in which the output voltage waveform is the integral of the input voltage
waveform is the integrator or Integration Amplifier. Such a circuit is obtained
by using a basic inverting amplifier configuration if the feedback resistor RF
is replaced by a capacitor CF.
expression for the output voltage V0 can be obtained by KVL eqn at
where C integration constant A
indicates that the output is directly proportional to the negative integral of
the input volts and inversely proportional to the time constant R1 CF
the input is sine wave -> output is cosine wave.
input is square wave -> output is triangular wave.
waveform with assumption of R1Cf = 1, Vout =0V
(i.e) C =0.
= 0 the integrator works as an open loop amplifier because the capacitor CF
acts an open circuit to the input offset voltage Vio.
offset voltage Vio and the part of the input are charging capacitor
CF produce the error voltage at the output of the integrator.
Integrator to reduce the error voltage at the output, a resistor RF
is connected across the feedback capacitor CF.
limits the low frequency gain and hence minimizes the variations in the output
voltages. The frequency response of the basic integrator, shown from this fb is
the frequency at which the gain is dB and is given by,
stability and low frequency roll-off problems can be corrected by the addition
of a resistor RF in the practical integrator.
-> refers to a constant gain as frequency of an input signal is varied over
a certain range.
frequency -> refers to the rate of decrease in gain roll off at lower
fig of practical Integrators,
f is some
relative operating frequency and for frequencies f to fa to gain RF
/ R1 is constant. After fa the gain decreases at a rate
of 20dB/decade or between fa and fb the circuit act as an
the value of fa and in turn R1 CF and RF
CF values should be selected such that fa<fb.
In fact, the input signal will be integrated properly if the time period T of
the signal is larger than
RF CF, (i.e) T >= RF CF @@@@ 6
commonly used in analog computers.
wave shaping circuits.