitors is -30^{o}C to +125^{o}C with nominal voltage ratings given for a **Working Temperature** of no more than +70^{o}C especially for the plastic capacitor types.

Generally for electrolytic capacitors and especially aluminium electrolytic capacitor, at high temperatures (over +85^{o}C the liquids within the electrolyte can be lost to evaporation, and the body of the capacitor (especially the small sizes) may become deformed due to the internal pressure and leak outright. Also, electrolytic capacitors can not be used at low temperatures, below about -10^{o}C, as the electrolyte jelly freezes.

The **Temperature Coefficient** of a capacitor is the maximum change in its capacitance over a specified temperature range. The temperature coefficient of a capacitor is generally expressed linearly as parts per million per degree centigrade (PPM/^{o}C), or as a percent change over a particular range of temperatures. Some capacitors are non linear (Class 2 capacitors) and increase their value as the temperature rises giving them a temperature coefficient that is expressed as a positive “P”.

Some capacitors decrease their value as the temperature rises giving them a temperature coefficient that is expressed as a negative “N”. For example “P100” is +100 ppm/^{o}C or “N200”, which is -200 ppm/^{o}C etc. However, some capacitors do not change their value and remain constant over a certain temperature range, such capacitors have a zero temperature coefficient or “NPO”. These types of capacitors such as Mica or Polyester are generally referred to as Class 1 capacitors.

Most capacitors, especially electrolytic’s lose their capacitance when they get hot but temperature compensating capacitors are available in the range of at least P1000 through to N5000 (+1000 ppm/^{o}C through to -5000 ppm/^{o}C). It is also possible to connect a capacitor with a positive temperature coefficient in series or parallel with a capacitor having a negative temperature coefficient the net result being that the two opposite effects will cancel each other out over a certain range of temperatures. Another useful application of temperature coefficient capacitors is to use them to cancel out the effect of temperature on other components within a circuit, such as inductors or resistors etc.

Capacitor **Polarization** generally refers to the electrolytic type capacitors but mainly the Aluminium Electrolytic’s, with regards to their electrical connection. The majority of electrolytic capacitors are polarized types, that is the voltage connected to the capacitor terminals must have the correct polarity, i.e. positive to positive and negative to negative.

Incorrect polarization can cause the oxide layer inside the capacitor to break down resulting in very large currents flowing through the device resulting in destruction as we have mentioned earlier.

The majority of electrolytic capacitors have their negative, -ve terminal clearly marked with either a black stripe, band, arrows or chevrons down one side of their body as shown, to prevent any incorrect connection to the DC supply.

Some larger electrolytic’s have their metal can or body connected to the negative terminal but high voltage types have their metal can insulated with the electrodes being brought out to separate spade or screw terminals for safety.

Also, when using aluminium electrolytic’s in power supply smoothing circuits care should be taken to prevent the sum of the peak DC voltage and AC ripple voltage from becoming a “reverse voltage”.

The **Equivalent Series Resistance** or **ESR**, of a capacitor, is the AC impedance of the capacitor when used at high frequencies and includes the resistance of the dielectric material, the DC resistance of the terminal leads, the DC resistance of the connections to the dielectric, and the capacitor plate resistance all measured at a particular frequency and temperature.

ESR Model

In some ways, ESR is the opposite of the insulation resistance which is presented as a pure resistance (no capacitive or inductive reactance) in parallel with the capacitor. An ideal capacitor would have only capacitance but ESR is presented as a pure resistance (less than 0.1Ω) in series with the capacitor (hence the name Equivalent Series Resistance), and which is frequency dependent making it a “DYNAMIC” quantity.

As ESR defines the energy losses of the “equivalent” series resistance of a capacitor it must therefore determine the capacitor’s overall I^{2}R heating losses especially when used in power and switching circuits.

Capacitors with a relatively high ESR have less ability to pass current to and from its plates to the external circuit because of their longer charging and discharging RC time constant. The ESR of electrolytic capacitors increases over time as their electrolyte dries out. Capacitors with very low ESR ratings are available and are best suited when using the capacitor as a filter.

As a final note, capacitors with small capacitance’s (less than 0.01μF) generally do not pose much danger to humans. However, when their capacitance’s start to exceed 0.1μF, touching the capacitor leads can be a shocking experience.

