quiz 1 solutions - ECE 412 Introduction to Filter Synthesis...

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ECE 412 Introduction to Filter Synthesis Quiz #1 Solutions University of Illinois at Chicago Spring 2013 Name (print): UIN: Problem 1 (4 points) The voltage gain transfer function H ( s ) = V out ( s ) /V in ( s ) of a linear circuit is given by H ( s ) = s s + 10 (a) Determine the magnitude response | H ( ) | and sketch it from ω = 0 to ω → ∞ . (b) Determine the phase response H ( ) and sketch it from ω = 0 to ω → ∞ . (c) Determine the magnitude and phase at ω = 10 rad/s, that is, | H ( j 10) | and H ( j 10). Solution (a, b, c) The transfer function H ( s ) evaluated at s = gives H ( s ) vextendsingle vextendsingle s = = + 10 Therefore the magnitude and phase responses are given by | H ( ) | = ω ω 2 + 100 H ( ) = 90 - tan 1 parenleftBig ω 10 parenrightBig Based on the expressions for the magnitude and the phase, we can make the following observations: The magnitude response | H ( ) | is 0 at ω = 0 and approaches 1 as ω → ∞ . | H ( j 100) | = 100 / 100 + 100 = 1 / 2 0 . 707. The phase response H ( ) is 90 at ω = 0 and approaches 0 as ω → ∞ .
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  • Spring '11
  • Vahe
  • Volt, University of Illinois, DR. VAHE CALISKAN, magnitude response |H

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