Let the initial voltages on the capacitors be represented as voltage sources in series with the capacitors and the initial currents through the inductors be represented as current sources in parallel with the inductors

Tellegen's theorem 1: Consider a lumped network n consisting of N+1 nodes and B branches, let=[ b2DbB,i=. Where

Relationship between branch and loop currents

Augmented loop matrix +1when branch b; is in loop lk and has the same orientation; B. =]; ={-1 when branch b; is in loop lk and has the opposite orientation; when branch; is not in loop lk

1. Augmented( incidence matrix of a directed graph nodes(N+1), branches(B)

You are asked to set off from any piece of the lands and pass through all the seven bridges under the condition that each bridge can be used only once, so that you can finally return to the starting point

We define transfer function H(s) as a ratio of the Laplace transform of system output (or response)(s) to the Laplace transform of the input(or forcing function)v(s) when all initial conditions are zero, then

When initial energy is present in a circuit, the Laplace transform method may be used to obtain the complete response. The first is the more fundamental, for it involves writing the differential equations for the network and then taking the Laplace transform of those equations

15-6 The partial-fraction-expansion method

15-5 Several basis theorems for the Laplace transform 1.The linearity theorem{fi(t)+()}=()+(s) Example: