• Definition of Active Band Pass Filter
• Passband & Stopband
• How does an active bandpass filter work
• Types of the active bandpass filter
• Frequency response & time response
• The transfer function of active BPF
• Applications of active BPF
• Advantages
• Comparison between Active Band Pass Filter & Active Band Stop Filter
• Short note on All-Pass Filter

Definition of bandpass filter:

“A Band Pass Filter (BPF) is an electronic filter or device which passes frequencies within a certain range and rejects or attenuates frequency outside the particular range.”

Now an Active Band Pass Filter is a filter, consists of active components and has a passband between two cut-off frequencies, f_ce (lower cut-off frequency), and f_cu (upper cut-off frequency) such that f_cu>f_ce. All the other frequencies outside the passband are attenuated.

Passband – “Pass-band is the particular range of frequencies which a filter pass through inside it.”

Stopband – “A filter always carries filters within a given band, and rejects the frequencies which are below the given range. This particular range is known as a Stopband”.

Working principle of an Active Band Pass Filter:

Bandwidth:

               In an active bandpass filter, the range of frequency between two cut-off frequencies, f_ce, and f_cu, is called the bandwidth.

                                          BW=(f_cu-f_cl)

The bandwidth of this filter is not mainly centered on the resonant frequency, i.e., f_r.

We can easily calculate the resonant frequency(f_r) if we know the value of f_cu and f_cl

If the bandwidth and ‘f_r‘ are known, the cut-off frequencies can be obtained from,

                                     f_cu = (f_cl+BW)

There are two types of Band Pass Filter exist, they are –

Wide Band Pass Filter:

A Wide Bandpass filter has a bandwidth, double or fourth, of its resonant frequency.

This filter is made by cascading a low-pass and a high-pass filter circuit.

A wide bandpass filter provides a cut-off frequency of the low pass section, which is greater than that of the high-pass area.

                                               

Characteristics of a wide bandpass filter-

• In a wide bandpass filter, a low pass filter’s cut-off frequency should be ten or more times than the high pass filter’s cut-off frequency present in the circuit.
• Each section of the filter(LPF & HPF) present in wide BPF should have the same passband gain.
• The high pass filter determines the lower cut-off frequency f_cl.
• The low pass filter determines the higher cut-off frequency fcu.
• The gain is always maximum at the resonant frequency, f_r, and equal to the passband gain for both filters.

Frequency Response of an Active Band Pass Filter:

                                                        

Here,

The voltage gain magnitude of the bandpass filter equals the voltage gain magnitudes of the high pass and the low pass filter.

                      

Where,

                     A_FL,A_FH= pass band gain of the low pass and high pass filter,

f= frequency of the input signal(Hz);

f_CL= lower cut-off frequency(Hz);

f_CU= higher cut-off frequency(Hz);

Center Frequency =

• NARROW BAND PASS FILTER: In general, a narrow bandpass filter is made of multiple feedback circuit with a single op-amp.

                                                                                  

Characteristics of a narrow bandpass filter:

• A narrow bandpass filter consists of two different blocks, i.e., two feedback paths; hence, it is known as ‘Multiple Feedback Filter.’
• An inverted op-amp is used here.
• We can change the center frequency without changing the gain or the bandwidth of this filter.

The gain of the filter-

                              

Bandwidth-

Transfer function of Active Band Pass Filter:

What is a Transfer Function?

“Transfer function is a complex number that has both magnitude and phase. In the case of filters, the transfer function helps to introduce a phase difference between input and output.”

A bandpass filter need is made of at least two energy-saving elements, which are capacitor and inductor. So a first-order bandpass filter is not possible. The transfer function of a second- bandpass filter can be derived as;

                          

Where T₁=R₁C₁, T₂=R₂C₂  T₃=R₃C₃

Applications of an Active Band Pass Filter:

1. An active bandpass filter is used in optics like LASER.
2. Bandpass filters are widely used in the audio amplifier circuits.
3. Bandpass filters are used to choose signals with particular bandwidth in the communication system.
4. In audio signal processing, this filter is used.
5. BPF is used to detect signal to noise ratio and sensitivity of a receiver.

Advantage of using a bandpass filter:

An active bandpass mainly controls the narrowband and passbands. It also removes distortion and has a sharp selectivity. Due to excellent electrical performance and mechanical reliability, BPF is used widely is the communication field.

Difference between Band Pass Filter & Band Stop Filter:

A bandpass filter carries frequencies within a given band and attenuates all the other frequencies below the range. In contrast, a band-stop filter does precisely the opposite and attenuates all the frequencies above the given frequency range.

Apart from that, a bandpass filter removes the energies outside of the passband, but a band-stop filter does not remove all the powers outside the passband at all.

What is an All-Pass Filter?

An active all-pass filter passes all frequency components of the input signal without attenuation and provides some phase shifts between the input and output signal.

                                                                   

All pass filter is generally used in digital reverberators. When signals are transmitted over transmission lines from one end to another, they undergo some phase changes. To avoid such phase changes and loss, the all-pass filters are used.

                                                                                      

The capacitor creates an inverting amplifier at high frequencies, which is in a short circuit.

The capacitor is an open circuit when the frequency is low, and it creates a unity gain voltage buffer, i.e., there will be no phase shift.

At the corner frequency ω=1/RC, the circuit generates a 90˚ shift. That implies the output appears to be delayed by a quarter from the input.

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• Definition of an active LPF
• What does an active LPF do?
• Components of an active LPF
• Frequency Response
• Design active LPF
• Frequency scaling
• Transfer Function
• What is a second-order LPF
• The transfer function of second-order active LPF
• Design a second-order active LPF
• Comparison between active low-pass and passive low-pass filter
• Why do we use active LPF
• Advantages of an active LPF
• FAQs

What is an Active Low Pass Filter?

First things first, let’s discuss what a simple Low Pass Filter is-

“Low Pass Filter is a type of filter which mainly passes signals with a frequency lower than the particular cut-off frequency and attenuates all the frequency higher than the cut-off range ”.

Now, an Active Low Pass Filter is made of active components like Op-amp, resistors, and it also carries lower frequency signals with less resistance and has a constant output gain from zero to a cut-off frequency.

Components of Low Pass Active Filter: 

Active filters consist of active components as the name implies such as Operational amplifier, transistors or FET within the circuitry.

An active filter typically consists of amplifiers, capacitors and resistances.

So generally, Low Pass Active Filter is any filter using an Op-amp to improve the performance and predictability in such a low cost.

How does an Active Low Pass Filter work

                               

In the above figure, it’s a commonly used low pass active filter.

Frequency Response of Low Pass Filter:

Active Low Pass Filter Design:

Resistance R =

              F_c = cut-off frequency

              Ω_c = cut-off frequency

              C = capacitance

A cut-off frequency can be varied by multiplying it with RC or C.

Transfer Function of a First Order Active Low Pass Filter:

Differential Equation for the filter –

Second-Order Active LPF:

What is a second-order LPFs?

To build a second-order filter, we usually use an op-amp, and therefore the second-order filter can also be called as a VCVS filter; where VCVS is referred to ‘Voltage Control Voltage Source’ amplifier. We design a second-order filter along with a first-order active RC filter.

As it is a low pass filter, it only allows the lower frequency signals to pass, and it attenuates all the higher frequencies above the specified frequency range.

A second-order low pass filter attenuates the higher frequency signals more precisely. The gain reduces at the rate of 12 dB per octave. In other way it is 40 dB/decade.

                                                                                   

In a second order filter,

When the resistor and capacitor values are different,

When the resistor and capacitor values are same,

Transfer Function of a Second Order Active Low Pass filter:

The Transfer Function is denoted as,

The magnitude of the Transfer function –

Where ω_c is the cut-off frequency.

Frequency-responses of second-order low-pass active filters is given.

                                                                          

Design of a second-order active low pass filter

First, we choose a value of the cut-off frequency, ω_c (or f_c).

Find R,

• Rf comes as –

                              R_f = K(2R) = 3.172 R.

• Find R1 while K = 1.586

Differences between Active Low Pass Filter & Passive Low Pass Filter:

• Active components are effectively costlier, that’s why the active filters are expensive as well, whereas the cost of passive filters is lower due to the presence of the passive components.
• Active Low Pass filter circuit is a complex one, while a passive low pass filter circuit has less complexity.
• To operate an active LPF, we need an external power supply for operating it. But passive filters do not require external power because it drives the energy for its operation from the applied input signal.
• Passive filters contain more components than an active low pass filter; that’s why they are heavier in weight.
• Active LPF is more sensitive during temperature change, but the passive ones show less sensitivity with the growth of temperature.

Why to use Active LPF?

Due to the less complex circuitry and lower price than the other active filters, we use Active LPF in many fields.

Check out them here – Low Pass Filter Applications.

• Low pass filter is used in ‘hiss’ filters.
• These filters are also used in ADCs. They act as anti-aliasing filter in that circuits.
• LPFs are also used to prevent the harmonic  emissions from the RF transmitters.
• These filters find applications in the music systems also. There these filters omits the high-frequency components.

Advantages of an Active Low Pass filter:

• For a transfer function with inductive characteristics, it can achieve satisfactory output with an acceptable range of frequencies.
• The high input impedance and low output impedance of the op-amp make the circuit excellent while cascading.
• Due to better amplification, it provides more gain.

What is 3db frequency in an active low pass filter?

3db is the power level, where the cut-off frequency is at 3dB below than the maximum value, and 3dB is usually half of the maximum power.

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In this article, we will discuss about few basic concept related to active high pass filter and try to answer few questions in following sections and we will try to learn about some important application of active high pass filters with advantage.

