Opamp Integrator

 

Opamp Integrator

 

Aim: -To design and simulate an Integrator circuit using opamp.
Components: -

Name	EDWin Components Used	Description	Number of components required
RES	RC05	Resistor	4
CAP	CASE-A600	Capacitor	1
OPAMP	741A	Comparator	1
VGEN	SMB_VGEN	Ac voltage source	1
VDC	SMB_VDC	Dc voltage source	2
GND	SMB_SPL0	Ground	5

Theory: -

A circuit in which output voltage is directly proportional to the integral of the input is known as an integrator or the integration amplifier. Such a circuit is obtained by using operational amplifier in the inverting configuration with the feedback resistor RF replaced by a capacitor, CF. Applying KCL the expression for output voltage is obtained as follows.

Since I_B is negligibly small

The current through the capacitor is related to voltage by the relation

Therefore,

However,

because A is very large. Therefore,

The output voltage can be obtained by integrating both sides with respect to time,

Therefore

where C is the integration constant and is proportional to the value of the output voltage at time seconds. Equation 4 indicates that the output voltage is directly proportional to the negative integral of the input voltage and inversely proportional to the time constant R₁C_F. For example if the input is a sine wave, the output will be a cosine wave; or if the input is a square wave output is a triangular wave.

When , the integrator works as an open loop amplifier. This is because the capacitor CF acts as an open circuit to the input offset voltage . This input offset voltage and the part of the input current charging capacitor C_F produce the error voltage at the output of the integrator. Therefore in a practical integrator, to reduce the error voltage at the output, a resistor R_F is connected across the feedback capacitor C_F. Thus R_F limits the low frequency gain and hence minimizes the variations in the output voltage. The addition of the resistor also corrects the stability and low frequency roll-off problems. Considering the frequency response the limiting frequencies are defined as follows. The frequency at which gain is 0dB is given by

The gain limiting frequency is given by

The circuit acts as an integrator in the frequency range f_ato f_bthe value of f_aand in turn R₁C_F and R_FC_F values should be selected such that f_a<f_bThus the output is proportional to the time integral of the input.

Procedure: -

EDWin 2000 -> Schematic Editor:

EDWin 2000 -> Mixed Mode Simulator:

Result: -

The output waveform may be observed in the waveform viewer.

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. 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