Opamp Differentiator

   Aim

   To design and simulate a Differentiator circuit using opamp.

   Components

 Theory

   A circuit in which output waveform is the derivative of the input waveform is known as the differentiator or the differentiation amplifier. Such a circuit is obtained by using operational amplifier in the inverting configuration connecting a capacitor, C₁ at the input. Applying KCL the expression for output voltage is obtained as follows.

Since

    But because A is very large. Therefore

   Thus the output v_o is equal to R_FC₁ times the negative instantaneous rate of change of the input voltage v_in with time. The gain of the circuit increases with increase in frequency at a rate of 20 dB/decade. This makes the circuit unstable. Also the input impedance X_C1 decreases with increase in frequency which makes the circuit susceptible to high frequency noise. When amplified the noise can completely override the differentiated output signal. The frequency at which gain is zero dB is given by

   The stability and high frequency noise problems can be corrected by the addition of two components:- R₁ and C_F. The gain limiting frequency f_b isgiven by

  R₁C_F and R_FC_F make the circuit more stable by preventing the increase in gain with frequency. The value of f_b and in turn R₁C₁ and R_FC_F values should be selected such that f_a<f_b<f_c where

   and f_c is the unity gain bandwidth of the opamp. Thus the input signal will be differentiated properly if the time period of the input signal is larger than or equal to R_FC₁

   i.e. .

   Procedure

   EDWinXP -> Schematic Editor: The circuit diagram is drawn by loading components from the library. Wiring and proper net assignment has been made. The values are assigned for relevant components.

   EDWinXP> Mixed Mode Simulator: The circuit is preprocessed. Waveform markers are placed at the input and output of the circuit. GND net is set as reference net. The Transient Analysis parameters have been set. The Transient Analysis is executed and output waveform is observed in the Waveform Viewer.

   Result

   The output waveform may be observed in the waveform viewer.