• What is an active high pass filter?
• Working Principle of an active HPF
• Time Response & Frequency Response
• Cut-off Frequency of an active HPF
• What is a transfer function for an active HPF
• Design a first order active order HPF
• Second order active HPF
• Transfer Function for second order HPF
• Advantages of active High Pass Filter
• Applications of a HPF
• FAQS

Active high pass filter definition:

An active high pass filter is nothing but a circuit contains an active component such as a transistor, an operational amplifier(op-amp), etc. These components are mainly used for better performance or better amplification.

What are the components of an active high pass filter?

We can make an active high pass filter by adding an op-amp across a passive high pass filter.

To imply simplicity, time effectiveness and due to growing technologies an op-amp designing, generally, an op-amp is used for an Active High Pass Filter design.

In an active high pass filter, the limitation we have is the op-amp bandwidth. It means that the op-amp will pass the frequency according to its gain and the open-loop characteristics of the op-amp.

Circuit Diagram of active high pass filter:

In the above figure, the CR network does the filtering, and the op-amp is connected as a unity-gain follower. The feedback resistor, R_f, is included to minimize the dc off-set.

Here,

The voltage across the resistor R,

Since op-amp gain is infinite, we can therefore derive.

Where

= Passband gain of the high pass filter,

f = Frequency of the input signal (Hz),

= cut-off frequency of the high pass filter (Hz)

    The Gain Magnitude,

And phase angle (in degree),

Working Principle of an active high pass filter:

First-order filters are the simplest form of any filters that contain only one reactive component, i.e., capacitor, as it is also used in passive filters. To transform it into an active filter, an op-amp is used to the output of a passive filter.

Now, the op-amp is used for different configurations. Each configuration has additional attributes to the performance of the filter.

The main thing to be remembered is a first-order filter’s roll-off rate. The roll-off rate is the rate of change in the gain of a filter in its desired stopband. It shows us the steepness in the curve and how fast the growth tends to increase with frequency.

First-order filters have a roll-off rate of 20dB/decade or 6dB/octave.

        Roll Off Rate = -20n dB/decade = -6n dB/octave

Time Response & Frequency Response of an active HPF

To operate a high pass filter, the verification can be done from the gain-magnitude equation as follows:

At very low frequency, i.e., f<f_c,

At f=f_c,

At f>>f_c,

The bandwidth of the active high pass filter shows the value of frequency from which signals are allowed to pass. As an example, if the bandwidth of that high pass filter is given as 50 kHz, that means the only frequencies from 50 kHz to infinity are allowed to pass the range of bandwidth.

The phase angle of the output signal is +450 at the cut-off frequency. The formula to calculate the phase shift of an active high pass filter is

                     Ø= arctan (1/2πfRC)

Active High Pass Filter Transfer Function

The impedance of the capacitor keeps frequently changing, so electronic filters have a frequency-dependent response.

The complex impedance of a capacitor is given as,

Where, s= σ +jω, ω is the angular frequency in radians per second.

The Transfer Function of a circuit can be found using standard circuit analysis techniques such as Ohm’s Law, Kirchoff’s Law, Superposition Theorem, etc.

The form of a T.F is derived from the ratio of Output Voltage to Input Voltage

The standard form of the transfer function is :

Where,

a₁ = Amplitude of signal

ω₀ = Angular cut-off frequency

Cut-off Frequency:

What do we mean by cut-off frequency ?

By cut-off frequency, we define the useful or essential part of a spectrum. It is simply a frequency level above or below a device or filter cannot response or can be operated properly.

The Cut-off frequency for an active high pass filter is the particular frequency at which the load(output) voltage equals 70.7% of the source(input) voltage. The origin or output voltage is more significant than 70.7% of the input or load voltage and vice versa.

The cut-off frequency also indicates the frequencies at which the power of the output path falls to half its maximum value. These half-power points correspond to a fall in the gain of 3dB(0.7071) relative to the maximum dB value.

Filter Designing of Active High Pass Filter:

To construct an active high pass filter, we need to implement the following steps-

A value of the cut-off frequency,

is chosen.

A value of the capacitance C, usually between 0.001 and 0.1µF, is selected.

The value of the resistance R is calculated using the relation,

Now, the values of R₁ and R_f are selected depending on the desired pass-band gain, using the relation,

Second-Order Active High Pass Filter:

What is a second-order filter?

The maximum delay in each sample used in generating each output sample is called the order of that particular filter.

Second-order filters mostly consist of two RC filter, which is connected together to provide a –40dB/decade roll-off rate.

Where DC gain of the amplifier =

The Transfer Function of a second-order active high pass filter can be obtained from the transfer function of the low pass filter by the transformation,

• Substituting s=jω, the transfer function is,

In the above equation, when ωà0, |H(jω)|=0. Thus the low-frequency gain of the filter is zero.

If we compare it with Butterworth filter transfer function, we get

The Frequency response of a second-order active high pass filter is shown in the above diagram. It is noted that the filter has a very sharp roll-off response.

The design procedure for a high pass will be as same as low pass.

The frequency response will be a maximally flat one, i.e., having a very sharp roll-off response.

Advantages of using Active High Pass Filter:

There are so many vital benefits of an active High Pass Filter, some of them are:

• Whenever there is a small signal is present, an active High pass Filter is used to increase the amplification factor, which also increases the amplitude of those small signals.
• Due to very high input impedance, active high pass filters can transfer efficient signals without any loss in any preceding circuit.
• Active filters usually have very low output impedance, which is perfect for transferring efficient signals to its next stage, mostly when they are used in different multistage filters.
• This type of filters gives us smooth frequencies.
• They have a sharp roll-off response.
• Strong broadcasting power to receivers to select desired channel frequency.
• Best for audio processing in any electrical or electronic device.
• Active HPF prevents amplification from DC etc.

Application of Active High Pass Filter:

• To transmit higher frequency in case of video related filters.
• We use HPF as a treble equalizer.
• We often use HPF as a treble boost filter.
• We are changing the frequency depending on different waveforms.
• Active High Pass filters are also used in oscilloscopes.
• In the generator, these filters are used.

 

Frequently Asked Questions

Where are high pass filters used?

      The high pass filters are used in all audio sources to remove unwanted noise that lurks below the important frequencies.

Many unwanted sounds can be hidden by some louder core of a high pitch signal and can be overlooked. We don’t get to hear the rumble due to the limits of hearing as the lowest parts of the spectrums are around 20-40 Hz. High pass filters also eliminate those noises or reduce it that makes them nearly silent.

Can I get the output of a high pass filter as a power source?

A high pass filter is an electronic filter that passes signals with higher frequencies which are above the cut-off frequency range and also attenuates the frequencies which are below the cut-off range.

Now, the output of the specific high pass filter has no DC(0Hz) voltage due to its specified cut-off frequency(f_c). The lower cut-off frequency of an active high pass filter is 70.7% or -3dB(dB= -20log V_out/V_in) of the voltage gain which it allows to pass can be used as a power supply as well.

What does corner frequency mean in regards to high pass filter?

The corner frequency, which is also called as cut-off frequency, defines a specific frequency at which the transfer attenuation reaches -3dB below(50%) the magnitude from the 0dB or pass-band level.

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• Definition of Low Pass Filter
• Circuit Diagram
• Active and Passive Low Pass filter
• What does a LPF do? How does it work?
• Operation
• Frequency Response
• Transfer Function of a LPF
• Designing a LPF
• Corner frequency of a low pass filter
• Ideal & Real Filter
• Low Pass Filter vs High Pass Filter
• Advantages of a LPF
• What are the uses of a low pass filter
• FAQs

Definition of LPF:

 “Low pass filter carries lower frequency signals with less resistance and has a constant output gain from zero to a cut-off frequency.”

Generally, a low pass filter does attenuation of frequencies above cut-off points.

Circuit Diagram of a Low Pass Filter:

There are two types of active filter exist, they are-

• Active Low Pass Filter – consists of mostly active components like op-amp, a transistor.

• Passive Low Pass Filter – consists of mostly passive components like capacitors, resistors, etc.

How does a Low Pass Filter Work?

What does a low pass filter do?

In figure 1.1, it’s a commonly used low-pass active filter.

The filtering is commonly done by the RC network, and the op-amp is used as a unity gain amplifier. The resistor R_F(= R) is included for Dc offset.

At DC, the capacitive reactance is infinite, and the dc resistive path to ground for both terminals should be equal.

Here, all the voltages V_i, V_x, V_y, V₀ are measured concerning ground.

The input impedance of the op-amp is always infinite; no current will flow into the input terminals.

According to the voltage divider-rule, the voltage across the capacitor,

Since the op-amp gain is infinite,

Where,

= pass-band gain of the filter

                 f = frequency of the input signal

= cut-off frequency of the signal

A_cL

 = closed-loop gain of the filter as a function of the frequency.

The Gain Magnitude,

And Phase Angle (in degree),

Operation of a Low Pass Filter:

The operation of the low-pass filter can be verified from the gain magnitude equation as follows-

At very low frequencies, i.e., f>>f_c,

At f=f_c,

              |A_cL|<A_F

Thus the filter has a constant gain of A_F from 0 Hz to the cut-off frequency f_c. At f_c, the growth is 0.707A_F, and after f_c, it decreases at a steady rate with an increase in frequency.

Here, the actual response deviates from the linear dashed-line approximation at the vicinity of ‘f_c.’

Frequency Response of Low Pass Filter:

How to make a Low Pass Filter?

Low pass filter design:

A value of the cut-off frequency ω_c is chosen.

Capacitance C is selected with a certain value; usually, the value is between 0.001 and 0.1µF. Mylar or tantalum capacitors are recommended for better performance.

The value of R is calculated from the relation,

              F_c = cut-off frequency in hertz

              Ω_c = cut-off frequency is in radian second.

