1. Establish a normal tree. tree branches--Us, C(, R) cot ree(chords)-i,,(, R) 2. Assign voltage and current variables. Assign a voltage (with polarity reference) to every capacitor and a current(with arrow) to every inductor; there are the state variables. Indicate the voltage across every tree branch and the current through every link in terms of the source voltages, source currents,and the state

The set of variables is a hybrid set that may include both currents and voltages. They are the inductor currents and the capacitor voltages. Each of these quantities may be used directly to express the energy stored in the inductor or capacitor at any instant of time. They collectively describe the energy state of the system. They are called the state variables

17-3 Loop analysis 17-4 Analysis of networks containing dependent sources

The node-to-datum voltage vector:

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