Page 162 - DSP Integrated Circuits

4.15 Wave-Flow Building Blocks 147

There are several types of adaptors corresponding to different types of inter-
connections [8]. In practice, only a few types of adaptors are used for connecting
two ports. All of them represent the same voltage and current constraints, but
they differ in the manner in which the reflected waves are computed. Arbitrarily
complex interconnection networks can be constructed using only two-port and
three-port adaptors.

Symmetric Two-Port Adaptor
Figure 4.31 shows the symbol for the symmetric
two-port adaptor that corresponds to a connection
of two ports;. The incident and reflected waves for
the two-port are
Figure 4.31 Symmetric
two-port
adaptor

and

At the interconnection we have, according to Kirchhoff's current and voltage
laws,

By eliminating voltages and currents we get the following relation between
incident and reflected waves for the symmetric two-port adaptor

Equations (4.42) through (4.44) are illus-
trated by the wave-flow graph in Figure 4.32.
The adaptor coefficient a is usually written on
the side corresponding to port 1. As can be
seen, the wave-flow graph is almost symmetric.
Note that a = 0 for RI = R 2. The adaptor
degenerates into a direct connection of the two
ports and the incident waves are not reflected
at the point of interconnection.
For #2 = 0 we get a = I and the incident Figure 4.32 Symmetric two-port
wave at port 1 is reflected and multiplied by —1 adaptor.