              C = in Farad

Finally, the values of R₁ and R_F are selected depending on the desired pass-band gain by using the relation,

Frequency Scaling:- Once a filter is designed, there may be a need to change its cut-off frequency. The method of converting an original cut-off frequency f_c to a new cut-off frequency is called ‘frequency scaling.’

To change a cut-off frequency, multiply R or C, but not both by the ratio:-

Corner frequency & Cut-Off Frequency of a Low Pass Filter:

The transition of a low pass filter is always swift and smooth from the pass-band to stopband. Also, a cut-off frequency is not any parameter to measure the goodness or badness in a range of frequency. The cut-off frequency is more accurately referred to as the -3dB frequency, i.e., it is the frequency at which the magnitude response is 3dB lower than the value at 0 Hz.

What is Pass-band?

“Pass-band is the particular range of frequencies which a filter pass through inside it.”

For low pass filters, the frequencies that move towards the end of the pass-band cannot have any significant gain or attention.

What is Stopband?

“A filter always carries filters within a given band, and rejects the frequencies which are below the given range. This particular range is known as a Stopband”.

As the limitations are there for low pass filters, the stopband attenuates at a particular frequency, which moves near the cut-off frequency closer to 0 Hz.

The transfer function of a Low pass Filter:

What is a Transfer Function?

“Transfer function is a complex number that has both magnitude and phase. In the case of filters, transfer function helps to introduce a phase difference between input and output.”

Since low pass filter allows low-frequency AC signals to pass through it, the output gets attenuated. We use different active and passive components to make a filter, which eventually has other characteristics. The transfer function tells us how one input is related to an output depending on the component’s characteristics. The transfer function can easily be determined from a graph of the output signal at various frequencies. We can also calculate the transfer function using Kirchoff’s Laws to derive the filter’s differential equation.

As more signal passes through it, the filter will apply a phase shift to the output signal for the input signal. Hence, the transfer function of a filter is a complex function of frequency. It also contains all the vital information we need to determine the magnitude of the output signal and its phase.

Ideal Filter & Real Filter:

Sometimes, for the reason of simplification, we often use the active filters to approximate ways. We upgrade them into an ideal and theoretical model, which is called ‘Ideal Filter.’

The use of these standards is insufficient, leading to errors; then, the filter should be treated based on accurate real behavior, i.e., as a ‘Real filter.’

The main key terms of an ideal filter are

• A gain unit
• Complete degradation of the input signal across the bands.
• The transition of response from one zone to another is quite abrupt.
• It does not create any distortion when the signal passes through the transit zone.

What are the differences between the Low pass filter & High pass filter?

What are the advantages of a Low Pass Filter?

• Low-Pass filters can easily remove aliasing effects from a circuit, which makes the circuit working smoothly.
• Low-Pass Filters are cost-effective so that it can be used easily.
• Low-Pass Filters have low output impedance; thus, it prevents the filters cut-off frequency from being affected because of the load.

Applications of a Low Pass Filter:

• A low-pass filter is used in ‘hiss’ filters.
• LPF is used in audio speakers to reduce high frequency.
• LPF can be used as an audio amplifier and an equalizer.
• In Analog to Digital converter, LPF is used as anti-aliasing filters to control signals.
• LPF is used in image smoothening, image blurring.
• LPF is also used in radio transmitters to block harmonic emissions.
• These filters are used in music systems to filter the high-frequency sounds, causing echo at higher sounds.

What is a passive low pass filter?

A passive low pass filter is a filter made of all passive components like capacitors, resistors, etc. It causes a lesser output level compared to the input level.

What is an RC low pass circuit?

An RC low pass circuit is made of only Resistors and Capacitors, as the name implies. It is an essential passive filter, as well. In this filter, the reactance of a capacitor varies inversely with frequency, and the value of the resistor remains constant as the frequency changes.

What is a Butterworth Low pass Filter?

A Butterworth filter is that type of filter where the frequency response is flat over the pass-band region. A Low-Pass Butterworth filter provides a constant output from DC source to a particular cut-off frequency and rejects the higher level frequencies.

How can a second order low pass filter be constructed?

We know that a first-order low-pass filter can be made by connecting a single resistor and capacitor whose single pole can give us a roll-off slope -20dB/decade. To make a second-order passive low pass filter, we connect or cascade two passive filters (first-order). It is also a two-pole network.

Write down the corner frequency of a second-order filter.

In a second-order low pass filter, we observe a -3dB corner frequency point and therefore, the pass-band frequency changes from its original value as calculated in the equation:

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Content

• In this article, we will discuss about few basic concept related to filter and few Frequently asked questions

• What is a filter ? filter definition
• How does a filter work?
• What are the types available ?
• What are the Active Filters? Explain with definition
• What are the Passive Filters? Explain with definition
• What are the points of conflict between active and passive types.
• What is the filter symbol?
• Examples
• What are the Applications of filter in optics and electronics industry ?
• What is the Response curves for most common types?
• What is Time response of a filter ?
• What is Frequency response of a filter?
• What is Order of a filter?
• How first-order output differs with A second-order filter ?
• What is Corner frequency, Cut off frequency, break frequency
• What is Bandwidth (BW) ?
• What is Resonant Frequency?
• What is Resonant Filters
• What is ideal and real filters ?

What is a Filter?

“A filter is a frequency selective network consisting of four terminals with reactive elements to transmit a specified range frequency.“

• The band of frequency transmitted through it is called Pass-band.
• The band of frequency, which gets attenuated by it, is called attenuated on Stop-band.

Filters are of two types- analogue digital. Now, based on the components used, They are of two types – Active types and Passive Types.

The below image represents a diagram of active types(one of the very popular and important types).

Know about Active High Pass Types. Click Here!

Characteristics of an active filter

As the titles suggest, these types are made using active components. Some of the active transistors are – transistors (BJT, FETs), any other electronics devices which are capable of amplifying a signal or can produce powers.

If there is a need to increase the characteristics, various stages are joined in a certain or specific ways.

How to design an active low pass filter?

To design an active types, we may use IC741, an Op-amp, configured with 8 pins. The op-amp is to be supplied with DC power along with resistors and capacitors of different values.

Passive Filters

Passive types are designed using passive devices.

Know about Applications of Active High Pass Types. Click Here!

Comparison of Active and passive types

An active type may have an advantage, increasing the signal power available in comparison with the input. Whereas a passive one dissipates energy from the signal. For various ranges of frequencies, such as at sound frequencies and under, an active type may realize a specified transfer function with no use inductors, that are comparatively big and costly components in contrast to resistors and capacitors, and that are more costly to create with the essential high quality and precise values.

Numerous stages may be cascaded when wanted to enhance attributes. By comparison, the layout of multiple-stage passive blockers needs to take into consideration every phase’s frequency-dependent loading of the previous stage. Since inductors aren’t utilized, they can be reached in really compact dimensions.

• Passive type suffers from attenuation of signals. There are various ways; one popular method of control or restoration is by using amplification through the Active type applications. The major point of conflict between the active and passive types is the ‘amplification’.

• Compared to a passive one, active type are composed of active components in operational amplifiers, transistors, or FET’s within their circuit design, as described in earlier sections. These components draw power from the external power source, use it for amplification of output. That’s an added advantage compared to a passive one.

Know about Active Low Pass Types. Click Here!

Why is an active filter needed at low frequencies?

• An active type is needed at lower frequencies because it helps achieve low output impedance while providing high input impedance. It also stabilizes different frequency ranges as multiple stages can be cascaded with it.

Difference between Active & Passive types

Know about Applications of Active Low Pass Types. Click Here!

These can be categorized and sub-categorized from several points of view. The most common divisions and sub-divisions are- active or passive type; high-pass type low-pass type, bandpass type, band-reject/notch type or all-pass type; digital or analog type discrete-time or continuous-time type; linear or non-linear type; infinite impulse response (IIR) or finite impulse response (FIR) and so on.

Examples:

Active types and Passive types are designed to modify certain band of frequency in a desired way. They have different types according to their needs. The categories are given below.

• Low pass types (LPF)
• High pass types (HPF)
• A bandpass types (BPF)
• Band reject/stop types (BSF)

Applications:

They are nowadays used in many purposes of the electronic circuit, and its applications are immense. Moreover, it’s possible to improve the circuit gain by using different filters in different ways, either active or passive types, especially in active types. Active types use amplifiers, and we know that it helps increase gain. This article will discuss two type, such as Low pass type, High pass type with appropriate diagrams and simulated wave shapes for both active and passive condition in the following sections with the importance of using higher-order in the HPF and LPF.

In electronics, some applications are as follows:

• In Radio communication System for Radio tuning to a specific frequency: They are used to enable radio receivers to only “see” or “detect” the desired signal and reject all the other signals by assuming their different signal frequency. So noise-free signals can be received. The high-frequency bandpass types are used for channel selection in central telephone offices.
• Power Supply Design: They are used to remove noise or high frequencies usually present on AC input lines. These are also applied to decrease the ripple.
• Analog-to-digital conversion (ADC): They are utilized in most of the ADC input to minimize aliasing.
• Modify digital images: It can be used to modify digital images also.
• Data analysis: They are also very helpful to remove specific frequencies in data analysis.

Frequency Response & Time Response:

Time-domain refers to the change of signal’s amplitude with respect to time. In contrast, in the frequency domain, Frequency refers to the occurrence of an event in a given period.

What is Bandwidth (BW)?

For filters, bandwidth is the difference between the upper and low -3dB points.

For example, if a bandpass filter has -3dB cut-off points and set to 200Hz and 600Hz, then the filter bandwidth will be = (BW) = 600-200 = 400Hz.

What do you mean by the Q Factor?

Q factor is given by the ratio of resonant frequency to the BW.

Q = 2 * π * (Maximum Amount of Energy Stored) / (Energy Dissipated per Cycle)

A greater Q value represents the filter is more selective as Q factor is a parameter which judges the selectivity.

