# Op-Amp Differentiator

## Applications of Operational Amplifiers in Tamil

## Differentiator

- A circuit that performs mathematical differentiation of input signal is called differentiator.
- The differentiator may be constructed from a basic inverting amplifier if an input resistor R
_{1}is replaced by a capacitor C_{1}.

Differentiator

- Since the differentiator performs the reverse of the integrator function. Thus the output V
_{0}is equal to R_{F}C_{1}times the negative rate of change of the input voltage V_{in}with time. - The –sign indicates a 180
^{o}phase shift of the output waveform V_{0}with respect to the input signal. - The gain of the circuit (R
_{F}/X_{C1}) R with R in frequency at a rate of 20dB/decade. This makes the circuit unstable. Also input impedance X_{C1s}with R in frequency which makes the circuit very susceptible to high frequency noise.

Basic differentiator

Frequency response of Differentiator

f_{a} = frequency at which the gain is 0dB and is given by

- Both stability and high frequency noise problems can be corrected by the addition of two components. R1 and CF. This circuit is a practical differentiator.
- From Frequency fa to feedback the gain Rs at 20dB/decade after feedback the gain S at 20dB/decade. This 40dB/decade change in gain is caused by the R
_{1}C_{1}and R_{F}C_{F}combinations. The gain limiting frequency f_{b}is given by,

Where R_{1}C_{1} = R_{F} C_{F}

R_{1}C_{1} and R_{F} C_{F} help to reduce the effect of high frequency input, amplifier noise and offsets.

All R_{1}C_{1} and R_{F} C_{F} make the circuit more stable by preventing the R in gain with frequency.

The input signal will be differentiated properly, if the time period T of the input signal is larger than or equal to R_{F} C_{1} (i.e) T > R_{F} C_{1} generally, the value of Feedback and in turn R_{1}C_{1} and R_{F} C_{F} values should be selected such that,

#### R_{F} C_{1} >> R_{1} C_{1}

- A workable differentiator can be designed by implementing the following steps.
- Select fa equal to the highest frequency of the input signal to be differentiated then assuming a value of C
_{1}< 1μf. Calculate the value of R_{F}. - Choose f
_{b}= 20f_{a}and calculate the values of R_{1}and C_{F}so that R_{1}C_{1}= R_{F}C_{F}.

## Uses:

- It is used in wave shaping circuits to detect high frequency components in an input signal and also as a rate of change and detector in FM modulators.

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