Bode plot
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A Bode plot graphically represents the frequency response of a system by plotting magnitude versus frequency and phase versus frequency. It allows approximation of the magnitude curve with straight lines, facilitating sketching of the plot without computation. This feature is lost for Bode plots in the z-domain but can be incorporated using a bilinear transformation to transform the z-plane unit circle to the w-plane imaginary axis.
Bode plot
- 1. Bode Plot
- 2. Bode plot is the graphical tool for drawing the frequency response of a system. It is represented by two separate plots, one is the magnitude vs frequency and the other one is phase Vs frequency.The magnitude is expressed in dB and the frequency is generally plotted in log scale. One of the advantages of the Bode plot in s-domain is that the magnitude curve can be approximated by straight lines which allows the sketching of the magnitude plot without exact computation. This feature is lost when we plot Bode diagram in z-domain . To incorporate this feature we use bi-linear transformation to transform unit circle of the z- plane into the imaginary axis of another complex plane, w plane, where where sampling time T = 0.1 sec
- 3. Example 1: Let us consider a digital control system for which the loop transfer function is given by
- 4. Putting we get the transfer function in w plane as
- 7. Gain margin and Phase margin