How to Sketch Bode Plots of First-Order Transfer Functions By Hand – Fusion of Engineering, Control, Coding, Machine Learning, and Science

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) $\begin{align*}W(s)=frac{10}{s+5}\end{align*}$

The procedure for sketching the Bode plot is:

Derive the canonical form of the transfer function
(2) $\begin{align*}W(s)=K\frac{1}{1+Ts}\end{align*}$

where $K$ and $T$ are constants
Derive a sinusoidal transfer function and write the polar form of the sinusoidal transfer function. The sinusoidal transfer function is obtained by setting $s=j\cdot \omega$ in (??).
Compute the magnitude function and phase function from the polar form of the sinusoidal function.
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)
Sketch the phase function.