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Genesys S/Filter Software
Directly Synthesizes Filters with
Arbitrary Transmission Zero
Placement

White Paper



The Agilent Genesys S/Filter synthesis program accepts
design specifications from the user and directly synthe-
sizes arbitrary custom filter schematic solutions.


Beyond `Look-up' design approach
Many electronic circuit synthesis programs today use a
"look-up" approach to design. This technique involves fit-
ting a preexisting schematic to the user's design criteria.

Over the years, hundreds of designs have been calculated,
and these designs can be frequency-and impedance-scaled
to fit many different scenarios. This technique usually
works well -- unless an engineer needs a slightly different
topology than the existing ones, or when a finite transmis-
sion zero needs to be added to an existing schematic to
notch-out an unwanted frequency. In the past, engineers
would often take a preexisting design, add some custom-
izing elements to it and launch a linear optimizer to recover
the desired network response. This approach requires
more of the engineer's time, and the engineer must often
settle for a nonoptimal response.
Genesys S/Filter synthesis program directly synthesizes
schematic solutions based on user input.
Direct synthesis
A filter's transfer function can be represented as a ratio of
S/Filter uses a technique called direct synthesis that sums of products, or as a ratio of products of sums:
does not suffer from these weaknesses. Contrary to the
"look-up" approach described above, direct synthesis takes
the user's design criteria, forms a purely mathematical
representation -- a transfer function -- and extracts a
schematic.
Figure 1. Solutions for the Chebyshev bandpass example Figure 2. Solutions for the Chebyshev bandpass example
with series elements first with shunt elements first


Using the products-of-sums representation, the equivalent S/Filter extracts a permutation in order from left to right
filter network can be obtained by extracting one product at (from the source to the load). The six permutations for
a time, where each successive product represents some the Chebyshev bandpass example correspond to the six
combination of circuit elements. S/Filter adds functionality schematics shown in Figure 1, when using the "series ele-
over existing direct synthesis programs by automating the ment first" option. The schematics shown in Figures 1 and
element extraction process and by providing high level 2 have been labeled to indicate what type of transmission
schematic customization tools and transform capabilities. zero each element represents. For example, a series capac-
itor blocks DC and therefore represents a DC transmission
The transfer function can generally be realized by extract-
zero. Notice that several of the schematics in Figure 1 are
ing pieces in any order, with each extraction sequence
identical except for the resonator element ordering (#3 and
generating a different schematic. For example, consider
#5). S/Filter automatically detects this redundancy, and
a second order (4th degree) Chebyshev bandpass filter.
for this example reports that there are only three "unique"
There are two zeros at DC, two zeros at infinity, and no
permutations. If the "Series Element First" option in S/
finite transmission zeros, giving a total of four zeros. The
Filter is unchecked, another array of filters is generated.
number of permutations for this filter is shown by the
The unique solutions with a shunt element first are shown
equation shown below.
in Figure 2 above.

(Total # Zeros)!
#Permutations = _____________________________________
(#DC Zeros)!(#Infinite Zeros)!(# Finite Zeros)!

4! 24
= _____ = __ = 6
2!2!0! 4


Thus, there are six permutations of the four transmission
zeros:

1. DC DC
2. DC DC
3. DC DC
4. DC DC
5. DC DC
6. DC DC



2
For many filters, hundreds, and in some cases, thousands of different filter schematics can be generated for a single set of
design criteria, with each schematic having the exact desired response. This gives the design engineer an unprecedented
array of choices for schematic realization of a particular filter. Figure 3 shows S/Filter within the Genesys design
environment.




Figure 3. S/Filter design screen. Figure 4. S/Filter design tab shown with initial design
parameters




Design example
The filter to be designed has the following requirements: Figure 4 shows the initial S/Filter screen with the design