Magnitude of Transfer Function Calculator

Calculate Magnitude of Transfer Function



Formula

The formula to calculate the Magnitude of the Transfer Function (|T(jω)|) is:

\[ |T(jω)| = \sqrt{G^2 + B^2} \]

Where:

Magnitude of Transfer Function Definition

The magnitude of a transfer function, in the field of control systems engineering, refers to the absolute value of the output signal in relation to the input signal. It is a measure of how much the system amplifies or attenuates the input signal. This is typically represented as a function of frequency, with the magnitude often expressed in decibels. The magnitude of the transfer function provides crucial information about the system’s stability and performance.

Example Calculation

Let's consider an example:

Using the formula to calculate the Magnitude of the Transfer Function:

\[ |T(jω)| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{dB} \]

This demonstrates that with a real part of 3 and an imaginary part of 4, the magnitude of the transfer function would be 5 dB.