DIFFERTIATORA circuit which produced the differentiation of input at its output is called as differentiator

There are two types of differentiator Ideal differentiator Practical differentiator

Ideal differentiator

The active differentiator circuit can be obtained by exchanging the position of resistor R and capacitor C in the basic active integrator circuit.

The op-amp differentiator circuit as shown in fig

.

Fig. Ideal Active Op-amp differentiator

VA=VB=0

Apply KCL

I1=CI ddt (VIN-VA) …... eq. 1.

If=V A−VoR f ..… eq. 2.

Equating 1 & 2eq.

C1ddt (Vin-VA)=VA−Vo

Rf

VA=0

C1 ddt Vin =

VoRf

Vo=-RfC1ddt Vin

This indicates that output is directly proportional to the C1Rf

times the differentiation of the input and product C1Rf is called as time constant differentiator.

Disadvantages of an Ideal Differentiator

The gain of differentiator increases as the frequency increases. Thus at some high frequency the differentiator may become unstable and break into the oscillation. There is possibility that of op-amp may go into the saturation

Also the input impedance decreases as the frequency increases. This make the circuit very much sensitive to the noise. Thus when such noise gets amplified due to high gain at high frequency, noise may completely override the differentiated output.

Hence the differentiator circuit suffers from the limitations on its stability and noise problems, at high frequencies. These problems can be corrected using some additional parameters in the basic differentiator circuit. Such a differentiator circuit is called as practical differentiator circuit.

Practical differentiatorThe noise and stability at high frequency can be

corrected, in the practical differentiator circuit using the resistance R1 in series with C1 and the capacitor Cr in parallel with resistance Rf .

The circuit is shown in the figure. The resistance Rcomp

is used for bias compensation.

Equation of gain

|A|=ffa

1+(ffb

)2

Where fa & fb are two break frequencies.

Fa=1

2π RfC1

Fb=1

2π R1C1

Step to design practical differentiator:-

Select Fa as the highest frequency of input signal & it is

given by Fa=1

2π RfC1

Select value of capacitor C1 below 1µF and calculate Rf

Let Fb =10Fa where, Fb=1

2π R1C1

Finally R1C1=RfCf and Rcomp=R1||Rf

EXAMPLE

Design a practical differentiator circuit that will differentiate an input signal with the fmax=100Hz

Given data :

Fa=100Hz

C1=0.1µf

Fa=1

2π RfC1

Rf= 1

2π∗100∗0.1∗10−6

Rf=15.91*103

Rf=15.91KHz

Let , Fb =10Fa

=10*100

=1000Hz

Fb=1

2π R1C1

R1= 12π FbC 1

R1= 1

2π∗1000∗0.1∗10−6

R1=1.59¿103

R1=1.59KHz

R1C1=RfCf

1.59¿103*0.1∗10−6=15.91*103*Cf

Cf=1.59¿103∗0.1∗10−6

15.91∗103

Cf=9.9937*10−9F Rcomp=R1||Rf

Rf=15.91KHz

=R1∗RfR1+Rf

=1.59¿103∗15.91∗103

1.59¿103+15.91∗103

Rcomp=1.44*103