EGR 277

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Lecture 6 EGR 261 Signals and Systems
Read Ch. 13, Sect. 1-5, 7 in Electric
Circuits, 9th Edition by Nilsson Ch. 4, Sect. 4
in Linear Signals Systems, 2nd Ed. by Lathi
Transfer Functions (Network Functions) A transfer
function, H(s), can be used to describe a system
or circuit in the s-domain in terms of its input
and output as illustrated below.
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Lecture 6 EGR 261 Signals and Systems

• H(s) is defined more specifically as
• Notes
• Transfer functions are always defined with zero
  initial condition (or zero initial stored
  energy). Therefore, VC(0) IL(0) 0, so the
  voltage sources in the models for capacitors and
  inductors disappear.
• Y(s) and X(s) typically represent voltages or
  currents.
• The input and the output must be designated by
  the user (there might be many possible transfer
  functions for a given circuit or system).
  However, most circuits or systems have
  well-defined inputs and outputs.
• H(s) completely characterizes the circuit or
  system. Once H(s) is known, you can calculate
  circuit outputs for various inputs without ever
  seeing the circuit or system again.

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Lecture 6 EGR 261 Signals and Systems
Example Find H(s) for the circuit shown below
if H(s) is defined as
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Lecture 6 EGR 261 Signals and Systems
Example Find H(s) for the circuit shown below
if H(s) is defined as
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Lecture 6 EGR 261 Signals and Systems
Finding the output, y(t) using H(s) and the
input, x(t)
So we can determine the output of a circuit by
taking the inverse Laplace transform of the
product of the transfer function and the Laplace
transform of the input to the circuit.
Example Find the output, y(t) for the circuit
below if the input is x(t) 25u(t)V.
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Lecture 6 EGR 261 Signals and Systems
Example Find the output, Vo, for the circuit
below if the input is Vi 10 u(t)V using the
transfer function H(s) found in a previous
example.
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Lecture 6 EGR 261 Signals and Systems
Unit Step Response and Impulse Response Although
H(s) can be used to find the output for any given
input, there are two special cases that are often
of interest 1) Impulse response - the output
when the input is ?(t) 2) Unit step response -
the output when the input is u(t) Impulse
response the output to a circuit when the input
x(t) ?(t) If x(t) ?(t), then X(s) 1, so
Y(s) H(s)?1 H(s), so y(t) L 1 H(s)
h(t).
Unit step response the output to a circuit when
the input x(t) u(t)
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Lecture 6 EGR 261 Signals and Systems
Example For the circuit shown A) Find the
transfer function H(s) I(s)/V(s)
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Lecture 6 EGR 261 Signals and Systems
B) Use the transfer function to determine the
output if v(t) 10e-2t V
C) Use the transfer function to determine the
impulse response
D) Use the transfer function to determine the
unit step response