An operational amplifier (op-amp) integrator circuit is a basic analog electronic circuit that performs mathematical integration of an input voltage signal. It uses an operational amplifier, which is a high-gain, direct-coupled amplifier with differential inputs, to achieve this function.
The op-amp integrator circuit consists of a single operational amplifier, a feedback capacitor (Cf), and an input resistor (Rin). The basic schematic of the op-amp integrator circuit is as follows:
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+Vcc +Vout
| ^
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Rin -|- Non-inverting Input --|
| |
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| +-----------|---- Cf
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-|---|>|----| Op-Amp |
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| +-----------|---- GND
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GND GND
In this configuration:
The non-inverting input (+) of the operational amplifier is connected directly to ground (GND).
The inverting input (-) of the op-amp is connected through a resistor (Rin) to the input voltage signal that needs to be integrated.
The output of the op-amp (Vout) is connected through a feedback capacitor (Cf) to the inverting input (-) of the op-amp.
The operation of the op-amp integrator circuit relies on the principle that the inverting input (-) of the op-amp tries to maintain the same voltage as the non-inverting input (+). Since the non-inverting input is at ground potential (0V), the inverting input also tries to stay at 0V.
When the input voltage changes, a current flows through the resistor (Rin) into the inverting input. This current causes the voltage at the inverting input to change over time. Since the capacitor (Cf) is connected between the output and the inverting input, it charges or discharges based on the voltage difference across it. As a result, the output voltage (Vout) ramps up or down over time, effectively performing the integration of the input voltage.
The mathematical relationship between the input voltage (Vin) and the output voltage (Vout) of the op-amp integrator circuit is given by the following equation:
Vout(t) = - (1 / (Rin * Cf)) * β«Vin(t) dt
Where:
Vout(t) is the output voltage at time t.
Vin(t) is the input voltage at time t.
Rin is the input resistor value.
Cf is the feedback capacitor value.
It's essential to note that for ideal integration, the op-amp should have infinite gain and infinite input impedance, and the feedback capacitor should be large enough to avoid signal distortion and noise. However, practical integrator designs might need to consider limitations and select appropriate values for the components accordingly.