Resonant Frequency

Resonant frequency is simply given by the frequency of the given resonant circuitry. A Resonant circuit is also popularly known as the tank circuit or the LC circuit. A resonant circuit is designed using parallelly placed inductors and capacitors and resistors.

 Oscillation of a system is given by the following equation –

Where,

f= frequency in Hertz

L= Inductance in Henry

C= Capacitance in Farads

Orders of Filters

Higher-order filters provided more excellent roll-off rates between passband and stopband. Higher-order filters are also required to achieve required levels of attenuation or sharpness of cut-offs.

Active type and Passive type also have variation in different types of orders, such as:

• First Order Low pass active types, First Order High pass active types, First-order Bandpass active types, First-order Band stops active types.
• Second order Low pass active types, Second order High pass active types, Second-order Bandpass active types, Second-order Band stops active types.

The frequency response of second-order are shown below –

Ideal type & Real type:

Sometimes, for the reason of simplification, we often use the active filters to approximate ways. Later they are modified and termed as ‘ideal filter’. Filters, which operate in reality considering all the possible factors, are real ones.

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1. What are the high-Pass filters?
2. How does a high-pass filter work?
3. What does a high-pass filter do in a circuit?
4. What is a high-pass filter symbol?
5. What are the type of high-pass filter ?
6. Different examples of high-pass filters
7. Time response and Frequency response of hpf
8. Cut-off frequency of hpf
9. Transfer function of high-pass filter
10. Comparison between high-pass and low-pass filter

                               

What is a High Pass Filter?

“High pass filter is a circuit that attenuates all signals of frequencies which belong to the below cut-off frequency and gives a constant output or gain above this particular frequency.”

In the above figure, the CR circuit does the ‘filtering’ work. The op amp is linked with a voltage follower. Now, the feedback system is also incorporated to cancel out the offset voltage according to the property of the operational amplifier.

Here,

The equation can be calculated using the property of ideal operational amplifier which states that an operational amplifier has infinite gain. Here, f represents input signal’s frequency.

Where= HPF’s passband gain,

f=Input signal’s frequency (It is also the cut-off freq.),

Operation of a High pass filter:

Here, the gain-magnitude equation does the job of verification at a lower level of frequency.

At f = f_c,

• At f>>f_c,

High Pass Filter Characteristics

Types of High Pass Filter:

• Passive High Pass Filters
• Active High Pass Filters

An active high pass filter is nothing but a circuit contains an active component such as a transistor, an operational amplifier(op-amp), etc. Using these devices gives us more efficiency.

Advantage of High Pass Filter :

Active high pass filters have several advantages over other types of filters. The major advantages are given below.

• 1. Amplification of weaker signal,
• 2. Efficient transmission of signal (with minimal loss),
• 3. Efficient performance when used in a multistage filter.

Working of high pass filter.

The most straightforward and simple type of filter is the First order Filter. It has a single reactive component. The transforming process is quite simple. You have to add just an op-amp.

Operational amplifiers have several configurations. Different configurations have different attributes and impact in the filter’s performance.

Now, note of the roll off rate of a first order filter. Roll off rate is defined as the rate at which the gain of a filter changes in the operational stop band. The rate represents the steepness of the curve and it also help us to find out the increase rate of the growth.

The first order filters come up with a growth rate 20 dB/decade or in other terms, it can be said the growth rate is 6db/Octave.

High Pass Filter Transfer Function

We know that the capacitor’s impedance varies with the frequency. That is why electronic-filters comes up with response which are dependent on frequencies.

The impedance of a capacitor is typically given by the following equation.

Where, s= σ +jω, ω represents the angular frequency.

The transfer Function is derived using some basic theorems of network theory.

The Transfer Function is given by ratio of output to the supplied input. The typical representation of transfer function is given as follow.

The typical transfer function is :

Where,

a₁ represents Amplitudes of signals

ω₀ represents Angular cut-off frequencies

Application of Active High Pass Filter:

• To transmit higher frequency in case of video related filters.
• The frequency is changed based upon various waveforms.
• The active ones finds application in the CROs, generators.

Passive High Pass Filters:

Why are passive high pass filters used?

A filter is called passive when there won’t be any external power, and the input signal also remains unamplified due to the passive components present in the Filter. The passive components may be the same as low pass, but the overall connection is always reversed. The passive components are Resistor(R) and Capacitor(C), so it is an RC filter combination.

The name “passive,” “high,” “pass,” and “filter” suggest that the Filter will only pass the higher frequency, i.e., it will block the low frequencies.

In the above circuit, the output voltage is determined across the resistor(R); when the frequency increases, the reactance of the capacitor decreases, so the output and gain increases simultaneously.

The formula to calculate the frequency of the RC circuit is,

f=1/2πRC

How to build an RC High Pass Filter:

To build an RC HPF, the components we need are as follows,

• A function Generator
• A 10nF ceramic capacitor
• A 10 K ohm resistor

Frequency:

                                    (0.00000001F) = 15,293 Hz, the greater the output, the more signal gets attenuated.

If we give an AC signal input to the circuit from a function generator and sets the signal to a low frequency, the capacitor will block the voltage signal. So the low-frequency signals which get blocked do not reach past the capacitor. The high-frequency signals keep going and pass to the output.

Passive High Pass Filters are used in:

• Audio amplifiers
• In speaker systems
• In different music control systems etc.

First Order High Pass Filter vs. Second Order High Pass Filter

• The second-order high-pass filter comprises two different reactive components.
• First-order HPF has a transfer function of the first order; on the other hand, second-order HPF has a transfer function of second order.
• The first order filter differs from the second order filter on the basis of the stopband. The slope of the graph of a second order is typically the algebraic double of the first order.

Passive RL High Pass Filter:

This circuit consists of a resistor and an inductor. The inductor in the circuit passes all the lower frequencies and reduce the voltages across it. It also keeps the output voltage closer to the input voltage.

There is a frequency response in dB below the circuit for a specific range of frequencies.

The lower cut-off frequency for an RL high-pass filter is determined by the inductor and the parallel combination of RF and RL, by the formula:

Where, R_EQ = R_F||R_L

How to build an RL High Pass Filter:

To build an RL HPF, we need,

• A function Generator
• A Resistor
• An Inductor
• Oscilloscope

For making the circuit, we may use a 470mH inductor and a 10KΩ resistor.

The circuit forms a high-pass filter and helps the high-frequency signals to pass through to the output. It also filters the low-frequency signals through the inductor.

Butterworth High Pass Filter:

What is a Butterworth Filter?

“Butterworth filter is probably the first and best-known filter approximation.”

The Butterworth filter is created to get a smooth frequency response graph in the passband.

Circuit Image –

                                                                            

Chebyshev High pass Filter:

The Butterworth filter is created to get a smooth frequency response graph in the passband. Filters can be classified into two categories. The categories are ‘Chebyshev Filter’ and ‘Inverse Chebyshev Filter’.

The filter response comes out to be response of a Butterworth filter, if the ripple value is fixed at 0%. Typically the ripple value is fixed at 0.5% for applications in digital filters.

Chebyshev frequency response

High Pass Filter vs. Low Pass Filter:

Why should we use the High Pass Filter?

• High pass filters are excellent for any electronics or electrical operations.
• HPF allows us to gain staging by providing more control over the process or experiment.
• Cutting off unwanted noise is another best feature so far.

Write some advantages of a High Pass Filter.

• Have a sharp roll-off response.
• The broadcasting power is powerful enough to receive the frequency of the necessary channel.
• The filter has advantages in audio processing applications as it blocks the Direct Current voltage from getting amplified.

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In this article we will study about the Schmitt trigger Comparator and Oscillator circuitry with different related parameters in detail. As we have seen till now that an op-amp is used in various fields of applications and being such a versatile device its importance as a part of analog circuits is immense. One of the most convenient applications of the op-amp is as a multivibrator circuit. We will be studying in detail about types and working of multivibrator circuit constructed using op-amps (op-amp multivibrators) and other passive devices such as capacitors, diodes, resistors etc.

Contents

• Introduction of Multivibrators
• Positive feedback usage in multivibrator
• What is Schmitt trigger ?
• Schmitt trigger comparator closed-loop circuit or bistable multivibrator
• Voltage transfer characteristics of Bistable multivibrator
• Astable multivibrator or Schmitt trigger oscillator
• Oscillator’s duty cycle

Introduction of Multivibrator and Schmitt trigger Circuitry

Multivibrator circuits are sequential logic circuits and are of many types depending on how they are created. Some multivibrators can be made using transistors and logic gates, whereas there are even dedicated chips available as multivibrators such as NE555 timer. The op-amp multivibrator circuit has a few advantages over other multivibrator circuits as they require much fewer components for their working, less biasing, and produces better symmetrical rectangular wave signals using comparatively fewer components.

Types of Multivibrators

There are mainly three types of multivibrator circuits present:

1. Astable multivibrator,
2. Monostable multivibrator
3. Bistable multivibrator.

The monostable multivibrator has single stable state, whereas the number of stable-states a bistable multivibrator has- is 2.

As we have learnt in the previous section about op-amp as a comparator, in the open-loop configuration the comparator can switch in an out of control manner between the positive saturation supply rail voltage and negative saturation supply rail voltage when an input voltage near to that of the reference voltage is applied. Hence, to have control on this uncontrollable switching between the two states, the op-amp is used in a feedback configuration (closed-loop circuit) which is particularly known as closed-loop Schmitt trigger circuit or bistable multivibrator.

Positive feedback usage in multivibrator and hysteresis effect

Till now, we have learnt about the negative feedback configuration in op-amps in the previous sections. There is also another type of feedback configuration known as positive feedback, which is also used for specific applications. In positive feedback configuration, the output voltage is fed back (connected) to the non-inverting (positive) input terminal unlike the negative feedback, where the output voltage was connected to the inverting (negative) input terminal.

