The formula to calculate the Magnitude of the Transfer Function (|T(jω)|) is:
\[ |T(jω)| = \sqrt{G^2 + B^2} \]
Where:
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.
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.
