An s-Plane to z-Plane Mapping Example
While surfing around the Internet recently I encountered the 's-plane to z-plane mapping' diagram shown in Figure 1. At first I thought the diagram was neat because it's a good example of the old English idiom: "A picture is worth a thousand words." However, as I continued to look at Figure 1 I began to detect what I believe are errors in the diagram.
Reader, please take a few moments to see if you detect any errors in Figure 1.
Figure 1: One (incorrect) Internet 's-plane to z-plane
I have drawn what I think is a corrected version of Figure 1. Given the various loci of points in Figure 1's s-plane, my version of a correct 's-plane to z-plane mapping' diagram shown in Figure 2.
Figure 2: Corrected 's-plane to z-plane mapping' diagram.
Hopefully my Figure 2 is worth 1001 words. If there are any errors in that figure I hope a perceptive reader lets me know.
Your phrase " The angle of departure from z = 1" makes no sense to me because the constant damping factor locus of points (circular light purple curve) on the z-plane does NOT intersect the z = 1 point.
Hi. Thanks to useful picture. But the bilinear transform is conformal transform, so angle between dark-purple and blue / dark-purple and green must be 45 degrees, as in source picture.
I'm sorry itxs. I don't understand what "angle between dark-purple and blue / dark-purple and green must be 45 degrees, as in source picture" means.
Great diagram. I teach a course in digital control and students tend to struggle with s to z-plane mapping. Picture definitely worth 100 words. Especially like the units of the jw in terms of pi which seems more understandable that units of ws. Thanks for sharing
To post reply to a comment, click on the 'reply' button attached to each comment. To post a new comment (not a reply to a comment) check out the 'Write a Comment' tab at the top of the comments.
Registering will allow you to participate to the forums on ALL the related sites and give you access to all pdf downloads.