Part 4 Frequency Response/section/1

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. .

صادق الكناني: التدريسي

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 صادق الكناني: التدريسي

TRANSFER FUNCTION

The 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

صادق الكناني: التدريسي

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.

2

1 1

1

2

1

1

2( ) 1 1

( )( )

( ) 21 1

k k

n n

jj jK j

zNH

D jj jp

صادق الكناني: التدريسي

Magnitude plot for a low-pass filter

TRANSFER FUNCTION of Low-pass RC Circuit

R=20 kΩ

C=1200 pF

At low frequencies At high frequencies

صادق الكناني: التدريسي

Frequency Response of the RC Circuit

2

1

1

( ) 1( ) Transfer Function

1( ) 1

Magnitude Response

Phase Res

1( )

1 ( )

( ) ( ) tan

1Where

ponse

o

o

o

o

s

H

H

V j CH

V j RCRC

C

j

R

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

صادق الكناني: التدريسي

Drawing Frequency Response of RC Circuit

a) Amplitude Response b) Phase Response

2

1( )

1 ( )o

H

1( ) ( ) tan o

H

Low 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.

صادق الكناني: التدريسي

HIGH Pass Filter

صادق الكناني: التدريسي

s=j

صادق الكناني: التدريسي

Vx

0.5Vx

0.5Vx Vx

صادق الكناني: التدريسي

Phase plot for a low-pass filter

TRANSFER FUNCTION of Low-pass RC Circuit

At low frequencies At high frequencies

R=20 kΩ

C=1200

pF

صادق الكناني: التدريسي

TRANSFER FUNCTION of High-pass RC Circuit

Magnitude plot for a high-pass filter

At high frequencies At low frequencies

R=20 kΩ

C=1200 pF

صادق الكناني: التدريسي

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 kΩ

C=1200 pF

صادق الكناني: التدريسي

TRANSFER FUNCTION of a Band-pass RC Circuit

صادق الكناني: التدريسي