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Chapter 14Frequency Response

Huseyin BilgekulEeng 224 Circuit Theory II

Department of Electrical and Electronic Engineering Eastern Mediterranean University

Chapter Objectives: Understand the Concept of Transfer Functions. Be Familiar with the Decibel Scale. Learn how to make Bode Magnitude and Phase plots.

Learn about series and parallel resonant RLC circuits. Know Different Types of Passive and Active Filters and their

Characteristics. Understand the use of scaling in circuit analysis. Be Able to use PSpice to obtain frequency response. Apply what is learnt to radio receiver and touch-tone

telephone.

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What is Frequency Response of a Circuit?

It is the variation in a circuit’s

behavior with change in signal

frequency and may also be

considered as the variation of the gain

and phase with frequency.

FREQUENCY RESPONSE

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TRANSFER FUNCTIONThe transfer function H() of a circuit is the is the frequency dependent ratio of the phasor output Y() to a phasor input X().

Considered input and output may be either the current or the voltage variable.

4 types of possible transfer functions.

Y( )H( )

X( )

= H( ) |

)(V

)(V gain Voltage )(H

i

o

)(I

)(V ImpedanceTransfer )(H

i

o

)(I

)(I gain Current )(H

i

o

)(V

)(I AdmittanceTransfer )(H

i

o

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Magnitude plot for a low-pass filter

TRANSFER FUNCTION of Low-pass RC Circuit

R=20 kΩC=1200 pF

At low frequencies At high frequencies

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Phase plot for a low-pass filter

TRANSFER FUNCTION of Low-pass RC Circuit

At low frequencies At high frequencies

R=20 kΩC=1200 pF

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TRANSFER FUNCTION of High-pass RC Circuit

Magnitude plot for a high-pass filter

At high frequencies At low frequencies

R=20 kΩC=1200 pF

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TRANSFER FUNCTION of High-pass RC Circuit

Magnitude plot for a high-pass filter

Phase plot for high-pass filter

At high frequencies At low frequencies

R=20 kΩC=1200 pF

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TRANSFER FUNCTION of a Band-pass RC Circuit

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Frequency Response of the RC Circuit

2

1

1( ) 1

( ) Transfer Function1( ) 1

Magnitude Response

Phase Res

1( )

1 ( )

( ) ( ) tan

1Where

ponse

o

o

o

o

s

H

H

V j CH

V j RCR C

C

j

R

a) Time Domain RC Circuit b) Frequency Domain RC Circuit

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Drawing Frequency Response of RC Circuit

a) Amplitude Response b) Phase Response

2

1( )

1 ( )o

H

1( ) ( ) tan

o

H

Low Pass FilterLow Pass Filter

The frequency value of o is of special interest.

Because output is considerable only at low values of frequency, the circuit is also called a LOW PASS FILTER.

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HIGHHIGH Pass Filter Pass Filter

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TRANSFER FUNCTION The transfer function H() can be expressed in terms of its numerator polynomial N() and its denominator polynomial D().

( )( )

( )

NH

D

The roots of N()=0 are called ZEROS of H() (j=z1, z2, z3, ….).Similarly The roots of D()=0 are called POLES of H() (j=p1, p2, p3, ….). A zero as a root of the numerator polynomial, results in a zero value of the transfer function. A pole as a root of the denominator polynomial, results in an infinite value of the transfer function.

21 1

1

2

1

1

2( ) 1 1( )

( )( ) 21 1

k k

n n

jj jK j zNH

D jj jp

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s=j

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Vx

0.5Vx

0.5VxVx