Converting Domains; Converting From The S-Domain To The Z-Domain - HP 3563A Operating Manual

Synthesis

Converting Domains

Converting Domains
The H P 3563A allows you to convert a synthesis table from the s domain to the z domain, and
vice-versa. To do this, press
17-1). Only one of these soflkeys is displayed, depending upon the selected domain. CONVRT TO Z
is displayed if the s-domain is selected; CONVRT TO S is displayed if the z-domain is selected. The
synthesis table can be in any data format before performing a domain conversion.
The analyzer displays SYNTH TABLE CONVERSION as it converts the synthesis
Note
table from one domain to another. In the case of the step invariance transform, this
message appears and disappears several times before the conversion completes.
Furthermore, converting between the s and z domains changes the contents of the
target synthesis table. Moving between the s and z domains (by selecting the
domain with the DOMAIN S Z softkey) does not affect the contents of the synthesis
table.
Additional examples are available in chapter 4 of the HP 3563A Getting Started
Guide.

Converting From the s-Domain to the z-Domain

The HP 3563A lets you convert s-domain synthesis tables into z-domain synthesis tables, and
vice-versa. The CONVRT TO Z softkey lets you convert an s-domain synthesis table into a z-domain
synthesis table; the CONVRT TO S softkey lets you convert a z-domain synthesis table into an
s-domain synthesis table. The CONVRT TO Z softkey appears if you are in the z domain; the
CONVRT TO S softkey appears if you are
softkey; see figure 17-1).
There is no perfect way to go between the s and
repeats every multiple of the sample frequency to produce a periodic frequency response. An
analog filter frequency-response is non-periodic. The HP 3563A provides the most popular
used
transforms by digital designers to transform analog designs into digital approximations. The
three methods available are:
•
Impulse Invariance Transformation
•
Step Invariance Transformation
•
Bilinear Transformation
If you start with a stable H(s), these three methods provide a stable digital filter design by mapping
left-half s-plane poles inside the unit circle of the z-domain.
1 7-48
followed by CONVRT TO S or CONVRT TO Z (see figure
SYNTH
in the s domain (as determined by the
domain. A digital filter frequency-response
z
DOMAIN S Z