Question

Write a note on analysis of second order system using Bode Plots.

Answer 1

The Bode plot for a linear, time-invariant system with transfer function H ( s ) {\displaystyle H(s)} H(s) ( s {\displaystyle 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 | H ( s = j ω ) | {\displaystyle |H(s=j\omega )|} |H(s=j\omega )| of frequency ω {\displaystyle \omega } \omega  (with j {\displaystyle j} j being the imaginary unit). The ω {\displaystyle \omega } \omega -axis of the magnitude plot is logarithmic and the magnitude is given in decibels, i.e., a value for the magnitude | H | {\displaystyle |H|} |H| is plotted on the axis at 20 log 10 ⁡ | H | {\displaystyle 20\log _{10}|H|} 20\log _{10}|H|.

The Bode phase plot is the graph of the phase, commonly expressed in degrees, of the transfer function arg ⁡ ( H ( s = j ω ) ) {\displaystyle \arg \left(H(s=j\omega )\right)} \arg \left(H(s=j\omega )\right) as a function of ω {\displaystyle \omega } \omega . The phase is plotted on the same logarithmic ω {\displaystyle \omega } \omega -axis as the magnitude plot, but the value for the phase is plotted on a linear vertical axis.