BODE DIAGRAMS
The Bode diagrams used in the analysis of continuous-time systems are not very practical when used directly in the z-plane. This is because of the e j ωT term present in the sampled data system transfer functions when the frequency response is to be obtained. However, it is possible to draw the Bode diagrams of sampled data systems by transforming the system into the w-plane by making the substitution
where ws is the sampling frequency in radians per second. The interpretation of this is that the wt-plane and the s-plane frequencies will be approximately equal when the frequency is less than one-tenth of the sampling frequency.
We can use the transformations given in (8.10) and (8.11) to transform a sampled data system into the wt-plane and then use the standard continuous system Bode diagram analysis.
Some example Bode plots for sampled data systems are given below.
Example 8.13
Consider the closed-loop sampled data system given in Figure 8.11. Draw the Bode diagram and determine the stability of this system. Assume that T = 0.1 s.