Capacitors have the ability to store an electrical charge in the form of a voltage across themselves even when there is no circuit current flowing, giving them a sort of memory with large electrolytic type reservoir capacitors found in television sets, photo flashes and capacitor banks potentially storing a lethal charge.

As a general rule of thumb, never touch the leads of large value capacitors once the power supply is removed. If you are unsure about their condition or the safe handling of these large capacitors, seek help or expert advice before handling them.

We have listed here only a few of the many capacitor characteristics available to both identify and define its operating conditions and in the next tutorial in our section about Capacitors, we look at how capacitors store electrical charge on their plates and use it to calculate their capacitance value.

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]]>The post Difference between motor and generator first appeared on The Amazing World of Electronics.

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]]>Actually, it’s the alternator which takes every necessary step of delivering power. Then again, an engine is a gadget which is utilized for siphoning water. Be that as it may, an engine can be utilized for some different uses and applications.

Only for purpose of observing, let’s get straight to the point by and by that the expression “generator” is a more extensive term and for the setting of the current article it is really the working of an alternator that we are alluding to when we utilize the expression “Generator”.

Additionally to be noted before we proceed to comprehend the distinction between a generator and an engine is the way that engines and generators are accessible in both AC/DC variations. We would remember this reality while proceeding with the article.

The basic premise of construction for both a generator and engine is Faraday’s law of Induction. (Faraday’s Law of Induction: The actuated electromotive power in any shut circuit is equivalent to the negative of the time rate of progress of the attractive transition encased by the circuit. Source: Wikipedia).

Generators and motors both have current conveying circles which are turned into an attractive field. The circles are folded over an armature. An Armature is comprised of iron center henceforth here the attractive field turns out to be really solid. The bearing of the current in the circles is then turned around bringing about development. This movement makes what is called EMF or electromotive power. Thus changing over one type of vitality into another. For this situation mechanical vitality to electrical and the other way around.

**Mechanical vitality is used to cause movement in the loops.****EMF produced is sine wave shifting with time.****The course of the current delivered is represented by fleming’s correct hand rule****A shaft and rotor system is utilized which is driven by mechanical power.****Armature winding is the point from where the electric flow is emitted.****A generator attributable to its operational structure needs more maintenance.**

**Electrical vitality is used to cause the movement in circles.****Induction is utilized for this situation.****The heading of the current created is administered by Fleming’s left-hand rule.****Here the mechanical power is produced by the development of the pole because of associations between the field and the armature.****Here the power is provided to the armature winding, which results in the task of the engine.****A motor requires insignificant upkeep.**

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]]>The post Solar Power Plant – Main Components, Working, Advantages, and Disadvantages first appeared on The Amazing World of Electronics.

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]]>Tesla has stepped up with regards to control up the Kauai island of Hawaii through a sunlight-based power plant as it were. Tesla is giving its modern battery packs, to store the vitality of sun to be utilized during the evening. They are guaranteeing that they can illuminate the whole island without daylight for up to 3 days. Also, gets energized back in only 7 hours of daylight, isn’t that astonishing!

Proficient generation of intensity from daylight is the main theme of research all around the world. Allows simply make sense of the stuff to change over daylight into power.

Silicon is a much-realized semiconductor having properties of the two metals and non-metals. To make a sun-oriented board, this silicon is doped by a pentavalent polluting influence changing over silicon into positive kind silicon otherwise called p-type silicon. What’s more, also another part is changed over into negative or n-type silicon. As the name proposes p-type have an abundance of gaps (positive charge) in it and n-type has unreasonable electrons. At that point these two are consolidated together one over the other up to the nuclear dimension. Because of their contact and having inverse charge electrons spill out of n-type to p-type and gaps make a trip from p-type to n-type in this way making a thin potential obstruction between them. The current so produced from this development of charges is named as dispersion current. In any case, we have to see one more thing that is because of this potential boundary, offering to ascend to an electric field which streams from the positive charge close n-type and negative charge close p-type intersection (the territory where potential is created or meeting region of p and n type). Because of this electric field electrons from p-type begins streaming towards n-type and openings from n-type towards p-type offering ascend to a flow called float flow. At first the dissemination current is more than the float current however as potential contrast increments because of dispersion it all the while builds the float current. Current quits streaming when float current ends up equivalent to dissemination current.

