# Closed-loop transfer function

A **closed-loop transfer function** in control theory is a mathematical expression (algorithm) describing the net result of the effects of a closed (feedback) loop on the input signal to the circuits enclosed by the loop.

## Overview

The closed-loop transfer function is measured at the output. The output signal waveform can be calculated from the closed-loop transfer function and the input signal waveform.

An example of a closed-loop transfer function is shown below:

The summing node and the *G*(*s*) and *H*(*s*) blocks can all be combined into one block, which would have the following transfer function:

## Derivation

We define an intermediate signal Z shown as follows:

Using this figure we write:

## References

This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

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