Unit-IV.ppsx

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Unit – IV

PASSIVE FILTERS

Unit – IV

PASSIVE FILTERS

Dr. T.V.Padmavathy

Professor/ECE

RMKCET

Dr. T.V.Padmavathy

Professor/ECE

(2)

Presentation Outline

Introduction

Electrical Properties of Symmetrical Networks

Properties of Symmetrical T Network

Properties of Symmetrical π Network

Filter Fundamentals

Classification of Filters

Constant k Low Pass filter

Constant k High Pass filter

Constant k Band Pass filter

Constant k Band Elimination Pass filter

m - Derived Filter

m-derived filter T-section

Low -pass m-derived T-section

High -pass m-derived T-section m-derived filter π-section

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Introduction

 Filters are networks which has the property of freely passing certain ranges of frequency while attenuating the rest of frequencies

Classification of Networks

 The behaviour of a network leads to a lots of classifications. They are,

Active Networks

Passive Networks

Active Networks

A network which has both passive and active elements like transistors, generators etc is known as active network.

Passive Networks

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Symmetrical Network

 When the electrical properties of the network are unaffected even after

interchanging the input and output terminals, the network is called symmetrical network.

Asymmetrical Network

 When the electrical properties of the network are affected after

interchanging the input and output terminals, the network is called asymmetrical network.

Electrical Properties of Symmetrical Networks

 Characteristic Impedance

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0

Z

Electrical Properties of Symmetrical Networks

Characteristic Impedance

 Characteristic impedance of a symmetrical network is the

impedance measured at the input terminals of the first network in a chain of infinite networks in cascade and is denoted as

Propagation Constant

 _{Propagation constant is defined as the natural logarithm of the ratio}

of the sending end current or voltage to the receiving end current or voltage of the line.

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Properties of Symmetrical T Network

Characteristic Impedance 1 1 2 2

4

2 1 2 1 0

Z

_T





The Characteristic impedance for symmetrical network is given by

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Properties of Symmetrical Network

4

2 1 2

1

2 1 0

Z Z

Z Z Z Z

 



Propagation Constant 1 2

1 ₂

(8)

Filter Fundamentals

Pass Band

 An ideal filter will have zero attenuation in certain range of frequencies.

 The range of frequencies in which attenuation is zero, indicating no loss

for an ideal filter is called pass band.

 Practical filters will have low attenuation in the pass band.

Attenuation Band

 The range of frequencies in which attenuation is infinite for an ideal

filter is called attenuation band.

 Practical filters will have very high attenuation in the attenuation

(9)

Characteristics of Practical filters

The practical filter characteristics are,

Propagation Constant

Characteristic impedance

Cut-off frequency

Classification of filters

Filters can be classified in to three types

Constant k filters

M-derived filters

Composite filters

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Classification of Filters

Common types of filters:

 _{Low-pass: pass low frequencies (below the cut-off frequencies)}

and eliminate high frequencies (above the cut-off frequencies)

 _{High-pass: send on high frequencies (above the cut-off}

frequencies) and reject low frequencies (below the cut-off frequencies)

 _{Band-pass: pass some particular range of frequencies, discard}

other frequencies outside that band

 _{Band-rejection: stop a range of frequencies and pass all other}

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Constant k Low Pass filter

Constant k Low Pass T Section filter

Constant k Low Pass Section filter

 The total series arm inductance of T

type filter is which is equal to

that of π filter.

 Since the total shunt arm

capacitance of π filter is and

is equal to that of T filter.

 The total series arm impedance of

both T and π filters are same, their design impedance and the cut off frequency will also be the same

L L L _ _

2 2

C C C _ _

2 2

k

R

c

f

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Constant k Low Pass filter- Design Equations

Design Impedance Rk

k

R C

L _

    

  

 

4 1

2 0

LC C

L

Z_T 

Cut-off Frequency

LC f_c

 1



Cut-off frequency interms of design impedance

R

_k

(13)

Constant k Low Pass filter- Design Equations

Design Elements c k

f

R

C



1 

c k

f

R

L





2

0 1 

       c k T f f R Z

Pass Band Attenuation _Band

2 Z 1 Z + -f

Characteristic Impedance of T and π Networks in terms of

R

k

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The total series arm capacitance of T

type filter is and is equal to

that of π filter.

The shunt arm inductance of π filter is

and is equal to that of T

filter.

The total series arm impedance and

total shunt arm impedance of both T and π filters are the same, then design impedance and cut-off frequency will

Constant k High Pass filter

C C C

C C

 2 2

2 . 2

L L L

L L

 2 2

2 .

2 _{Constant k High Pass T Section filter}

(15)

Constant k High Pass filter- Design Equations

Design Impedance

k

R C

L _

Cut-off frequency interms of design impedance 

  

 

 

LC C

L

Z₀_T ₂

4 1 1



LC f_c



4 1



C

R

f

k

c

_

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Design Elements

Constant k High Pass filter- Design Equations

c k f

R C



4 1



c k

f R L



4



Characteristic Impedance of T and π Networks in terms of

2

0 1 

      

f f R

Z c

k T

Attenuation

Band Pass _Band 0

+

-2 0

  

f R

Z k

(17)

Constant k Band Pass filter

 _{The band pass filter passes the}_{signal between the two cut off}

frequencies and attenuates the rest of frequencies.