Daylight goes to earth as little vitality particles called photons. This photon strike the p-type area and exchange its vitality to opening and electron combine along these lines energizing the electron and it makes tracks in an opposite direction from gap. The electric field we have because of potential distinction at p-n intersection makes its electron to make a trip to n-type district along these lines making the flow stream.

In any case, there more to know, to make this electric field sufficient so it must venture out to n-type locale and not recombine with the opening it has been isolated from. To make this electric field solid the n-type and p-type areas are associated with negative and positive terminals of battery, this procedure is known as invert inclination condition. Doing this builds the likelihood of electron voyaging up and down the best approach to n-type area once isolated from a gap. Along these lines expanding the productivity of a sunlight based board.

The working standard is that we utilize the vitality of photons to get the float current streaming in the circuit utilizing switched inclination p-n intersection diode (p-type and n-type silicon blend).

sun based power plant primary parts

**1. Solar Panels**

It is the core of the sun based power plant. Sun powered boards comprises various sun based cells. We have around 35 sun powered cells in a single board. The vitality created by each sun powered cell is little, yet consolidating the vitality of 35 of them we have enough vitality to charge a 12 volt battery.

**2. Solar Cells**

It is the vitality producing unit, made up of p-type and n-type silicon semiconductor. It’s the core of sun based power plant.

**3. Battery**

Batteries are utilized to create the power back or store the abundance vitality delivered amid day, to be provided amid night.

**4. D.C. to A.C. Converter (Inverter)**

Sun oriented boards deliver coordinate current which is required to be changed over into exchanging current to be provided to homes or power framework.

As daylight falls over a sun oriented cells, a substantial number of photons strike the p-type area of silicon. Electron and opening pair will get isolated in the wake of retaining the vitality of photon. The electron goes from p-type district to n-type area because of the activity of electric field at p-n intersection. Further the diode is switched one-sided to expand this electric field. So this present begins streaming in the circuit for individual sun powered cell. We consolidate the current of all the sun based cells of a sun based board, to get a critical yield.

**Working of sunlight based power plant**

Sun based power plant have an extensive number of sun oriented boards associated with one another to get a huge voltage yield. The electrical vitality originating from the joined exertion of sun powered boards is put away in the Lithium particle batteries to be provided during the evening, when there is no daylight.

**Energy Storage**

Capacity of the vitality created by the sun based boards is an essential issue. In some cases the unused vitality created amid daytime is utilized to siphon water to some stature, with the goal that it could be utilized to produce power utilizing its potential vitality when required or for the most part during the evening time.

For current being Tesla is giving its mechanical vitality pack to store vitality and as of now it is illuminating a whole island. Tesla has likewise made an offer to Australia that it could give its battery pack to crisis power outages.

The expense of assembling of sun based boards has diminished quickly in most recent couple of years, same is said to be valid with the mechanical vitality pack (Lithium particle batteries), as the creation and request expands their expense will diminish in coming couple of years.

Most perfect and sustainable wellspring of vitality.

It is accessible in wealth and unending.

It gives power requiring little to no effort, as fuel is free.

With new research in this area we currently have a decent power stockpiling arrangement.

Remembering the contamination and cost of petroleum product, it’s turning into the most solid wellspring of clean vitality.

It requires a great deal of land to be caught until the end of time.

Introductory expense of establishment is excessively high.

The vitality stockpiling alternatives are not effective and also expensive if proficient.

Power creation is very low when contrasted with atomic or different assets to deliver control.

There is an issue in the event that it is overcast for few days.

Their generation causes contamination.

Sun oriented power plant is controlling urban areas in most effective way.

Sunlight based boards could be utilized to create power separately for each house particularly in remote zones.

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]]>The post Difference Between Contactor and Relay first appeared on The Amazing World of Electronics.

The post Difference Between Contactor and Relay appeared first on The Amazing World of Electronics.

]]>The course book definitions are sufficiently comparable it doesn’t generally encourage us. Both play out a similar undertaking of exchanging a circuit! So What truly separates the two gadgets?

Relays are classified as carrying loads of 10A or less, while a contactor would be utilized for burdens more noteworthy than 10A, yet this definition, while straightforward, gives a fragmented picture. It forgets any physical contrasts, or benchmarks.

Contactors are only intended to work with regularly open (Form A) contacts. Relays then again can and frequently are both Normally Open as well as Normally Closed relying upon the coveted capacity. This implies with a contactor, when it is de-empowered there is (ordinarily) no association. With a relay, there could be.

To confound things a bit, contactors are regularly fitted with assistant contacts which can be NO or NC anyway these are utilized to play out extra capacities related to the control of the contactor.

For instance, the contactor may transmit capacity to the engine, while the assistant contact is in the control circuit of the engine starter and generally used to turn on a pilot light showing the engine is working.

Since contactors are ordinarily conveying high loads, they regularly contain extra wellbeing highlights like spring-stacked contacts to help guarantee the circuit is broken when de-invigorated. This is critical on the grounds that in high load circumstances contacts can weld themselves together.

This can make the perilous circumstance of a circuit being stimulated when it should be off. Spring-stacked contacts help to diminish this possibility and guarantee all circuits are broken in the meantime. Since relays are normally for lower control, spring-stacked contacts are considerably less normal.

Another wellbeing highlight regularly incorporated into contactors, because of the high loads they commonly convey, is curve concealment. Attractive curve concealment works by expanding the way a circular segment would need to travel.

On the off chance that this separation is expanded more distant than the vitality can survive, the bend is smothered. Since transfers aren’t intended for high loads, arcing is to a lesser degree a worry and curve concealment is substantially less regular on relays.

Finally, contactors are generally associated with over-burdens that will intrude on the circuit if the current surpasses a set edge for a chosen era, as a rule, 10-,30seconds. This is to help ensure the hardware downstream of the contactor from harm because of current. Over-burdens are considerably less basic on Relays.

Contactors are normally worked for and utilized in 3-stage applications where a hand-off is all the more generally utilized in single stage applications.

A contactor combines 2 posts, without a typical circuit between them, while a relay has a typical contact that associates with an unbiased position. Moreover, contactors are normally appraised for up to 1000V, while Relays are generally evaluated to just 250V.

While choosing between the two, some exceptionally broad principles you can pursue to help

**10A or less current****Up to 250VAC****1 stage**

**9A or more current****Up to 1000VAC****1 or 3 stage**

Continuously counsel the particulars of the things you are thinking about utilizing and examine with an authorized circuit repairman. This is for educational purposes as it were.

Practically speaking, you ought to take a gander at the capacity also. For any circuit where an over-burden condition could happen, and an inability to de-stimulate the circuit will make a perilous condition, at that point a contactor is likely the best decision in light of the extra security highlights.

For exchanging low power, when the extra security highlights of a contactor are redundant, a transfer is ordinarily the more efficient decision.

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]]>The post The Difference Between MCB & MCCB first appeared on The Amazing World of Electronics.

The post The Difference Between MCB & MCCB appeared first on The Amazing World of Electronics.

]]>The Miniature Circuit Breaker is an electromechanical gadget which, consequently, turn off the circuit at whatever point the irregular condition happens. It effectively faculties the overcurrent caused by the short out.

The working rule of the smaller than usual circuit is extremely straightforward. Their fundamental capacity is to shield the gear from overcurrent. It has two gets in touch with one is versatile, and the other one is settled. At the point when the current increments from as far as possible, their versatile contacts are detached from the settled contacts which make the circuit open and separates them from the fundamental supply.

The MCCB remains for Moulded Case Circuit Breaker. It is a shielding gadget which shields the circuit from over-burdening. It is fundamentally utilized in a place where flexible stumbling requires. The current rating is up to 2500 amps. It is fundamentally utilized for high current applications. The MCCB has a physically worked switch for stumbling the circuit.

The MCCB has two courses of action. One of them for the oven temperature and the other for the overcurrent. It comprises bimetallic contact which grows and contracts when the temperature of the MCCB changes.

Amid the ordinary working conditions, the contact enables the current to course through the circuit. In any case, as the current ascents past the predefined esteem, at that point, their contacts will warm and grow until the point when the contacts are open. Accordingly, disengaged the circuit from the principal supply and shields the gear from harm.

