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Embedded T>vo-Port Networks 79
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"
+ Two-port +
v. ABeD
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Figure 4.5.
A typicaJ cascaded, two-port subnetwork.
matrices:
T=T, XT 2 XT 3
X .,. XTjx '" XT n
• (4.9)
This is a popular means for analysis, but it will be shown to incorporate some
gross inefficiencies.
The two-port networks for series Z and shunt Yare shown both separately
and combined in Figure 4.6. The definition of the ABCD parameters is clear
from (4.7) and (4.8); e.g., A=V./Vb when Ib=O. Applying this approach to
the Z and Y two-port networks in Figure 4.6, their product is
(4.10)
For emphasis and review, the L-section ABCD matrix on the right-hand side
of (4.10) was obtained using complex arithmetic as follows. The upper
left-hand corner element was obtained as I· I + Z·Y. The upper right-haf!d
element has even more trivial operations, namely I·O+Z·l. Similarly, the
lower left-hand element was found from O· I + I .Y. Finally, the lower righthand
element resulted from 0·0+ I·/. Further cascading will cause multiplication
by another branch matrix having two I's and a O. Clearly, this is an
ineffective technique for cascaded two-terminal elements such as the Z and Y
branches most commonly encountered. It is reasonable if most of the subnetwork
ABCD matrices are nontrivially full. It will obtain the complete ABCD
matrix for the entire network. However, the reader should confirm what the
fundamental ABCD definitions from (4.7) and (4.8) show: two network
analyses with ZL = IE-IO and ZL = IE+ 10 will provide the overall ABCD
matrix values. This matrix is sometimes required. Kajfez (1980) described its
use in noise figure calculations, and (3.66) is another application that will be
considered in much more detail. A more efficient ABCD calculation is now
Figure 4.6. An L section by cascading Z and Y two~port networks.