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Vector Wave Variables
It is straightforward to extend wave digital filtering principles to the vector case (this has been outlined in [131]; the same idea has apeared in the context of digital waveguide networks in [166,169]). For a component vector oneport element with voltage
and current
, it is posible to define wave variables and by

(2.43a) 
for a symmetric positive definite matrix ; powernormalized quantities may be defined by

(2.44a) 
where
is some right square root of , and
is its transpose. The power absorbed by the vector oneport will be

(2.45) 
Kirchoff's Laws, for a series or parallel connection of component vector elements with voltages
and
,
can be written as
and the resulting scattering equations will be
in terms of the wave variables
,
defined as per (2.43) and the port resistance matrices
,
. These are the defining equations of a vector adaptor; their schematics are essentially the same as those of Figure 2.12, except that they are drawn in boldsee Figure 2.14. As before, we use the same representation for powernormalized waves.
Figure 2.14:
Threeport vector adaptors (a) a vector series adaptor and (b) a vector parallel adaptor.

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Next: Coupled Inductances and Capacitances
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Stefan Bilbao
20020122