Opamp Differentiator
Aim
To design and simulate a Differentiator circuit using opamp.
Components
Name

EDWin Components Used 
Description 
Number of components
required 
RES 
RC05 
Resistor 
4 
CAP 
CASEA600 
Capacitor 
2 
OPAMP 
741A 
Comparator 
1 
VGEN 
VGEN 
Ac voltage source 
1 
VDC 
VDC 
Dc voltage source 
2 
GND 
SPL0 
Ground 
5 
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, C_{1} 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_{F}C_{1}
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: R_{1} and C_{F}. The gain
limiting frequency f_{b} isgiven by
R_{1}C_{F} and R_{F}C_{F}
make the circuit more stable by preventing the increase in gain with frequency. The value
of f_{b} and in turn R_{1}C_{1}
and R_{F}C_{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_{F}C_{1}
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.