ADJOINT NETWORK OF PERIODICALLY SWITCHED LINEAR CIRCUITS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 206

quency reversal theorem of periodically switched linear circuits with a
rigorous proof. Both theorems are assessed using example circuits in
Section 6. The chapter concludes in Section 7.

1. Tellegen's Theorem

Tellegen's theorem, introduced by B. Tellegen half a century ago, is a
fundamental law for lumped electrical networks [76, 77, 78]. In the time
domain, it is given by

where and denote the branch voltages and currents of the
circuit, respectively, and B is the total number of branches in the net-
work. Eq.(10.1) also holds for any two circuits N and having the

same incidence matrix

and

where and denote respectively the branch currents and volt-
ages of and are the time variables of N and respectively.
Eqs.(10.2) and (10.3) are called the strong form of Tellegen's theorem.
It is intuitive to show that following weak form of Tellegen's theorem
also holds

The weak form of Tellegen's theorem is of particular usefulness because it
incorporates the branch voltages and currents of two separate networks
N and in a single and closed expression.