**The MCB is a kind of switch which shields the framework from over-burden current while the MCCB shields the framework from over temperature and short out current.****The stumbling circuit of the MCB is settled while in MCCB it is versatile.****Note: The stumbling circuit kill on and the stream of electrical flow. At the point when overcurrent moves through the MCB and MCCB it stops the switch and thus shields the hardware from harm.****The MCB has single, two, or three-shaft variant, though the MCCB has single, two three or four post-adaptation.****Note: Pole in MCB is the number of stages utilizes by the electrical switch for the exchanging and assurance.****The intruding on a current of the MCB is the 1800amps, and for MCCB it is 10k – 200 k.****Note: The intruding on current is the most extreme current that the electrical switch can hinder without being disturbed.****The remote on/off isn’t conceivable in MCB while it is conceivable in MCCB by the utilization of shunt wire.****The rating current of MCB is 100 amps through the rating current of MCCB is 10 – 200 amps.****Note: The evaluated current is the most extreme current that the electrical switch should draw.****The MCB is for the most part utilized in a low current circuit while MCCB is utilized for the overwhelming current circuit.****The MCCB is utilized for the residential reason, and MCCB is utilized in substantial ventures.****The MCB and MCCB both are the thermomagnetic gadgets and are arranged under low voltages breaker..**

If you have any questions do not hesitate to leave a comment.

The post The Difference Between MCB & MCCB first appeared on The Amazing World of Electronics.

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]]>The post Air Circuit Breaker (ACB) first appeared on The Amazing World of Electronics.

The post Air Circuit Breaker (ACB) appeared first on The Amazing World of Electronics.

]]>This circuit breaker will work noticeably all around; the extinguishing medium is an Arc at the climatic weight. In a considerable lot of the nations air electrical switch is supplanted by oil This circuit breaker. About oil This circuit breaker we will examine later in the article. In this way, the significance of ACB is as yet best decision to utilize an Air This circuit breaker up to 15KV. This is on the grounds that; oil This circuit breaker may burst into flames when utilized at 15V

**Plain air circuit breaker****Air impact Circuit Breaker**

Plain air circuit breaker is additionally called as Cross-Blast Circuit Breaker. In this, the circuit breaker is fitted with a load which essentially encompasses the contacts. This chamber is known as circular segment chute.

This arc is made to drive in it. In accomplishing the cooling of the air circuit breaker a curve chute will help. From the unmanageable material, a bend chute is made. The inner dividers of bend chute are molded so that circular segment isn’t constrained into closeness. It will crash into the winding channel anticipated on a circular segment chute divider.

The arc chute will have numerous little compartments and has numerous divisions which are metallic isolated plates. Here every one of little compartments carries on as a smaller than normal bend chute and metallic detachment plate acts like circular segment splitters. All circular segment voltages will be higher than the framework voltage when the curve will part into a progression of bends. It is best for low voltage application.

Air blast circuit breakers are utilized for framework voltage of 245 KV, 420 KV and furthermore even more. Air impact circuit breakers are of two kinds:

**Axial blast breaker****Axial blast with sliding moving contact.**

n the axial blaster breaker the moving contact of the pivotal impact breaker will be in contact. The spout opening is a settled to the contact of a breaker at an ordinary shut condition. A blame happens when high weight is brought into the chamber. Voltage is adequate to support high-weight air when moved through spout opening.

**It is utilized where visit task is required due to lesser circular segment vitality.****It is without chance from the fire****small in size.****It requires less support.****Circular segment extinguishing is substantially quicker****The speed of the circuit breaker is substantially higher.****The time term of the circular segment is the same for all estimations of current.**

**It requires extra support.****The air has moderately bring down circular segment quenching properties****It contains high limit air blower.****From the air pipe intersection, there might be a possibility of pneumatic force spillage****There is the possibility of a high rate ascent of re-striking current and voltage hacking.**

**It is utilized for insurance of plants, electrical machines, transformers, capacitors, and generators****Air electrical switch is additionally utilized in the Electricity sharing framework and GND about 15Kv****Used in Low and in addition High Currents and voltage applications.**

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]]>The post Phase Splitter first appeared on The Amazing World of Electronics.

The post Phase Splitter appeared first on The Amazing World of Electronics.

]]>The **Phase Splitter** is another type of bipolar junction transistor, (BJT) configuration where a single sinusoidal input signal is split into two separate outputs that differ in phase from each other by 180 electrical degrees.

The input signal of a transistor phase splitter is applied to the base terminal with one output signal taken from the collector terminal and the second output signal taken from the emitter terminal. Thus the *transistor phase splitter* is a dual output amplifier producing complementary outputs from its collector and emitter terminals which are out-of-phase by 180^{o}.

