# Integral Receiver Amplifier (OPAMP) / The Integrator Amplifier

In this article, we will discuss Integral Receiver Amplifier (OPAMP) / The Integrator Amplifier. Transactional amplifiers can be used as part of a positive or negative feedback amplifier using only pure resistors in both the input and feedback loop, or as a collector or extractor type circuit.

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By replacing this feedback resistance with a capacitor, we have an RC Network connected to the feedback path of transactional amplifiers, producing another type of transactional amplifier circuit, often called the Op-amp Integral Receiver circuit, as shown below.

## Integral Receiver Op-amp Circuit

As the name suggests, the Integral Receiver Op-amp is a transactional amplifier circuit that performs the mathematical process of integration. In other words, since the Integral Receiver op-amp produces an output voltage, we can ensure that the output responds to changes in input voltage over time. is proportional to the integral of the input voltage.

In other words, the size of the output signal is determined by the time that a voltage is present at the input when charging or emptying the capacitor when the current passing through the feedback loop occurs, when the necessary negative feedback occurs through the capacitor.

One step voltage, when the Vin is first applied to the input of an integrated amplifier, the load-free capacitor C has very little resistance. It acts as a short circuit that allows maximum current to flow through the input resistance. The current does not flow into the amplifier input, and point X is a virtual world that results in zero output. Since the capacitor's impedance is very low at this point, the gain rate of XC/RIN is also very small, and the total voltage gain is less than one (voltage tracker circuit).

As a feedback capacitor, C begins to charge under the influence of input voltage. Its impedance (Xc) gradually increases in proportion to the charging speed. The capacitor charges at a speed determined by the RC time constant ( τ ) of the serial RC network.

Since the capacitor is connected between the inverting input of the op-amp (which has virtual soil potential) and the output of the op-amp (now negative), the potential voltage developed along the capacitor gradually increases the Vc and causes the charging current to decrease. As the capacitor's impedance increases, this capacitor produces a linearly increased ramp output voltage that continues to increase until fully charged, resulting in an increased Xc/Rin ratio.

At this point, the capacitor acts as an open circuit that blocks more DC current flow. The ratio of the feedback capacitor to input resistance (XC/RIN) is now infinite, resulting in infinite gain. The result of this high gain (similar to the open loop gain of op-amps) is that the output of the amplifier goes to saturation, as shown below. (Saturation occurs when the amplifier's output voltage is violently released into one voltage supply track or another with little or no control between them).

The rate at which the output voltage rises (change rate), resistance and the value of the capacitor are determined by the "RC time constant". By changing this RC time constant value, changing either Capacitor (C) or Resistance (R), for example, the time it takes for the output voltage to reach saturation can also be changed.

If we apply an ever-changing input signal, such as a square wave, to the input of an Integral Receiver Amplifier, the capacitor charges and discharges in response to changes in the input signal. The output of this output signal results in the resistance/capacitor combination being a saw tooth waveform affected by the RC time constant. Because at higher frequencies, there is less time for the capacitor to fully charge. This type of circuit is also known as Ramp Generator and the transfer function is given below.

## Integral Receiver Op-amp Ramp Generator

We know from the first principles that the voltage on the plates of a capacitor is equal to dividing the load on the capacitor into the Q/C emitter capacitance. Then the voltage output on the capacitor is Vout. Therefore: -Vout = Q/C. If the capacitor charges and discharges, the charge rate of the voltage on the capacitor is given as follows:

However, dQ/dt is an electric current, and since the node voltage of the integrative op-amp in the inverting input terminal is zero, since X = 0, the input current flowing from the input resistance is given as follows:

The current passing through the feedback condenser C is given as follows:

Assuming that the input impedance of the op-amp is infinite (ideal op-amp), the current does not flow into the op-amp terminal. Therefore, the node equation in the inverted input terminal is given as follows:

Here's how we get the ideal voltage output for the Integral Receiver Op-amp:

To simplify the mathematics a little, this can also be rewritten as follows:

Where: ω = 2πε and output voltage Vout, input voltage is 1/RC times the integrator of vin over time.

Thus, the circuit has the transfer function of an inverter integrator with a gain constant of -1/RC. The minus sign ( – ) indicates a phase shift of 180o, as the input signal is directly connected to the inverter input terminal of the operational amplifier.

## AC or Continuous Integral Receiver Op-amp

If we replace the above square wave input signal with that of a changing frequency sine wave, the Op-amp Integrator performs less like an integrator. It begins to act more like an active "Low Pass Filter". It passes low-frequency signals while weakening high frequencies.

At zero frequency (0Hz) or DC, the capacitor acts as an open circuit due to its colorance, thereby preventing any output voltage feedback. As a result, very little negative feedback is provided from the output to the entrance of the amplifier.

Therefore, with only a single capacitor C in the feedback path, the op-amp at zero frequency is effectively connected as a normal open loop amplifier with very high open loop gain. This causes the op-amp to become unstable, causing unwanted output voltage conditions and possible voltage rail saturation.

This circuit binds a high-value resistance in parallel with a capacitor, which is constantly charging and discharging. The addition of R2 along capacitor C of this feedback resistance gives the properties of an inverter amplifier with finiting closed-loop voltage gain given to the circuit by R2/R1.

As a result, this feedback resistance shorts out R2 due to the effects of capacitive reassurance, which reduces amplifier gain at high frequencies. While at normal operating frequencies the circuit acts as a standard integrator, at very low frequencies approaching 0Hz, when there is an open circuit due to C recess, the magnitude of the voltage gain is limited and controlled by the following ratio: R2/R1.

## DC Gain Controlled AC Integral Receiver Op-amp

Unlike the DC integrator amplifier, whose output voltage will be integral to a waveform at any given moment, the output waveform will be triangular when the input is square wave. Also, when the input is triangular, the output waveform is also sinusoidal. This then forms the basis of the Active Low Pass Filter, as previously seen in the filters section tutorials given as corner frequency.