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we arrive at
Following the similar procedures, one can show that
and
T
HEOREM
10.1
In the steady state, for a given lumped periodically switched
linear circuit, there exists another lumped periodically switched linear cir-
cuit having the same topology, switching frequency, and reversed time.
The weak and strong forms of Tellegen's theorem for periodically switched
linear circuits in the phasor domain are given by (10.10), (10.11) and
(10.12), respectively.
Note that :
The phasor of the branch voltages and currents of both
N
and that
of
are evaluated at the same frequency.
The constraint imposed on the time variable of in (10.6) reveals
that the switching clock sequence of is reversed as compared with
that of
N,
as shown in Fig. 10.1. This time reversal property of the
adjoint network of periodically switched linear circuits is similar to
that of linear time-invariant circuits [75] and ideal switched capacitor
networks [11, 79].
The difference between Tellegen's theorem for periodically switched
linear circuits and that of linear time-invariant circuits is the sum-
mation operator representing the fundamental characteristics of pe-
riodically switched linear circuits.
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