A single-transistor phase splitter circuit is nothing new as we have seen its basic building blocks in previous tutorials. the phase splitter, phase-inverter circuit combines the characteristics of a common emitter amplifier with that of a common collector amplifier. As with the CE amplifier and CC amplifier circuits, the phase splitter circuit is forward biased to operated as a linear class-A amplifier to reduce output signal distortion.

But first let’s refresh our knowledge of the common emitter (CE) amplifier circuit and the common collector (CC) amplifier circuit configurations.

The *common emitter* circuit with voltage divider biasing is the most widely used linear amplifier configuration as its easy to bias and understand.

The input signal is applied to the base terminal, and the output signal is taken from across the load resistance, R_{L} connected between the collector and the positive supply rail, V_{CC} as shown. Thus the emitter is common to both the input and output circuits.

As well as providing voltage amplification determined by the ratio of: R_{L}/R_{E}, the main characteristic of the Common Emitter (CE) configuration is that it is an inverting amplifier producing a phase reversal of 180^{o} between the input and the output signals.

To operate as a class-A amplifier the circuit is biased so that the quiescent current fed into the base, I_{B} positions the collector terminal voltage at approximately half the supply voltage value. The ratio of resistors R_{1} and R_{2} is chosen so that the transistor is correctly biased providing maximum undistorted output signal.

The *common collector amplifier* uses the single transistor in the common collector configuration with the collector being common to both the input and output circuits. The input signal is applied to the transistors base terminal and the output is taken from the emitter terminal as shown.

As the output signal is taken from across the emitter resistor, R_{E} no collector resistor is used so the collector terminal is connected directly to the supply rail, V_{CC}. This type of amplifier configuration is also known as a voltage follower or more commonly an *emitter follower* as the output signal follows the input signal.

The main characteristic of the Common Collector (CC) configuration is that it is a non-inverting amplifier as the input signal passes directly through the base-emitter junction to the output. Hence the output is “in-phase” with the input. Due to this it has a voltage gain of slightly less than one (unity).

As with the previous common emitter configuration, the transistor of the common collector amplifier is biased using a voltage divider network to half the supply voltage to give good stabilisation for its DC operating conditions.

If we combine the configuration of the common emitter amplifier with that of the common collector amplifier and take the outputs from both the collector and the emitter terminals at the same time, we can create a transistor circuit that produces two output signals which are equal in magnitude but inverted with respect to each other.

The **Phase Splitter** uses a single transistor to produce inverting and non-inverting outputs as shown.

We said previously that the voltage gain of the common emitter amplifier is the ratio of R_{L} to R_{E}, that is -R_{L}/R_{E} (the minus sign indicates an inverting amplifier). If we were to make these two resistors equal in value (R_{L} = R_{E}), then the voltage gain of the common emitter stage would be equal to -1 or unity.

As the common collector, emitter follower amplifier circuit naturally has a non-inverting voltage gain of near unity (+1), the two output signals, one from the collector and one from the emitter, will be equal in amplitude but 180^{o} out-of-phase. This makes the unity gain transistor phase splitter circuit very useful to provide complementary or anti-phase inputs to another amplifier stage, such as a class-B push-pull power amplifier.

For proper operation, the voltage divider network connected across the supply rail and ground must be chosen to produce the correct stabilising of the DC conditions for the output voltage swing from both the collector and emitter terminals producing symmetrical outputs.

A single transistor phase splitter circuit is required to drive a push-pull power amplifier stage. Design a suitable circuit if the supply voltage is 9 volts, the Beta value of the NPN 2N3904 transistor used is 100, and the quiescent collector current is 1mA and the input signal has an amplitude of 1V peak.

To prevent distortion of the emitter terminal output signal, the d.c. biasing voltage of the emitter terminal must be greater than the maximum value of the input signal, in this case 1 volt peak. If we set the DC quiescent emitter terminal voltage at twice the input value to ensure a distortion free output swing, the V_{E} will equal 2 volts.

As V_{E} is set at 2 volts and the emitter current, which is also the collector quiescent current, flowing through it is given as 1mA, the value of emitter resistance, R_{E} is calculated as:

For the voltage gain of the common emitter side of the phase splitter circuit to equal -1 (unity), the collector load resistance R_{L} must be equal to R_{E}. That is R_{L} = R_{E} = 2kΩ. Thus the voltage dropped across the collector load resistance is calculated as:

Applying Kirchhoff’s Voltage Law, V_{CC} – V_{C} – V_{CE} – V_{E} = 0. Thus 9 – 2 – 5 – 2 = 0. We would expect to see this because as R_{L} = R_{E} and the current flowing through both resistors is approximately the same value, so the I*R voltage drop across each resistor would therefore be the same at 2.0 volts.