An op-amp operated in a positive feedback configuration tends to stay in that particular output state in which it is present, i.e. either the saturated positive or saturated negative state. Technically, this latching behaviour in one of the two states is known as hysteresis.

If the input applied signal in the comparator consists of some additional harmonics or spikes (noise), then the output of the comparator might switch to the two saturated states unexpectedly and uncontrollably. In this case, we won’t get a regular symmetrical square wave output of the applied input sinusoidal waveform.

But if we add some positive feedback to the comparator input signal, i.e. use the comparator in a positive feedback configuration; we will be introducing a latching behaviour in the states, what we technically call as hysteresis into the output. Until and unless there is a major change in the magnitude of the input AC (sinusoidal) voltage signal, the hysteresis effect will continue to make the output of the circuit remain in its current state.

What is Schmitt trigger ?

The Schmitt trigger or bi-stable multi-vibrator operates in positive feedback configuration with a loop-gain greater than unity to perform as a bi-stable mode. Voltage V₊ can be.

The above figure represents the output voltage versus the input voltage curve (which is also known as the voltage transfer characteristics), particularly showing the hysteresis effect. The transfer characteristic curve has two specific regions, the curve as the input voltage increases and the part of the curve in which the input voltage decreases. The voltage V₊ does not have a constant value, but instead, it is a function of the output voltage V₀.

Voltage transfer characteristics

In the voltage transfer characteristics, V_o = V_H, or in high state. Then,

Higher Cross-over voltage V_TH

If signal is less than that of V₊, the output stays at its high state. The cross-over voltage V_TH occurs when V_i = V₊ and expressed as follows:

When V_i > V_TH, the voltage at the inverting terminal is more than at the non-inverting terminal. Voltage V₊ then turn out to be

Lower Cross-over voltage V_TL

Since V_L < V_H the input voltage V_i is still more than V₊, and the output rests in its low state as V_i carry on to increase; If V_i decreases, as long as the input voltage V_i is larger than V₊, the output remains at saturation state. The cross-over voltage here and now occurs when V_i = V₊ and this V_TL expressed as

As V_i continues to decrease, it remains less than V₊; therefore, V₀ remains in its high state. We can observe this transfer characteristic in the above figure. A hysteresis effect is shown in the net transfer characteristic diagram.

What is Schmitt trigger oscillator ?

Astable multivibrator or Schmitt trigger oscillator

Astable multivibrator accomplished by fixing an RC network to the Schmitt trigger circuit in –ve feedback. As we will advance through the section, we will see that the circuit has no stable states and therefore, it also known as the astable multivibrator circuit.

As noticed in the figure, an RC network is set in the negative feedback path, and the inverting input terminal is connected to the ground through the capacitor while the non-inverting terminal is connected to the junction between the resistors R₁ and R₂ as shown in the figure.

At first, R₁ and R₂ is to be equal to R, and assume the output switches symmetrically about zero volts, with the high saturated output represented by V_H = V_P and low saturated output indicated by V_L = -V_P. If V₀ is low, or V₀ = -V_P, then V₊ = -(1/2)V_P.

When V_x drops just slightly below V₊, the output switches to high so that V₀ = +V_P and V₊ = +(1/2)V_P. The equation for the voltage across the capacitor in an RC network can be expressed as:

Where τ_x is the time constant which can be defined asτ_x= R_xC_x. The voltage V_x increases towards a final voltage V_P in an exponential manner with respect to time. However, when V_x turn out to be slightly greater than V₊ = +(1/2)V_P, the output shifts to its low state of V₀ = -V_P and V_x = -(1/2)V_P. The R_xC_x network gets triggered by a negative sharp transition of the voltages, and hence, the capacitor C_x start discharging, and the voltage V_x decreasing towards value of –V_P. We can therefore express V_x as

Where t1 refers to the time instant when the output of the circuit switches to its low state. The capacitor discharge exponentially V₊ = -(1/2)V_P, the output again shifts to high. The process repeats itself continuously over time, which means a square-wave output signal is produced by the oscillations of this positive feedback circuit. The figure below shows the output voltage V₀ and the capacitor voltage V_x with respect to time.

Time t₁ can be found by substituting t=t₁ and V_x = V_P/2 in the general equation for the voltage across the capacitor.

From the above equation when we solve for t₁, we get

For time t₂ (as observed in the above figure), we approach in a similar way, and, from a similar analysis using the above equation, it is evident that the difference between t₂ and t₁ is also 1.1R_xC_x. From this, we can infer that the time period of oscillation T can be defined as T = 2.2 R_xC_x

And the frequency thus can be expressed as  

 

Duty cycle of Oscillator

The percentage of time the output voltage (V₀) of the multi-vibrator is in its high state is particularly termed as the duty cycle of the oscillator.

The oscillator’s duty cycle is           

As observed in the figure, depicting output voltage and capacitor voltage versus time, the duty cycle is 50%.

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What is comparator circuit ?

A comparator or a voltage comparator is a device used to compare two voltage levels. We can determine which voltage level is higher from the comparator’s output. It is an application of typical op-amps, and it has applications furthermore.

What does a comparator circuit do ?

A comparator compares two given input voltage and provides the output indicating which voltage has a more excellent value. The circuit takes input using inverting and non-inverting terminals and provides output from the output terminal. The output range lies between the positive saturation voltage and negative saturation voltage.

Op Amp comparator circuit

The below image represents a circuit diagram of the comparator circuit. As we can observe that the circuit comprises only an op-amp, and voltage inputs are supplied in it through the inverting and non-inverting terminals.

Comparator circuit design

The comparator circuit is designed using an op amp. To make it ready for operation, input voltages are provided. There is no feedback system incorporated with it. A reference voltage and a voltage signal are provided through the op-amp. The positive and negative saturation voltage inputs are also provided. The indicative output is collected from the output of the op-amp.

How comparator circuit works ?

The working principle of the comparator is pretty simple. In general, it compares between two voltage sources and provides a greater output. Below mentioned two points state the working.

• If the voltage in the non-inverting terminal is higher than the inverting terminal voltage, the output is switched to the op-amp’s positive saturation voltage.
• If the inverting terminal’s voltage is higher than the voltage in the non-inverting terminal, the output is switched to the op-amp’s negative saturation voltage.

Voltage comparator circuit using op amp 741

Op-amp 741 is an integrated circuit containing an op amp. A voltage comparator can be created using op amp 741. The below image represents a non-inverting voltage comparator’s circuit diagram using op amp 741.

Comparator block diagram

The operation of a comparator can be represented by using block diagrams. The following image represents a block diagram of a comparator,

Comparator circuit relay

Relays are switches that can control a circuit. It can turn On or OFF a circuit and can connect and disconnect a circuit from another circuit. A comparator is broadly utilized as the utilization of the relays.

Comparator circuit uses

A comparator is a valuable and essential device. There are several applications of comparators. Some of the applications of the comparators are listed below.

• Null Detector: If a value is zero, a null detector detects it. A comparator is typically a high-gain amplifier, and for controlled inputs, a comparator is suitable for detecting Null.
• Level Shifter: A level shifter can be designed using a single op-amp. Using a suitable pull-up voltage, the circuit allows for a lot of versatility in selecting the voltages to be interpreted.
• Analog-to-digital Converter (ADC): Comparators are used to create analog-to-digital converters. In a converter, the output indicates which voltage is higher. This operation is the same as a 1-bit quantization. That is why comparators are used in almost every analog-to-digital converter.
• Other than the mentioned applications, there are many other comparators like – Relaxation Oscillator, in Absolute Value Detectors, in Zero-Crossing Detectors, in Window Detectors, etc.

Comparator fuzz circuit

Fuzz circuits can be developed using comparators. LM311 IC is such an example of comparator fuzz. We will discuss this later about LM311.

How to make a comparator ?

A comparator is a particular and straightforward electrical device to build. To build a comparator, we need an op amp and supply voltages. At first, the op-amp is provided with positive and negative saturation voltages. The output will vary in that range of voltages. Then inputs are provided in their inverting and non-inverting terminals. The reference voltage is provided in the non-inverting terminal, and the input voltage is provided in the inverting terminal. There is no feedback system associated with this circuit.

Voltage comparator circuit

A comparator circuit can detect the high-valued voltages between two voltages. Comparators, which typically compare to voltages, are known as a voltage comparator circuit.

Phase comparator circuit diagram

A phase comparator is an analog logic circuit capable of mixing and multiplying. It detects the differences in phases between two given signals by generating a voltage signal. The below image represents the phase comparator circuit diagram.

Ic comparator circuits

As mentioned earlier, a comparator compares two voltage signals and produces an indicative output. Comparators are incorporated inside an integrated circuit for better usability. The below image represents the circuits for comparator ic.

lM358 comparator circuit

lm358 is a comparator ic consisting of two comparators inside it. It has eight pins. This ic doesn’t require any independent external power supply for functioning each comparator. The circuit diagram of the ic is given below.

Comparator internal circuit

The comparator is designed using an op amp—the op amp as further circuitry. The internal circuitry inside an ic is given below in the diagram. Observing the diagram, we can see that it consists mainly of transistors, diodes, and resistors. The internal diagram can be divided into three parts based on their operation. They are – input stage, gain stage, and output stage.

Comparator circuit schematic

The schematic diagram of a comparator is given below. The internal schematic diagram is the same as an internal comparator circuit. It has diodes, transistors, and resistors. The internally connected components work as a comparator.

Schmitt trigger comparator circuit

Schmitt trigger is a viral circuit used to improve noise immunity and reduce the likelihood of multiple switching.

