Learning Objectives:

1. Construct a Bode plot that shows both magnitude and phase shift as functions of transfer function input frequency.

A Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. Both quantities are plotted against a horizontal axis proportional to the logarithm of frequency. Given that the decibel is itself a logarithmic scale, the Bode amplitude plot is log–log plot, whereas the Bode phase plot is a lin-log plot.
The Bode plot for a linear, time-invariant system with transfer function \(H(s)\) (s being the complex frequency in the Laplace domain) consists of a magnitude plot and a phase plot.
The Bode magnitude plot is the graph of the function \(\vert H(s = j\omega) \vert\) of frequency \(\omega\) (with j being the imaginary unit). The \(\omega\)-axis of the magnitude plot is logarithmic and the magnitude is given in decibels, i.e., a value for the magnitude \(\vert H \vert\) is plotted on the axis at \(20 \log_{10} \vert H \vert\).
The Bode phase plot is the graph of the phase of the transfer function in degrees plotted logarithmically as a function of \(\omega\).

Solved Example: 9963-01

When the gain margin is positive and phase margin is negative, the system is: (DFCCIL Executive Electrical 2018)

A. Unstable

B. Highly stable

C. Oscillatory

D. Stable

Correct Answer: A

Solved Example: 9963-02

The transfer function of a system is \(\dfrac{{10\left( {1 + 0.2s} \right)}}{{\left( {1 + 0.5s} \right)}}\)

A. -0.2 and -0.5

B. 5 and 2

C. -5 and -2

D. 0.2 and 0.5

Correct Answer: B

Solved Example: 9963-03

Slope of the asymptote in Bode plot for a second-order system is: (LMRC Assistant Manager Electrical- 2018)

A. 18 dB per octave

B. 6 dB per octave

C. 3 dB per octave

D. 12 dB per octave

Correct Answer: D

Solved Example: 9963-04

A system is _______ when gain margin is positive whereas the phase margin is negative. (PSTCL JE EE Oct 2016)

A. Stable

B. Unstable

C. Probabilistic

D. Undetermined

Correct Answer: B