This means then that the DC bias voltage for the non-inverting output (emitter terminal) is 2.0 volts (0 + 2), and the DC bias voltage for the inverting output (collector terminal) is 7.0 volts (9 – 2). In other words, the DC quiescent output voltages of the two outputs are at different values.

The transistors DC current gain, Beta is given as being 100. As for a common emitter amplifier, Beta is the ratio of collector current to base current, that is; β = I_{C}/I_{B}, the value of the base biasing current required is calculated as:

Then for a DC current gain of 100, the quiescent base current, I_{B(Q)} is given as 10uA. It is common practice that the value of the quiescent current flowing through the base-to-ground resistor of the voltage divider network is ten times (x10) greater than the base current. Thus the current flowing through R_{2} will be 10*I_{B} = 10*10uA = 100uA.

The base voltage, V_{B} is equal to the emitter voltage V_{E} plus the 0.7 volt forward voltage drop of the base-emitter pn-junction, that is: 2.0 + 0.7 = 2.7 volts. Therefore the value of R_{2} is calculated as:

As there is 100uA flowing through R_{2} and 10uA flowing into the transistors base terminal, it must therefore follow that there is 110uA (100uA + 10uA) flowing through the top resistor, R_{1} of the voltage divider network. If the supply voltage is 9 volts and the transistors base voltage is 2.7 volts. The value of resistor R_{1} is calculated as:

Thus the voltage divider network used for the DC biasing of the splitter circuit consists of R_{1} = 57.3kΩ and R_{2} = 27kΩ.

Putting the above calculated values together gives us the *single transistor phase splitter circuit* of:

As a single transistor phase splitter circuit produces two output versions of the input signal, a non-inverted version identical in phase to the input signal, and an 180^{o} phase inverted version of the input signal with both outputs having a similar amplitude. This would make the phase splitter circuit ideal for use in driving *push-pull* or *totem-pole* configured outputs for amplification or DC motor control.

Consider the circuit below.

As the complementary outputs are taken from the collector and the emitter of the transistor Q1, when the upper transistor Q2 is forward biased and conducting on the negative half-cycle (due to the inversion), the lower transistor Q3 is OFF, so the negative half of the waveform is passed to the load resistor, R_{L}.

On the positive half-cycle of the input waveform, the lower transistor Q3 is forward biased and conducting, while the upper transistor, Q2 is OFF, so the positive half of the waveform is passed to the load resistor, R_{L}.

Thus at any one time only one of the output transistors, Q2 or Q3 is sufficiently forward biased and conducting only one half of the input signal waveform. The two output transistors alternate conduction from one to the other as determined by Q1, with both halves of the input signal being combined together to produce an inverted output waveform across R_{L}. Load resistor R_{L} has a DC biasing voltage centered around the difference between V_{C} and V_{E}. Resistor R_{5} is used to limit the maximum current flow.

We have seen here in this tutorial that by combining a common emitter circuit with a common collector circuit, we can create another type of single transistor circuit which is not really a CE amplifier nor a CC amplifier but instead a phase splitter circuit that produces two voltages of the same amplitude but of opposite phase.

Sometimes it is necessary to have two signals which are both equal in amplitude but are 180^{o} out-of-phase with each other and there are different ways to create a dual output phase splitter circuit, including the use of differential amplifiers and operational amplifiers. But the single transistor phase splitter circuit configuration is the easiest to build and understand.

The single transistor phase splitter circuit is biased to operate as a class A amplifier with the two complementary (inverted and non-inverted) outputs taken from the collector and the emitter terminals respectively of the transistor. To operate correctly the gain of each output must be set to 1, unity gain.

Single transistor **phase splitter circuits** are useful for driving Class-B push-pull amplifiers, center-tapped transformer for inverters or totem-pole outputs for motor control, as when one transistor is ON the other transistor is OFF.

The post Phase Splitter first appeared on The Amazing World of Electronics.

The post Phase Splitter appeared first on The Amazing World of Electronics.

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