1 Lecture #19 EGR 272 – Circuit Theory II Frequency Response This is an extremely important topic in EE. Up until this point we have analyzed circuits.

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1 Lecture #19 EGR 272 – Circuit Theory II Frequency Response This is an extremely important topic in EE. Up until this point we have analyzed circuits without considering the effect on the answer over a wide range of frequencies. Many circuits have frequency limitations that are very important. Example: Discuss the frequency limitations on the following items. 1) An audio amplifier 2) An op amp circuit Read: Chapter 14 in Electric Circuits, 6 th Edition by Nilsson

2 Lecture #19 EGR 272 – Circuit Theory II Example: Discuss the frequency limitations on the following items (continued) 3) A voltmeter 4) The tuner on a radio (band-pass filter)

3 Lecture #19 EGR 272 – Circuit Theory II Defining frequency response Recall that a transfer function H(s) is defined as: Where Y(s) = some specified output and X(s) = some specified input In general, s =  + jw. For frequency applications we use s = jw (so  = 0). So now we define: Since H(jw) can be thought of as a complex number that is a function of frequency, it can be placed into polar form as follows: Example: Find H(jw) for H(s) below. Also write H(jw) in polar form.

4 Lecture #19 EGR 272 – Circuit Theory II When we use the term "frequency response", we are generally referring to information that is conveyed using the following graphs:

5 Lecture #19 EGR 272 – Circuit Theory II Example: A) Find H(s) = V o (s)/V i (s) B) Find H(jw)

6 Lecture #19 EGR 272 – Circuit Theory II Example: (continued) C) Sketch the magnitude response, |H(jw)| versus w D) Sketch the phase response,  (w) versus w E) The circuit represents what type of filter?

7 Lecture #19 EGR 272 – Circuit Theory II Example: A) Find H(s) = V(s)/I(s) B) Find H(jw)

8 Lecture #19 EGR 272 – Circuit Theory II Example: (continued) C) Sketch the magnitude response, |H(jw)| versus w D) Sketch the phase response,  (w) versus w E) The circuit represents what type of filter?

9 Lecture #19 EGR 272 – Circuit Theory II Example: A) Find H(s) = V o (s)/V i (s) B) Find H(jw)

10 Lecture #19 EGR 272 – Circuit Theory II Example: (continued) C) Sketch the magnitude response, |H(jw)| versus w D) Sketch the phase response,  (w) versus w E) The circuit represents what type of filter?