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

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

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

Relationship between branch and loop currents

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

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

15-6 The partial-fraction-expansion method

15-4 Laplace transform of some simple time function 1. The unit step function

We define the unit impulse as a function of time which is zero when its argument, generally (t-o), is less than zero; which is also zero when argument is greater than zero; which is infinite when its argument is zero; and which has unit area

14-8 Definition of the Fourier transform The exponential form of the Fourier series