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96 Ladder Network Analysis
the load impedance is a resistance. Equation (4.62) shows that when the load
power is set equal to
(4.64)
then
TL=2010gjE,I·
(4.65)
4.5.4. Conclusion to Network Responses. Some impedance and power response
functions were described. Scattering parameters were defined by two
linear, complex equations in the same style as previously used for ABCD, Z,
and y parameters. The mathematics of scattering parameters is straightforward,
but lack of familiarity with the general case makes its development
worthwhile. For instance, scattering parameters are often described for a
50-ohm port reference impedance. This is the circumstance that has revolutionized
accurate, automatic measuring equipment for all kinds of networks
over extremely wide frequency ranges. However, there are some network
responses that are explained better in terms of scattering parameters with
some arbitrariness of port normalization, and this will be a necessity in
Chapter Seven. Various wave response functions were then defined, and an
efficient means for extending the ladder recursion analysis method for S21
calculation was explained.
Singly terminated (lossless source) responses have not been mentioned
explicitly (e.g., V 2 /V, in Figure 4.16). It is easy to extract these numbers from
a ladder network analysis algorithm and calculate the logarithm of that
magnitude. Unfortunately, the selectivity expression of interest typically is
I V"rI
SEL=2010g lO V dB, (4.66)
L
where V,d may be the input voltage at a midband frequency. This reference
voltage may be contingent upon a certain input current or power, or similar
load conditions. Then the excitation will have to be maintained at that level at
all response frequencies. This can be confusing when the analysis scheme
requires load power to be specified at every frequency. Experience has shown
that one should not approach these definitions carelessly. Renormalizing at
each frequency, by making the source excitation variable equal to unity, helps
to eliminate confusion.
Finally, most response functions have an associated angle that makes the
calculation of group time delay possible. Group delay, in seconds, is defined
to be
dep
dw'
T =--
G
(4.67)
where angle ep is in radians. Time delay may be converted to degrees per I
megahertz by multiplying (4.67) by 360E6; this is especially useful for oscilla-