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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, 6th Edition by Nilsson

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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)

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Lecture #19 EGR 272 – Circuit Theory II

Defining frequency response

Recall that a transfer function H(s) is defined as:Y(s)

H(s) X(s)

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:s jw

H(jw) H(s)

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:

H(jw) H(jw) ( )w

Example: Find H(jw) for H(s) below. Also write H(jw) in polar form.

4sH(s)

(s + 10)(s + 20)

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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:

H(jw) vs w - referred to as the or the

20log( H(jw) ) vs w - referred to as the

(w) vs w - referred to as the

magnitude response amplitude response

log - magnitude (LM) response

phase re sponse

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Lecture #19 EGR 272 – Circuit Theory II

Example:

A) Find H(s) = Vo(s)/Vi(s)

B) Find H(jw)Vo(s)

+

_ Vi(s)

+

_

R 1

sC

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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?

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Lecture #19 EGR 272 – Circuit Theory II

Example:

A) Find H(s) = V(s)/I(s)

B) Find H(jw)V(s)

+

_

1 sC

I(s) R sL

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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?

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Lecture #19 EGR 272 – Circuit Theory II

Example:

A) Find H(s) = Vo(s)/Vi(s)

B) Find H(jw)Vo(s)

+

_ Vi(s)

+

_

2k

10mH 3k

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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?