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Chapter 14Filter Circuits

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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Ideal Filter Magnitude Responses

H()

c

Lowpass Filter

H()

c

Highpass Filter

H() H()

1 2 21

Bandpass Filter Bandstop Filter

Magnitude responses of different type of ideal filter functions.

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Actual Filter Magnitude Responses

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LOWPASS FILTER

0

2 2 2

1( ) 1

( )1( ) 1

(0) 1and ( ) 0

At the cutof or Rolloff frequency

1 1 1( )

21

i

c

c c

c

V j CH

V j RCRj C

H H

HRCR C

A low pass filter is designed to pas only frequencies from DC up to the cutoff frequency c.

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LOWPASS FILTER

Regulator: (a) effect of spike in current on the input side; (b) noise reduction.

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HIGHPASS FILTER

A high pass filter is designed to pass all the frequencies above its cutoff frequency c.

0

2 2 2

( )( )

1( ) 1

(0) 0 and ( ) 1

At the cutof or Rolloff frequency

1 1 1( )

21

i

c

c c

c

V R j RCH

V j RCRj C

H H

HRCR C

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BANDPASS FILTER

A bandpass filter is designed to pass all the frequencies within a band of frequencies, 1 < < 2

0

1 2

2 1

1 2

( )( ) (0) 0 and ( ) 1

1( )

1The center frequency is given by

The Lower and Upper cutoff frequencies are and

The Bandwidth is B= -

1( ) 1and ( ) ( )

2

i

o o

o

V RH H H

V R j L C

LC

H H H

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BANDSTOP FILTER

A Bandstop filter is designed to stop or eliminate all the frequencies within a band of frequencies 1 < < 2 .

0

1 2

2 1

1 2

1( )

( ) (0) 1and ( ) 11( )

1The center frequency is given by

The Lower and Upper cutoff frequencies are and

The bandwidth is B= -

1( ) 1and ( ) ( )

2

i

o o

o

j LV CH H HV R j L C

LC

H H H

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Active first-order low-pass filter

0 ( ) 1( ) ,

1( ) 1

f

f f fi i f f

i i f f ff

f

R

Z j C RVH Z R Z R

V Z j C j R CRj C

1 1( )

1f

ci f f f f

RH

R j C R R C

Active filters use also active devices such as OP AMPs.

Passive filters use only passive devices such as inductors and capacitors only.

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Active first-order High-pass filter

0 ( ) 1( ) ,

( )

1( )

1 1

fi i f f

i i i

f i fc

i i i iii

ZVH Z R Z R

V Z j C

R j C RH

j C R C RR j C

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Active Bandpass Filter A bandpass filter is obtained by cascading a LPF and a HPF together with an inverting amplifier to provide the desired gain.

Active Bandpass Filter Block Diagram. Frequency Response

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Active Bandpass Filter Example

2 11

o 2

i 1 2

2

1 2

21 2

2

1

1

1 2

1

2

2

1 1,

(

V 1( )

V 1 1

1

1 1

, , ,

( )1 1

)

f

i

f

i

oo

f

oi

i

f

R j C RH

R j C R j C R

R j C R

R j C R j C R

B QB

jR

Hj jR

RC RC

RH

R

Three cascaded stages are used to realize the bandpass filter.

A LPF cascaded with a HPF and an inverter stage.

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Active Bandreject Filter A bandreject filter may be constructed by parallel combination of a LPF and a HPF filter and a summing amplifier.

Active Bandreject Filter Block Diagram. Frequency Response

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Active Bandreject Filter Example

o 2

i 1 2

1

2 1

2

1 1 1

2 1

11 2

1 2

V 1( )

V 1 1

1

1 1

2 ( )1

1 1

0 and ( )

2( )

f

i

f

i

f

i

f

i

fo o

i

R j C RH

R j C R j C R

jR

j jR

j jR

j jR

RH

R

RH

R

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Simplified Block Diagram of a Superheterodyne AM Radio Receiver

The input signal is downconverted in frequency to an intermediate frequency (IF) before amplification.

Good IF filters are required.

The signal is again downconverted in frequency after IF amplification.

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Frequency Assignments for Touch-tone Dialing

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Three-way, crossover network with 6 dB per octave.

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Three-way, crossover network with 12 dB per octave at cutoff.

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Detection Scheme for Touch-tone Dialing

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