Dear Dennis...
EN-Genius Network's Dennis Feucht answers your design
queries in his new Circuit Design Clinic!
August, 2008
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EN-Genius Network presents a new, interactive
analog design service to readers! Send us your design questions (with
relevant data; schematics in JPEG or GIF, please) for some free
engineering advice from EN-Genius Network's circuit
consultant, Dennis Feucht, on how you might solve a design problem or
improve circuit performance. Submissions may be edited for clarity or
brevity, and submitters and their email addresses will remain anonymous
(unless otherwise indicated). Please send your questions to Dennis here.
Design Techniques For New Engineers
From s to z: the Complex-Frequency Domain
by Dennis L Feucht
This article ventures into the discrete complex-frequency domain, with its discrete complex frequency denoted as z. We start with the polar form of s and introduce the definition of z. Only a few decades ago, this was the specialized area of DSP, but now DSP is in the mainstream of what an electronics engineer needs to know. DSP waveforms are discrete in time but still continuous, or analog, in value. Digital waveforms are both discrete in time and value.
The behavior of switching circuits is characterized by discrete time intervals. Usually, the basic time interval is a regular interval that is the switching period, Ts. The switching frequency is fs = 1/Ts. Successive periods of a discrete-time waveform, x(t), can be expressed in the continuous complex-frequency domain of s as x(t) delayed by successive integer multiples, n, of Ts, or as x(t − n∙Ts). In the s-domain these delays are Laplace-transformed.
...download complete article here (494 KB PDF)
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