ELEC 226, Spring 2003

Prof. Rich Kozick

Prof. Rich Kozick

- Find the initial voltage across all capacitors and the initial current through all inductors. Be sure to clearly define the voltage polarities and current directions.
- Draw the circuit in the s-domain for t > 0:
- Replace all voltage, current, and source waveforms by their Laplace transforms.
- Replace resistors, capacitors, and inductors by their s-domain equivalent circuit elements using Table 13.1. Note that these equivalent circuit elements include the s-domain impedance as well as the initial conditions.

- Analyze the circuit in the s-domain to find expressions for the
Laplace transform of the voltages and/or currents of interest
(e.g., I
_{1}(s), I_{2}(s), ..., V_{1}(s), V_{2}(s), ...).For this circuit analysis, you can use all of the tools that we studied in Chapters 1-5, including Ohm's law (generalized to impedances, V(s) = I(s) Z), KCL, KVL, series/parallel equivalent impedances, voltage/current dividers, delta-Y transformations, node voltage analysis, mesh current analysis, source transformation, Thevenin/Norton equivalent circuits, superposition, and op amps (ideal model and realistic models).

- Find the inverse Laplace transform to obtain the waveforms
for the voltages and/or currents of interest
(e.g., i
_{1}(t), i_{2}(t), ..., v_{1}(t), v_{2}(t), ...).

H(j w) = (Phasor of output) / (Phasor of input)What is the meaning of frequency response? How do you measure it in the lab?

The *transfer function* H(s) is defined similarly in the s-domain
(assuming all initial conditions are zero):

H(s) = (Laplace transform of output) / (Laplace transform of input)The frequency response is equal to the transfer function evaluated along the s = jw (imaginary) axis. Why??

The transfer function is a ratio of polynomials: H(s) = N(s) / D(s)

- The roots of the numerator N(s) are called the
*zeros*. - The roots of the denominator D(s) are called the
*poles*.

Why are the terms poles and zeros used? What is their significance? How are they used to analyze and design frequency-selective filters? Let's look at some familiar RC, RL, and RLC circuits from the point of view of transfer functions, poles, and zeros.