In the above equation, the output is - times the integral of the input voltage, where the term (R 1 * C f) is known as the time constant of the integrator. Integrating both the sides of the above equation, I = C f = -C f Įquating the above two equations of I, we get, Since the input current to an op-amp is ideally zero, the current flowing through the input resistor, due to Vin, also flows through the capacitor C f.įrom the input side, the current I is given as,įrom the output side, the current I is given as, Node X will also be at ground potential, due to the virtual ground. Output Voltage Calculationįrom the circuit, it is seen that node Y is grounded through a compensating resistor R 1. The rate of change of the output voltage is proportional to the value of the applied input voltage. If a constant positive voltage (DC) is applied to the input of the integrating amplifier, the output voltage will fall negative at a linear rate, in an attempt to keep the inverting input terminal at ground potential.Ĭonversely, a constant negative voltage at the input results in a linearly rising (positive) voltage at the output. Hence, the output voltage is ideally zero. If the input voltage is 0 V, there will be no current through the input resistor R 1, and the capacitor is uncharged. The negative feedback to the inverting input terminal ensures that the node X is held at ground potential (virtual ground). Ideal Operational Amplifier Integrator CircuitĪn operational amplifier integrator circuit produces an output voltage which is proportional to the area (amplitude multiplied by time) contained under the waveform.Īn ideal op-amp integrator uses a capacitor C f, connected between the output and the op-amp inverting input terminal, as shown in the figure below. Integrating circuits have frequency limitations while operating on sine wave input signals. Integrator circuits are usually designed to produce a triangular wave output from a square wave input. Op-amp differentiating and integrating circuits are basically inverting amplifiers, with appropriately placed capacitors. An active integrator provides a much lower output resistance and higher output voltage than it is possible with a simple RC circuit. A passive integrator is a circuit which does not use any active devices like op-amps or transistors but only passives like resistors and capacitors.Īn integrator circuit, which consists of active devices is called an Active Integrator. In an integrating circuit, the output is the integration of the input voltage with respect to time. Operational amplifier can be configured to perform calculus operations such as differentiation and integration. Ideal Operational Amplifier Integrator Circuit.
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