Bode Plots

It is a plot of the magnitude of the open loop transfer function G(jω)H(jω) in dB and the phase of G(jω) H(jω) in degrees, both versus the frequency ω in logarithmic scale (i.e., log₁₀ ω). The diagrams are made on a semi log graph paper with linear scale for both log magnitude in dB and phase angle φ(ω) in degrees along vertical axis and a logarithmic co-ordinate for frequency ω along the horizontal axis.

The stability of the close loop system can be determined by observing the behaviour of these plots.

Although it is not possible to plot the curves at zero frequency because of the logarithmic frequency (log 0 = –∞), for this we generally plot the curve at ω = 0.1 (i.e., log 0.1 = –1) instead of zero frequency.

Before the inception of computers, Bode plots were often called the “asymptotic plots” because the magnitude and phase curves can be sketched from their asymptotic properties without detailed plotting.

Advantages of the Bode Plot

• In the absence of a computer, a Bode plot can be sketched by approximately the magnitude and phase with straight line segments (asymptotes).
• Relative stability of a close loop control system can be conveniently assessed by plotting its open loop transfer function by Bode plot method.
• Gain margin, phase margin, ωgc and ωpc are determined more easily on the Bode plot as compared to Nyquist plot.
• For design purpose, the effects of adding controller or compensators and their parameters are more easily visualized on the Bode plot as compared to Nyquist plot.

  The multiplication of magnitudes can be converted into addition (in dB). It shows both the low and high frequency characteristics of the transfer function in one diagram.

Disadvantage of the Bode Plot

Absolute and relative stability of only minimum phase systems can be determined from the Bode plot. Unlike Nyquist plot, it can’t be used for the study of stability of systems with non-minimum transfer functions.