A schmitt trigger is a comparator circuit with separate input switching levels for changing the outputs. The schmitt trigger comparator circuit is depicted in the below diagram.

555 timer comparator circuit

555 timer is an oscillator circuit. It is known as 555 timers as there are three resistors of 5 kilo-ohms that are internally connected to provide the reference voltages for both the timer circuits’ comparators. A555 timer ic is used in delay timers, LED flashers, pulse generations, etc. A basic block diagram of 555 timer ic is given below. There are two comparators, an NPN transistor, a flip-flop, three 5k resistors, and an output driver.

comparator circuit using lm324

lm324 is a general-purpose op-amp IC that has four op-amps inside it. It can be used as a comparator also. The op-amps have properties of higher stability, wider bandwidth. LM324 has 14 pins. The pin diagram of lm324 is given below.

Pin No.	Description
1	First Comparator’s Output
2	First Comparator’s Inverting input
3	First Comparator’s Non-inverting input
4	5V supply voltage
5	Second Comparator’s Non-inverting input
6	Second Comparator’s Inverting input
7	Second Comparator’s Output
8	Third Comparator’s Output
9	Third Comparator’s Inverting input
10	Third Comparator’s non-inverting input
11	Ground PIN (GND)
12	Fourth Comparator’s non-inverting input
13	Fourth Comparator’s Inverting input
14	Fourth Comparator’s Output

The circuit diagram of the LM324 comparator is depicted in the below diagram.

lm139 comparator circuit

lm139 is another comparator ic. It has four separate precision comparators. The ic is designed to function under a single power supply. It is specially developed for directly interacting with Transistor-Transistor Logic and Complementary MOS logic. The ic comes with a propagation delay of 0.7 microseconds.

The below image depicts the internal circuit diagram of the lm139 comparator.

lm319 comparator circuit

lm319 is another comparator ic having 14 pins. It has two separate precision comparators. The ic is designed to function under a wide range of supply voltages. It is specially developed for directly interacting with Transistor-Transistor Logic and Complementary MOS logic, RTL, DTL. The ic comes with a propagation delay of 0.025 microseconds.

lm311 voltage comparator circuit

lm311 is another comparator ic having eight pins. It has a single comparator. The ic comes with a response time of a minimum of 0.200 nanoseconds and a typical voltage gain of 200.

The below image depicts the internal circuit diagram of the lm311 comparator.

lm339 comparator circuit

lm339 is another comparator ic. It has four separate precision comparators. The ic is designed to function under a single power supply and for a wide range of voltages. It is specially developed for directly interacting with Transistor-Transistor Logic and Complementary MOS logic and DTL, ECL, MOS logic. The ic comes with a propagation delay of 0.7 microseconds.

Op amp comparator circuit example

Op-amp comparator circuits are used in various applications. For example – to ensure if an input value has reached the peak or the specific value or not, or for quantization in an ADC, also in window detectors, zero-crossing detectors, etc.

Voltage window comparator circuit

A window comparator refers to the circuit that works only in a particular frame or window or voltage. And a voltage comparator compares two signals and provides the output. For a window comparator circuit, there is something called the sandwich effect: if the input voltage goes higher than the low-level reference voltage. The circuit is ON, and if the input voltage gets higher than the high-level reference voltage, then the circuit is OFF.

Components required for a voltage window comparator:

• LM741 op-amps (2)
• 4049 Inverter Chip (1)
• A resistor of 470 ohms (1)
• 1N4006 Diodes (2)
• LED

The voltage window comparator circuit is given in the below image.

<image: vol-win1>

Latching comparator circuit

A latched comparator is developed using a StrongArm latch. The StrongArm latch is considered the primary decision amplification stage. The next stage is processed out with a latching element to carry the output load.

Op amp comparator circuit with hysteresis

The difference between Upper Trip Point and Lower Trip Point is Hysteresis. Hysteresis comes with the concept of Schmitt Trigger. If a typical comparator is designed with positive feedback, that circuit causes hysteresis. The below image depicts the circuit diagram.

Regenerative comparator circuit

A Schmitt trigger circuit is also called regenerative comparator circuits. They are used to improve noise immunity and reduce the likelihood of multiple switching Regenerative comparator circuits to design other complex circuits. They are used in ADCs, slicer circuits, memory sensing, etc. The Schmitt Trigger circuit diagram is referred to as the regenerative comparator circuit’s circuit diagram.

Temperature comparator circuit

A temperature circuit is a digital electronic circuit that measures whether the input temperature is below the specified reference temperature. It is one of the primary examples of a comparator circuit. Temperature sensors include a comparator.

Frequently Asked Questions

1. How does a comparator circuit work ?

Answer: The working principle of the comparator is pretty simple. In general, it compares between two voltage sources and provides a greater output. Below mentioned two points state the working.

• If the voltage in the non-inverting terminal is higher than the inverting terminal voltage, the output is switched to the op-amp’s positive saturation voltage.
• If the inverting terminal’s voltage is higher than the voltage in the non-inverting terminal, the output is switched to the op-amp’s negative saturation voltage.

2. Comparator circuit types

Answer: There are several types of comparators. Some of the widely used amplifiers are listed below.

3. Why is the output voltage in the comparator circuit of an op amp equal to the saturation voltage ?

Answer: Comparator circuits do not have any feedback associated with them. The op-amp thus has an open-loop gain. For an ideal op-amp, the open-loop gain is infinite, and for a practical op-amp, the gain is very high. Now, the saturation voltage of typical op-amps is +- 15 V. The op-amp gets saturated at +13 or -13 V. Now, the op-amp gets quickly saturated for a small input voltage. That is why the output voltage in the comparator circuit equal to the saturation voltage.

4. In an op amp comparator circuit, why is a reference voltage used

Answer: Comparison is made between two or more quantities. To indicate which is more significant, we need a reference to decide. We need to determine which voltage is more significant for a comparator. That is why a reference voltage is used to make the decision.

5. How does the digital comparator circuit distinguishes between a lesser and more significant number

Answer: A digital comparator compares two binary numbers. The comparator first finds out the equivalent voltage of the binary numbers and then determines which number is less, which number is significant.

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Introduction to Instrumentation Amplifier

An instrumentation amplifier is a particular type of amplifier which is derived from meeting some specific purposes. Instrumentation amplifier provides higher gain, high CMRR (common-mode rejection ratio) and high input impedances. So, we can say that it tries to possess most of the characteristics of an ideal op-amp.

An instrumentation amplifier is often called as In-Amp or InAmp. This article will discuss in detail about circuit, design, formulas, and equations related to the Instrumentation amplifier.

3 Op-Amp Instrumentation Amplifier

A typical Instrumentation amplifier consists of 3 regular op-amps. Two of them are used in a single-stage, whereas the other is used to separate a stage. All three amplifiers work as a differential amplifier, and all of them are connected with negative feedbacks. As instrumentation amplifiers are consisting of 3 amplifiers, they are often called three op-amp amplifier.

Instrumentation Amplifier Circuit

The below image represents a typical circuit diagram of an instrumentation amplifier. Carefully observe the picture as we are going to reference the photo for the rest of the article.

The input voltages are Vi1 and Vi2.

The resistances are R1 (2), R2 (2), R3, R4(2).

The voltage at A and B terminals are VA and VB, respectively.

The current through the R4, R3, and R4 branch is I.

The output of the Amplifier -1 is the Vo1, and that of amplifier -2 is Vo2.

The output of the 3^rd amplifier is Vout.

Instrumentation Amplifier Design

An instrumentation amplifier is a combination of 3 typical amplifiers. They are connected in a specific order to build an instrumentation amplifier. We can segregate the instrument amplifier design into two-part.

The first part is “Two input and two output”. Two standard operational amplifiers are connected, as shown in the amplifier circuit figure. Both of them are provided with negative feedback as it stabilizes the circuit more. The output of both the amplifier is connected with three resistors.

The second part is a basic “Differential Amplifier”.  The output of both the previous amplifier acts as input for the last amplifier. Outputs are connected with two identical valued resistors with the amplifier. The positive section is grounded, and negative feedback is associated with the negative terminal and the o/p of this op-amp is the final output of the instrument amplifier.

Instrumental Amplifier Derivation

Let us derive the functional equations and formulas for the instrumentation amplifier. To derive the equations, let us know what happens inside the whole instrument amplifier. As we have previously mentioned, the separation of two stages so, we will calculate it partly.

At the first stage, the input is provided to the non-inverting terminals of both the amplifiers. The amplifier is differential amplifiers.  So, they find out the difference between the given input voltages. Now, refer to the circuit diagram; the input voltages are Vi1 and Vi2. The inverting terminal of the circuit is connected with negative feedback from the output of the amplifiers. Let us say the inverting terminals of both the amplifiers are having potentials VA and VB, respectively. They appear at the node connecting with the resistance lines and branch.

Considering the virtual short-circuit works, the A and B terminal receive the same amount of voltage as the inputs. So, we can say, VA = Vi1, VB = Vi2. The whole stage works like a differential amplifier. That means the difference between the two inputs voltage will be amplified at the output. The output will be again the differences between the two outputs voltage. That can be expressed as follow:

Vo1 – Vo2 = k (Vi1 – Vi2)

Here k is the gain of the amplifier.

At stage two, the difference of the amplifiers is fed as the input for the amplifier. The amplifier at this stage simply works like a typical amplifier. The resistances are connected with the information are of the same values as the differential amplifiers’ requirement. The inverting terminal is associated with the ground, and the amplifier is though of having virtual grounds. In the next section, we will derive the mathematical calculations for an instrument amplifier.

Instrument Amplifier Equation

The input voltages are Vi1 and Vi2.

If the virtual shorting works, then VA = Vi1 and VB = Vi2

Now, there is no current flow from A and B to the resistance branch. There is only a typical current through the branch, and that is current I. ‘I’ is given as:

I = (Vi1 – Vi2) / R3.

