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.

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 :

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.

Here fb is the gain limiting frequency, fb = 1/(2*pi* R1* C1) fa<fb<fc

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.

FAQ :

1. Why Capacitor is used in differentiator?

A. 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?

A. 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?

A. The differentiator is constructed from basic inverting amplifier by replacing the input resistor R1

with the input capacitor C1.

Hope, you like this. If you have any doubts regarding to the differentiator, feel free to comment.

Differentiator Using Op Amp - Study2night