quiz 1 solutions

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

• Notes
• 4

This preview shows page 1 - 2 out of 4 pages.

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 → ∞ .

Subscribe to view the full document.

• Spring '11
• Vahe
• Volt, University of Illinois, DR. VAHE CALISKAN, magnitude response |H

{[ snackBarMessage ]}

###### "Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern