# Circuit Idea/Op-amp Inverting RC Integrator

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How to Transform the Passive RC Integrator into an Active One
(Reinventing the Op-amp Inverting RC Integrator)

Circuit idea: The op-amp compensates the voltage drop across the capacitor adding as much voltage to the input voltage source as it loses across the capacitor.

Fig. 1. How do we transform the imperfect passive current-to-voltage converter into a perfect op-amp one?

## Speculation: The active version is just an improved passive one

Active RC integrator = passive RC integrator + op-amp + great idea ?

## Problem: The capacitor affects the current

The main idea is that in picture we have a constant voltage source, which, across the resistor , will drive a constant current. At the beginning, when the voltage is up, the conductor material will be a support for potential propagation and the voltage will be applied all on capacitor, but the current will be zero.If the capacitance is infinite, there will be no current in resistor, and the resistor will be connected to "wind".When the voltage reach steady state ,as the capacitor between the armature, has a finite resistence , the current will be non zero, and the resistor will be not conected in "wind" but at ground through in-between armature material.The non-zero current will drop a voltage across the resistor, and the output voltage will be the source voltage without the resistence voltage.We can replace the capacitor with a current source, which will be the present disturbance or Norton equivalent voltage source only for discharge time.We prefer the last one. Do not consider the ohmic non linear effects.

## Basic non-electrical idea: Removing a disturbance by an "antidisturbance"

Let see the polarity of disturbance in "passive" picture.The current will flow in conventional way from + wire to - wire through capacitor. As we know the output of an op-amp is a voltage source ,but it's input a current source.(Voltage source has small infinite resistence, ideally zero, but in reality fractions of ohms, even ohms).The Norton replacement of current source with voltage source series with a high resistence equal with in-between armature resistence make the op-amp feasible. The polarity in "passive" circuit for C Norton replacement with voltage source will be with + connected to minus of initial voltage source. See this link www.circuit-fantasia.com/circuit_stories/understanding_circuits/current_source/inv_op-amp_current_source/circuit1_1000.jpg

## Basic electrical idea: Removing voltage by an "antivoltage"

### Building the electric circuit

Active RC integrator = passive RC integrator + "helping" voltage source

## Op-amp inverting RC integrator

### Building the electronic circuit

Op-amp RC integrator = passive RC integrator + "helping" op-amp

## Applications of the op-amp RC integrator

Op-amp RC integrator = op-amp V-to-I converter + I-to-V C integrator

## Comparison with other techniques

Deboo integrator.