The current ‘I’ can also be calculated using the node analysis. It comes as follow.

I = (Vo1 – Vo2) / (R4 + R3 + R4)

Or, (Vo1 – Vo2) = (Vi1 – Vi2) * (R3 + 2R4) / R3

The above equation explains the operation of the first stage. For the second stage, the op-amp’s output is the final output of the instrumentation amplifier.

From the operation of a difference amplifier, we can write that,

Vout = (R2 / R1) x (Vo2 – Vo1)

Or, Vout = (R2 / R1) x (R3 + 2R4) x (Vi1 – Vi2) / R3

This is the instrumentation amplifier equation or the output equation of an instrumentation amplifier. Now, look at the derivation section of this article. Vo1 – Vo2 = k (Vi1 – Vi2). The obtained equation is in the same format.

Instrumentation Amplifier Gain

The amplifier’s gain is referred to as the factor by which the amplifier amplifies the input signal. The resistance values represent the gain of an instrumentation amplifier. The gain also depends on the type of feedbacks being used. The positive feedback provides higher gain, whereas negative feedback provides better stabilities of the system.

The instrumentation amplifier’s general equation is Vo1 – Vo2 = k (Vi1 – Vi2), representing the gain as: ‘k’.

Instrumentation Amplifier Gain Formula

As mentioned earlier, the amplifier gain can be derived from the output equation of the amplifier. The output equation is as follow:

Vout = (R2 / R1) x (R3 + 2R4) x (Vi1 – Vi2) / R3

Comparing this equation with the following equation:

Vo1 – Vo2 = k (Vi1 – Vi2)

We can write,

k = (R2 / R1) x (R3 + 2R4) / R3, this is the instrumentation amplifier gain formula.

Instrumentation Amplifier IC

Typical amplifiers are packaged through Integrated Circuit or ICs. So, if we want to build an Instrumental amplifier using regular op-amps, we have to use op-amp ICs. There is also a separate IC available for Instrumentation amplifiers. There is no need for connecting one op-amp with another. These types of ICs are used commercially where more numbers of ICs are used at a time.

Instrumentation Amplifier Module

Instrumentation amplifiers modules are a combination of a few electronic devices, and the main of them is the Instrumentation Amplifiers. Two of the excellent instrumentation amplifiers are AD623, AD620.

The modules are used explicitly in medical engineering devices of low powers, low power signal amplifier, thermocouples. Some of the characteristics are – a) It provides higher gain, b) Better stability, c) Low power d) High Accuracy.

Instrumental Amplifier IC List

As an instrumentation amplifier can be build using different ICs, we have made a list of all ICs that can be used for Instrumental Amplifiers. The IC numbers are given in the list.

Name of the IC	IC Specification	Comments
Instrumentation Amplifier	INA128	Single-Chip.
Dual Instrumentation Amplifier	INA2128	16 pin IC
Typical Op-Amp	LM324	IC had four amplifiers.
Instrumentation Amplifier	AD623	Eight pin IC having a single instrumentation amplifier
Precision Instrumentation Amplifier	AD624	16 pin IC
Operational Amplifier	IC741	Four pin IC and works as a single unit of the op-amp.

Instrumentation Amplifier Load Cell

The performance of the instrumentation amplifier gradually increases upon connecting the load cell. The amplifier provides higher CMRR, higher input impedances and thus improves the performance. The detailed connection for the instrumentation amplifier with load cell is shown in the below image.

Instrumentation Amplifier offset voltage

Every op-amp has its offset voltage. The offset voltage is defined as the must need a voltage that must be applied between two inputs to nullify the difference between them and this offset value of every op-amp is specified in the datasheet provided by the manufacturer. For Instrumentation amplifiers, the offset voltage is significantly less, which is desirable.

Instrumentation Amplifier Output Waveform

To observe an instrumentation amplifier’s output, we have to connect it with a CRO (Cathode Ray Oscilloscope). We provide input as sine waves as two input signals, and work is measured from the last amplifier. Co-axial probes are connected with the pins to observe the output waveform. The below image depicts the output. The output is the amplified difference between the applied input voltages.

Instrumentation Amplifier transfer function

The transfer function of a system refers to the process which describes or provides output for each input. As the amplifier takes two inputs and amplifies them, the transfer function will reflect the same. The transfer function can be written as:

Vo1 – Vo2 = k (Vi1 – Vi2)

Here Vi1 and Vi2 are the two inputs, and k is the gain.

Dual Instrumentation Amplifier

A dual instrumentation amplifier is a special kind of instrumentation amplifier having great accuracy. It is designed in a certain way to provide high gain, greater accuracy from a minimal size of IC. It also has a low offset voltage. For a wider bandwidth and a connected external resistor, the dual amplifier can provide gain up to 10,000.

The INA2128 IC is used as a dual instrumental amplifier. Some of the significant Applications of dual instrumentation amplifier are sensor amplifiers, medical engineering devices, and battery-operated equipment.

Instrumentation Amplifier vs Operational Amplifier

Points of Reference	Operational Amplifier	Instrumentation Amplifier
Basic Structure	Build up of Bipolar Junction Transistors or Metal Oxide Field-Effect Transistors.	The buildup of three Differential Amplifiers
Gain	Normal Gain	Higher Gain
Buffer Connection	An operational amplifier can be used to make a buffer circuit.	A buffer circuit is a part of the whole circuit.
IC specification	IC741	AD623

Instrumentation Amplifier advantages and disadvantages

Instrumentation Amplifiers is developed to gain more advantages over typical differential amplifiers. That is why instrumentation amplifiers are used in most commercial applications. But it has some advantages too. Let us discuss some of the instrumentation amplifiers advantages and disadvantages.

Advantages

1. Accuracy and Precision in Measurement: Instrumentation amplifiers are used for testing and measurement purpose. Instrument amplifiers don’t need to match the input impedances. That is why they are so useful for testing. The better parametric values like higher CMRR, high input impedance also gain advantages.

2. Gain: Instrumentation amplifiers provide greater values for open-loop gain. It is a clearer advantage which is also an essential requirement for the amplifiers.

3. Stability of the System: Inside the Instrumentation Amplifiers, all normal op-amps are connected in negative feedback. As we know, negative feedback stabilises the system; the Instrumentation amplifier’s stability is also high.

4. Scalability: Instrumentation amplifiers are incredibly scalable. It provides the option to scale the signal at the input level. That is why the overall amplification is much greater than other amplifiers. The range for scaling is high for that reason also.

5. Accessibility: Instrumentation amplifiers come in ICs. There are eight-pin ICs are available. So, it is easier to handle and use. Also, there are not many factors to take during the amplification. The user just has to know the input signal well. Let us find the disadvantages of the instrumentation amplifiers.

Disadvantages

1. The Instrumentation amplifier suffers from the issue of long-range transmission. The amplifier tends to mix up the original signals with the noises if the input signal is sent for an extended range for communication. The issue can be resolved if the cable type can be improvised so that the noise gets cancelled at the primary stage or no noise enters the transmission line.

Instrumentation Amplifier Characteristics

Let us look at the characteristics of the instrumentation amplifiers at a glance.

• Instrumentation Amplifiers are Differential Amplifiers made up of three op-amps.
• It provides a higher open-loop gain than typical op-amps.
• It has higher CMRR, higher input impedance, low offset voltages, lower output impedances, making it close to the ideal op-amp.
• Instrumentation amplifiers provide higher accuracy and precision when used in testing and measuring.
• Instrumentation amplifiers are available in ICs for commercial purposes.

2 op amp instrumentation Amplifier

Typical instrumentation amplifiers are made up of 3 amplifiers but it is also possible to make an instrumentation amplifier using a two op-amp. The below image depicts the a 2 op amp based Instrumentation Amplifier Circuit.

instrumentation amplifier noise analysis

There are particular types of instrumentation-amplifiers available for measuring the weakest signal in a noisy environment. They are known as noise instrumentation-amplifiers. These types of instrumentation amplifiers are used for noise analysis.

Instrumentation amplifier for current sensing

Separate current sensing amplifiers are available in the market for current sensing. But an instrumentation amplifier can also operate current sensing. The primary difference between the two amplifiers is in the input topology.

Frequently Asked Questions

1. Why use an instrumentation amplifier?

Answer: Instrumentation-amplifiers provide higher gain, higher CMRR, higher input impedances, lower output impedances. Thus, we can observe it possesses very close properties of an ideal op-amp. That is why an instrumentation-amplifier is used.

2. When to use an instrumentation amplifier?

Answer: Instrumentation-amplifiers are required every time the user requires a higher gain with better stability of the system to amplify a signal. If the user needed very accurate testing results and measurements, then the instrumentation amplifier comes as a solution.

3. What is an Instrumentation amplifier for load cell?

Answer: The performance of the instrumentation-amplifier gradually increases upon connecting the load cell. The amplifier provides higher CMRR, higher input impedances and thus improves the performance. The detailed connection for the instrumentation amplifier with load cell is shown in the below image. (Point to be noted – Connect all the ground.

4. What is a circuit diagram of an instrumentation amplifier for a biosignal with a gain of a thousand?

Answer: The standard connection of the instrumentation-amplifier provides a specific gain. But adding up an external resistor will give you a boost of thousand.

5. What is the working principle of an instrumentation amplifier?

Answer: The working principle of the instrumentation amplifier is the same as that of a Differential amplifier. It takes the input voltages and amplifies the difference to provide that amplified difference as the output.

Basically: Output = Gain * (Input1 – Input2)

6. What are the advantages of using an instrumentation amplifier over an ordinary differential amplifier in measuring low signals and voltages?

