Lecture 181 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001

Lecture 182 Complex Waveforms as Input When complex waveforms are used as inputs to the circuit (for example, as a voltage source), then we (1) must Laplace transform the inputs (2) determine the transfer function (3) feed the input through the transfer function The transfer function, H(s), is the ratio of some output variable to some input variable

Lecture 183 Class Example Extension Exercise E14.7

Lecture 184 Transfer Function The transfer function, H(s), is All initial conditions are zero (makes transformation step easy) Can use transfer function to find output to an arbitrary input Y(s) = H(s) X(s) The impulse response is the inverse Laplace transform of transfer function h(t) = L -1 [H(s)] with knowledge of the transfer function or impulse response, we can find response of circuit to any input

Lecture 185 Class Example Extension Exercise E14.8

Lecture 186 Pole/Zero (Plot) Poles directly indicate the system transient response characteristics; consider poles from a 2nd order system: For a pole-zero plot place "X" for poles and "0" for zeros using real-imaginary axes Poles in the right half plane signify an unstable system

Lecture 187 Class Example Extension Exercise E14.9

Lecture 188 Steady State Response Given an input of the form x(t)=X M cos(ω 0 t+θ), the steady-state response is where  (j  ) is the phase angle of the transfer function, that is,  H(j  )

Lecture 189 Class Example Extension Exercise E14.10