 _{The band pass filter can be obtained by following a}_{low pass filter}

with an high pass filter or a low pass filter and high pass filter can be combined into a single filter

 Band pass filter can be obtained by T section or π section

combining the elements of both T type LPF and T type HPF (or)

 By combining the elements of π type of LPF and π type of HPF

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Constant k Band Pass filter

T-Section Band Pass Filter  The total series arm impedance and

total shunt arm impedance of the T type

and π type BPF are the same

 The design impedance and cut-off frequencies and will be the same

 The series arm contains resonant circuits and the shunt arm contains

parallel resonant circuits

 For band pass characteristics the series resonant frequency and shunt resonant

k

R

1

f f ₂

(19)

Constant k Band Pass filter- Design Equations

Design Impedance Cut-off Frequency Design Elements 2 1 1 2 C L R or C L

R_k  _k 

2 1 2

0

f







1 2 0 1 2

.

4 R

f

C

f

k











1 . f f R L k   





2 0 1 2 2 2

.

4 R

f

R

L

k k









f



R

_k

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 _It _eliminates_{or stops a} _{particular range of frequencies} _and

passes the rest of frequencies.

 _{The band elimination filter is also called band stop filter.}

 _{A BEF can be obtained by connecting a} _{LPF in parallel with a}

HPF, in which the cut off frequency of LPF is below that of HPF.

 The band stop filters can be easily obtained by converting the series

resonant circuit of band pass filter into shunt resonant circuit and vice versa

Constant k Band Elimination filter

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Constant k Band Elimination filter

T-Section Band Stop Filter

π- Section Band Stop Filter  The total series arm impedance and

total shunt arm impedance of the T type

and π type BEF are the same

 The design impedance and cut-off frequencies and will be the same

 The series arm contains resonant circuits and the shunt arm contains

parallel resonant circuits

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Constant k Band Elimination filter- Design Equations

Design Impedance 2 1 1 2 C L R or C L

R_k  _k 

2 1 2

0

f



Design Elements Pass Band Attenuation Band Pass Band





2 2 1 1 2

. f f C R f f k   





2

4 f f R

L k

 





₂ ₁



1 4 1 f f R C k   



f₂ f₁



R

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m - Derived Filter

 m-derived filters or m-type filters are a type of electronic filter

designed using the image

 The m-derived filter is a derivative of the constant k filter method

 The starting point of the design is the values of Z and Y derived from

the constant k prototype and are given by

where k is the nominal impedance of the filter

 The designer now multiplies Z and Y by an arbitrary constant m (0 <

m < 1)

 There are two different kinds of m-derived section; series and shunt

 To obtain the m-derived shunt half section, an admittance is added to

1/mZ to make the image impedance

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m-derived filter T-section

 Constant-k section suffers from very slow attenuation rate and

non-constant image impedance .

 Thus we replace Z₁ and Z₂ to Z’₁ and Z’₂ respectively.

Let’s Z’₁ = m Z₁ and Z’₂ to obtain the same Z_iT as in constant-k section.

4 '

'

4

2 1 2

1 2

1

Z

m

Z

mZ

Z

_iT













(25)

4 '

4

2 1 2

1 2

1

Z

m

Z

mZ

Z











m

Z

m

Z

4

1 '

2 1 2 2

2







Z

₁

/2

Z

₁

/2

Z

₂

Z'

₁

/2

Z'

₁

/2

Z'

₂

mZ

₁

/2

mZ

₁

/2

Z

₂

_/m

1 2

4 1

Z m

m



(26)

Low -pass m-derived T-section

L m

m

4 1 2

mC

mL/2 mL/2

For constant-k section

L

j

Z

₁





C

j

Z

₂



1 /



Lm

j

Z

'

₁









j

L

m

Cm

j

Z



4

1

1 '

2 2







and







2



2 2 1 2 1 2

1

/

2 '

'

/

'

/

4 '

'

1 Z

Z

e







Propagation Constant











2







2

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High -pass m-derived T-section

2C/m L/m 2C/m C m m 2 1 4 

C

j

m

Z

'

₁



/







C

m

j

m

L

j

Z



4

1 '

2 2







and







2



2 2 1 2 1 2

1

/

2 '

'

/

'

/

4 '

'

1 Z

Z

e

















2







2

2 2 2 1

/

1

1 /

2

4 /

1 /

/

'



c c

m

C

m

j

m

L

j

C

j

m

Z

















2







2

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m-derived filter π-section

mZ ₁ m Z₂ 2 m Z₂ 2





m Z m 4 1

2  2 ₁





m Z m 4 1

2  2 ₁









2 2 2 1 2 1 2 1 / 1 4 / 1 / ' ' c o iT i Z m Z Z Z Z Z Z Z



      1 1

'

mZ

Z







m

Z

m

Z

4

1 '

2 1 2 2 2







Note that

The image impedance is

(29)

Low -pass m-derived π-section

mL 2 mC 2 mC





m L m 4 1 2  2





m L m 4 1 2  2

L

j

Z

₁





Z

₂



1 /

j



C

For constant-k section

2 2

1

Z

L

/

C

Z

o

Z







2

2 2

1

L

4 Z

o

/

c

Z













Then

and

Therefore, the image impedance reduces to











_c



o

c i Z m Z 2 2 2 / 1 / 1 1



    

(30)

Composite Filters

m=0.6 m- m=0.6

derived m<0.6 constant

k T



2

1

_

2 1

Matching section

Matching section High-f

cutoff Sharp_cutoff

Z _iT Z iT Z _iT

Z _o Z _o

m<0.6 for m-derived section is to place the pole near the cutoff frequency w_c

For 1/2 p matching network , we choose the Z’₁ and Z’₂ of the circuit so that

o

Z Z

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Thank You