Answer: The advantages are –

• Accuracy and Precision in Measurement: Instrumentation amplifiers are used for testing and measurement purpose. Instrument amplifiers don’t need to match the input impedances. That is why they are so useful for testing. The better parametric values like higher CMRR, high input impedance also gain advantages.
• Gain: Instrumentation amplifiers provide greater values for open-loop growth. It is a more clear advantage which is also an essential requirement for the amplifiers.
• Stability of the System: Inside the Instrumentation Amplifiers, all normal op-amps are connected in negative feedback. As we know, negative feedback stabilises the system; the Instrumentation amplifier’s stability is also high.
• Scalability: Instrumentation amplifiers are incredibly scalable. It provides the option to scale the signal at the input level. That is why the overall amplification is much greater than other amplifiers. The range for scaling is high for that reason also.
• Accessibility: Instrumentation amplifiers come in ICs. There are eight-pin ICs are available. So, it is easier to handle and use. Also, there are not many factors to handle during the amplification. The user has to know the input signal well.

7. Why is CMRR important in instrumentation amplifier?

Answer: CMRR is an essential parameter for measuring the performance of an op-amp. CMRR estimates how much amount of common-mode signal will appear in the output measurement. Instruction Amplifier, being an op-amp explicitly used for measuring and testing purposes, should have the lowest CMRR. It is a basic need for the op-amp; otherwise, it will affect the measurement.

8. What is the difference between an instrumentation amplifier and an inverting adder using two op-amps?

Answer: The difference will be in workings and as well as in the parametric values. Inputs for an instrumentation amplifier is never supplied in the inverting terminals. So, there will be changes. Also, the instrumentation amplifiers have buffer circuits, and the feedbacks of them are negative feedback which increases the system’s stability. So, there are massive deviations from the actual results.

9. What is the purpose of a buffer within an instrumentation amplifier?

Answer: The buffer inside the instrumentation amplifier is helpful in many ways. The buffer increases the input impedance, which is very necessary. It also eliminates the difference between two input voltages; thus, the offset voltage value gets decreased. It also affects the CMRR.

10. What are good rules of thumb for building instrumentation amplifiers?

Answer: There is no such hard and fast rules for designing or building instrumentation amplifiers. But there are some best practices. Some of them are – a) Design the circuit symmetrically, b) Implement the gain in the first stage, c) Considers the factors of CMRR, thermocouple effects and resistance values, d) Design the second stage.

11. How to remove offset voltage in the instrumentation amplifier?

Answer: The offset voltage of any amplifier is removable by feeding an adjustable current from a voltage source. A high-valued resistor should be placed between the current and the op-amp.

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Contents

• What is Integrator?
• Working principle of Integrator
• Op-amp integrator circuit
• Output of an integrator
• Derivation of Op-amp as integrator
• Practical op-amp integrator
• Applications of integrator
• What is Differentiator ?
• Op-amp as Differentiator
• Working Principle of Differentiator
• Output waveform of a differentiator
• Applications of Differentiator

What is Integrator?

Definition of Integrator

If the feedback path is made through a capacitor instead of a resistance , an RC Network has been established across the operational amplifiers’ negative feedback path. This kind of circuit configuration producing helps in implementing mathematical operation, specifically integration, and this operational amplifier circuit is known as an Operational amplifier Integrator circuit.

The output of the circuit is the integration of the applied input voltage with time.

Integrator circuits are basically inverting operational amplifiers (they work in inverting op-amp configuration, with suitable capacitors and resistors), which generally produce a triangular wave output from a square wave input. Hence, they are also used for creating triangular pulses.

Op-amp as Integrator

Working principle of Integrator

Operational amplifiers can be used for mathematical applications such as Integration and Differentiation by implementing specific op-amp configurations.

When the feedback path is made through a capacitor instead of a resistance , an RC Network has been established across the operational amplifiers’ negative feedback path. This kind of circuit configuration producing helps in implementing mathematical operation, specifically integration, and this operational amplifier circuit is known as an Operational amplifier Integrator circuit. The output of the circuit is the integration of the applied input voltage with time.

Op-amp integrator circuit

Output of an integrator

Integrator circuits are basically inverting operational amplifiers (they work in inverting op-amp configuration, with suitable capacitors and resistors), which generally produce a triangular wave output from a square wave input. Hence, they are also used for creating triangular pulses.

The current in the feedback path is involved in the charging and discharging of the capacitor; therefore, the magnitude of the output signal is dependent on the amount of time a voltage is present (applied) at the input terminal of the circuit.

Derivation of Op-amp as integrator

As we know from the virtual ground concept, the voltage at point 1 is 0V. Hence, the capacitor is present between the terminals, one having zero potential and other at potential V₀. When a constant voltage is applied at the input, it outcomes in a linearly increasing voltage (positive or negative as per the sign of the input signal) at the output whose rate of change is proportional to the value of the applied input voltage.

From the above circuitry it is observed, V₁ = V₂ = 0

The input current as:

Due to the op-amp characteristics (the input impedance of the op-amp is infinite) as the input current to the input of an op-amp is ideally zero. Therefore the current passing from the input resistor by applied input voltage V_i has flown along the feedback path into the capacitor C₁.

Therefore the current from the output side can also be expressed as:

Equating the above equations we get,

Therefore the op-amp output of this integrator circuit is:

As a consequence the circuit has a gain constant of -1/RC. The negative sign point toward an 180^o phase shift.

Practical op-amp as aintegrator

If we apply a sine wave input signal to the integrator, the integrator allows low-frequency signals to pass while attenuates the high frequencies parts of the signal. Hence, it behaves like a low-pass filter rather than an integrator.

The practical integrator still has other limitations too. Unlike ideal op-amps, practical op-amps have a finite open-loop gain, finite input impedance, an input offset voltage, and an input bias current. This deviation from an ideal op-amp can affect working in several ways. For example, if V_in = 0, current passes through the capacitor due to the presence of both output offset voltage and input bias current. This causes the drifting of the output voltage over time till the op-amp saturates. If the input voltage current is zero in case of the ideal op-amp, then no drift should be present, but it is not true for the practical case.

To nullify the effect caused due to the input bias current, we have to modify the circuit such that R_om = R₁||R_F||R_L

In this case, the error voltage will be 

Therefore the same voltage drop appears at both the positive and negative terminals because of the input bias current.

For an ideal op-amp operating in the dc state, the capacitor performs as an open circuit, and hence, the gain of the circuit is infinite. To overcome this, a high resistance value resistor R_F is connected in parallel with the capacitor in the feedback path. Because of this, the gain of the circuit is limited to a finite value (effectively small) and hence gets a small voltage error.

• V_IOS refers to the input offset voltage
• I_BI refers to the input bias current

What is Differentiator ?

Definition of Differentiator

If the input resistance in the inverting terminal is replaced by a capacitor, an RC Network has been established across the operational amplifiers’ negative feedback path. This kind of circuit configuration helps in implementing differentiation of the input voltage, and this operational amplifier circuit configuration is known as an Operational amplifier differentiator circuit.

An operational amplifier differentiator basically works as a high pass filter and, the amplitude of the output voltage produced by the differentiator is proportionate to the change of the applied input voltage.

Op-amp as a Differentiator

As we have studied earlier in the integrator circuit, op-amps can be used for implementing different mathematical applications. Here we will be studying the differential op-amp configuration in detail. The differentiator amplifier is also used for creating wave shapes and also in frequency modulators.

An operational amplifier differentiator basically works as a high pass filter and, the amplitude of the output voltage produced by the differentiator is proportionate to the change of the applied input voltage.

Working Principle of Differentiator

When the input resistance in the inverting terminal is replaced by a capacitor, an RC Network has been established across the operational amplifiers’ negative feedback path. This kind of circuit configuration helps in implementing differentiation of the input voltage, and this operational amplifier circuit configuration is known as an Operational amplifier differentiator circuit.

In a differentiating op-amp circuit, the output of the circuit is the differentiation of the input voltage applied to the op-amp with respect to time. Therefore the op-amp differentiator works in an inverting amplifier configuration, which causes the output to be 180 degrees out of phase with the input. Differentiating op-amp configuration generally responds to triangular or rectangular input waveforms.

A Differentiator Circuit

As shown in the figure, a connection of capacitor in series with the input voltage source has been made. The input capacitor C₁ is initially uncharged and hence operate as an open-circuit. The non-inverting terminal of the amplifier is connected to the ground, whereas the inverting input terminal is through the negative feedback resistor R_f and connected to output terminal.

Due to the ideal op-amp characteristics (the input impedance of the op-amp is infinite) as the input current, I to the input of an op-amp is ideally zero. Therefore the current flowing through the capacitor (in this configuration, the input resistance is replaced by a capacitor) due to the applied input voltage V_in flows along the feedback path through the feedback resistor R_f.

As observed from the figure, point X is virtually grounded (according to the virtual ground concept) because the non-inverting input terminal is grounded (point Y is at ground potential i.e., 0V).

Consequently, Vx = Vy = 0

With respect to the input side capacitor, the current carrying through the capacitor can be written as:

With respect to the output side feedback resistor, the current flowing through it can be represented as:

From the above equations when we equate the currents in both the results we get,

The differentiating amplifier circuit requires a very small time constant for its application (differentiation), and hence it is one of its main advantages.

The product value C₁R_f is known as differentiator’s time constant, and output of the differentiator is C₁R_f times the differentiation of V_in signal. The -ve sign in the equation refers that the output is 180^o difference in phase with reference to the input.

When we apply a constant voltage with one step change at t=0 like a step signal in the input terminal of the differentiator, the output should be ideally zero as the differentiation of constant is zero. But in practice, the output is not exactly zero because the constant input wave takes some amount of time to step from 0 volts to some V_max volts. Therefore the output waveform appears to have a spike at time t=0.

Therefore for a square wave input, we get something like shown in the below figure,

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