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

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

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

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

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

The node-to-datum voltage vector:

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

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

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

18-5 Combination of i-v characteristics 1. Series combination