10-08-2013, 12:30 PM
The Op-amp Integrator Amplifier
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If we were to change the purely resistive ( Rƒ ) feedback element of an inverting amplifier to that
of a frequency dependant impedance, ( Z ) type complex element, such as a Capacitor, C. What
would be the effect on the output voltage? By replacing this feedback resistance with a capacitor
we now have an RC Network across the operational amplifier producing an Op-amp Integrator
circuit as shown below.
Op-amp Integrator Circuit
As its name implies, the Op-amp Integrator is an operational amplifier circuit that performs the
mathematical operation of Integration, that is we can cause the output to respond to changes in
the input voltage over time. The integrator amplifier acts like a storage element that "produces a
voltage output which is proportional to the integral of its input voltage with respect to time". In
other words the magnitude of the output signal is determined by the length of time a voltage is
present at its input as the current through the feedback loop charges or discharges the capacitor
as the required negative feedback occurs through the capacitor.
When a voltage, Vin is firstly applied to the input of an integrating amplifier, the uncharged
capacitor C has very little resistance and acts a bit like a short circuit (voltage follower circuit)
giving an overall gain of less than one. No current flows into the amplifiers input and point X is a
virtual earth resulting in zero output. As the feedback capacitor C begins to charge up, its
reactance Xc decreases this results in the ratio of Xc/Rin increasing producing an output voltage
that continues to increase until the capacitor is fully charged.
Ramp Generator
We know from first principals that the voltage on the plates of a capacitor is equal to the charge
on the capacitor divided by its capacitance giving Q/C. Then the voltage across the capacitor is
output Vout therefore: -Vout = Q/C. If the capacitor is charging and discharging
The AC or Continuous Op-amp Integrator
If we changed the above square wave input signal to that of a sine wave of varying frequency the
Op-amp Integrator performs less like an integrator and begins to behave more like an active
"Low Pass Filter", passing low frequency signals while attenuating the high frequencies.
At 0Hz or DC, the capacitor acts like an open circuit blocking any feedback voltage resulting in
very little negative feedback from the output back to the input of the amplifier. Then with just the
feedback capacitor, C, the amplifier effectively is connected as a normal open-loop amplifier
which has very high open-loop gain resulting in the output voltage saturating.
This circuit connects a high value resistance in parallel with a continuously charging and
discharging capacitor. The addition of this feedback resistor, R2 across the capacitor, C gives the
circuit the characteristics of an inverting amplifier with finite closed-loop gain of R2/R1. The
result is at very low frequencies the circuit acts as an standard integrator, while at higher
frequencies the capacitor shorts out the feedback resistor, R2 due to the effects of capacitive
reactance reducing the amplifiers gain.