18-4 Decomposition of a circuit into linear and nonlinear parts

n--a large constant voltage source (t)-- small time-varying- voltage source(small signal) >>(3) bsin +i=(),+ (o)=: JOX tniog gin9go int---(1)←0=()2utJ

《电路》（英文版）18-2 Simple nonlinear resistor circuits

1. Nonlinear resistor A nonlinear resistor is an element whose voltage and current are related by a nonlinear equation

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