How to Sketch Bode Plots of First-Order Transfer Functions By Hand

In this control engineering and control theory tutorial, we explain how to sketch the Body plot of a first-order transfer function function.

In particular, we consider this example:

(1)  

The procedure for sketching the Bode plot is:

1. Derive the canonical form of the transfer function
   

   (2)  

   
   where and are constants
2. Derive a sinusoidal transfer function and write the polar form of the sinusoidal transfer function. The sinusoidal transfer function is obtained by setting in (??).
3. Compute the magnitude function and phase function from the polar form of the sinusoidal function.
4. Compute the log-magnitude function from the magnitude function, and sketch it by sketching the elementary functions. While sketching, identify the break frequency (corner frequency)
5. Sketch the phase function.

The YouTube tutorial explaining these steps is given below.