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46 Some Tools and Examples ofFilter Syntlu!sis
Example 3.8.
Use Program B3-3 to multiply
(s' + 3s + 2)(5s' + 4s- 10)(3s'+ I) = 15s 6 + 57s' + 41s 4 -47s 3 - 48s' - 22s - 20,
(3.44)
using the program's chaining feature. Also, multiply the left-half-plane and
right-half-plane quadratic factors found in Example 3.7 to confirm the earlier
results.
3.2.3. POHier Transfer. Power delivered from a complex source to a complex
load will be encountered repeatedly in the following sections. It will be
specialized to the real-source case for classical network synthesis in this
chapter. Consider the source and load connection shown in Figure 3.3. It is
well known that the maximum available source power is
IE,I'
Pas = 4R •
,
(3.45)
which occurs when Z = Z:. Kurokawa (1965) developed relationships for less
power transferred into other load impedance values. An important parameter
is the generalized reflection coefficient
Z-Z:
a=-- (3.46)
Z+Z, .
It defines a Smith chart with the center corresponding to Z:; this will be
explained in detail in Section 7.2. The power delivered to the load relative to
the maximum available turns out to be
L=l-Ial'.
Pas
(3.47)
The numerator of the reflection coefficient indicates that its magnitude is zero
when Z=Z:, so that P=P as ' as mentioned. Program A2-1, introduced in
Section 2.1, makes the evaluation of the preceding two equations quite
elementary for any range of load impedances, given a fixed source impedance.
In this chapter the source impedance is considered to be resistor RI' and Z
Z. '" R, + jXs '1-------------,
Figure 3.3.
+
~ E, r Z=R+iX l
i,
p
Power transfer from a flxed comptex source to a variable complex. load impedance.