Cutoff Frequency from Transfer Function

by Posted on

How to Find Cutoff Frequency

There are many methods by which cutoff frequency can be calculated.

Ezoic

Cutoff Frequency from Transfer Function

The frequency response of a circuit, affected by varying sinusoidal source frequencies, is analyzed using a transfer function. This function is the ratio of the output to input voltage, expressed in the s domain.

 

  \begin{equation*} H(s)=\frac{V_{0}(s)}{V_{i}(s)} \end{equation*}

 

When using a sinusoidal source, the transfer function will be given as the magnitude and phase of the output voltage to the magnitude and phase of the input voltage in a circuit. In such a case, j\omega will be used instead of s.

 

  \begin{align*} H(s)=\frac{V_{0}(j\omega)}{V_{i}(j\omega)} \end{align*}

 

For example, consider the transfer function

 

  \begin{align*} H(s)=\frac{20(s+10)}{s+100)} \end{align*}

 

To obtain the corner frequency from the above equation, H(s) can be replaced as

 

(1) \begin{align*} H(s)=\frac{2(1+s/10))}{1+(s/100))} \end{align*}

Ezoic

 

 

(2) \begin{align*} 2(1+(s/10)) \frac{1}{(1+(s/100))}\equiv H_{1}(s)H_{2}(s) \end{align*}

 

So, from this equation, the corner frequency is calculated as \omega_{01}(s)=10 rad/s and \omega_{02}(s)=100 rad/s. In order to choose the range of frequencies, we must consider the values of corner frequency.

Cutoff Frequency from Bode Plot

Ezoic

This graph is essential in control engineering to assess system stability. It features two plots: the Bode magnitude plot, showing response magnitude in decibels, and the phase plot, detailing phase shifts in degrees.

In the Bode plot, the corner frequency is defined as the frequency at which the two asymptotes meet each other or cut each other.

The transfer function H(s)=\frac{V_{0}(s)}{V_{i}(s)} of a system carries extensive information about the gain and stability of the system. Bode plots give an estimated picture of a given
H(s) from which a fair idea of the gain of the system and its stability properties can be
achieved.

Bode Plot
Example of a Bode Plot

Published by howdy