In this Article, we will learn about the differentiator using op amp and how differentiator is used as a op amp . Also we will learn more about its applications and its disadvantages. Also we will check about the reasons for how is the differentiator became as practical differentiator.
.jpeg "differentiator output Waveforms")
Differentiator using op amp :-
Definition :
Differentiator is a circuit in which the output voltage waveform is the differentiaton of the applied input signal.
The differentiator circuit is obtained by using a basic inverting amplifier configuration if input resistance is replaced by capacitor C1.
Also Read : Integrator using operational amplifier
Circuit Diagram :
The input Signals are applied to the capacitor C1. At low frequency, the reactance of the capacitor is high resulting a low gain and low output voltage from op amp.
At high frequencies, the reactance of the capacitor is much less resulting in a higher gain and higher output voltage from the differentiator amplifier.
The capacitor blocks C1 at input blocks only DC. The circuit can be analyzed by applying kirchoff 's current law at node V2.
At node V2,
ic = ib + if ----(1)
ib = 0 ( ideal case )
if >> ib ( in practical case )
By Connecting Compensation resistor Rom at non-inverting terminal, it is possible that ib = 0.
Hence, ic = if ---- (2)
ic is the current passing through capacitor C1 in the circuit .
ic = C1*d/dt ( Vin )
if = V2 - V0 / Rf in the circuit
From, ic = if ( condition )
=> C1*d/dt ( Vin ) = V2-V0/ Rf ----(3)
In the Circuit, Vid = 0
Vid = V1-V2 = 0
V1 = V2
In the Circuit, Non Inverting terminal is connecting to the ground So, V1= 0.
Once V1=0, => V2 = 0
Therefore, put V2=0, in the equation (3)
Therefore, C1* d/dt (Vin) = -Vo/Rf
The output voltage formula Vo = -(Rf)*(C1)*d/dt(Vin) .
Therefore, the output signal voltage (Vo) in the above differentiator circuit is proportional to
derivative of input signal voltage Vin with respect to time t.
- The differentiator performs reverse of the integrator's function.
- A Cosine Wave input will produce a sine wave output.
- A triangular wave output will produce a square wave output.
Input & Output Waveforms :
.jpeg "differentiator output Waveforms")
Drawbacks:
1. Unstability:
The gain of the circuit increases with increase in frequency at a rate of 20db/decade.
This makes circuit unstable.
2. High Frequency Noise:
The input impedance XC1 decreases with increase in frequency which makes circuit very
susceptible to high frequency noise.
Both the stability and high frequency noise problems can be controlled by the addition of
two components a resistor R1 in series to capacitor C1 and a capacitor Cf parallel to Rf
(Feedback Capacitor) are connected to basic differentiator circuit is the practical differentiator.
Practical Differentiator :
Frequency Response :
- The frequency response of the basic differentiator is fa = 1/(2*pi* R1* C1)
- f to fb the gain increases at 20 db/decade.
- Frequency f>fb gain decreases at 20 db/decade.
fc is the unity gain bandwidth of op amp.
Applications:
1. Differentiators are used in wave shaping circuits to detect high frequency components in
an input signal.
2. Differentiator is used as a rate of change detector in FM Modulator.
3. Edge detection in pulse circuits.
4. Used in analog computers to solve differential equations.
5. Used in control systems for rate error correction.
6. Used in signal processing for slope detection.
Also Read : Integrator using operational amplifier
FAQ :
1. Why Capacitor is used in differentiator?
The Capacitor is used in differentiator because it blocks the DC content if anything is present.
So the output voltage is zero. Hence the Capacitor allows AC type input voltage and dependent on
the frequency of input signal.
2.What is the purpose of differentiator?
The Output of the differentiator is the derivative of input signal over a frequency range based on
Circuit time constant and bandwidth of the amplifier. The input signal is applied to the inverting
input so the output is inverted relative to the polarity of the input signal.
3.Why we call it as differentiator and What factor makes the differentiator?
The differentiator is constructed from basic inverting amplifier by replacing the input resistor R1
with the input capacitor C1.
4. What is practical differentiator?
A practical differentiator is a modified version of basic differentiator where a resistor is added in series with capacitor and a capacitor is added in feedback path to improve stability and
reduce noise.
reduce noise.
5. What is the difference between integrator and differentiator?
An integrator produces output proportional to the integral of input signal, while differentiator
produces output proportional to derivative of input signal. Integrator acts like low-pass filter, while differentiator behaves like high-pass filter.
An integrator produces output proportional to the integral of input signal, while differentiator
produces output proportional to derivative of input signal. Integrator acts like low-pass filter, while differentiator behaves like high-pass filter.
Hope, you like this. If you have any doubts regarding to the differentiator, feel free to comment.