chp4-microwave filters_withexamples

1

EKT 441MICROWAVE COMMUNICATIONS

CHAPTER 4:

MICROWAVE FILTERS

2

INTRODUCTION

What is a Microwave filter ? linear 2-port network controls the frequency response at a certain point in

a microwave system provides perfect transmission of signal for

frequencies in a certain passband region infinite attenuation for frequencies in the stopband

region a linear phase response in the passband (to reduce

signal distortion).f2

3

INTRODUCTION

The goal of filter design is to approximate the ideal requirements within acceptable tolerance with circuits or systems consisting of real components.

f1

f3

f2

Commonly used block Diagram of a Filter

4

INTRODUCTION

Why Use Filters? RF signals consist of:

1. Desired signals – at desired frequencies

2. Unwanted Signals (Noise) – at unwanted frequencies

That is why filters have two very important bands/regions:

1. Pass Band – frequency range of filter where it passes all signals

2. Stop Band – frequency range of filter where it rejects all signals

5

INTRODUCTION

Categorization of Filters Low-pass filter (LPF), High-pass filter (HPF), Bandpass filter

(BPF), Bandstop filter (BSF), arbitrary type etc. In each category, the filter can be further divided into active

and passive types. In active filter, there can be amplification of the of the signal

power in the passband region, passive filter do not provide power amplification in the passband.

Filter used in electronics can be constructed from resistors, inductors, capacitors, transmission line sections and resonating structures (e.g. piezoelectric crystal, Surface Acoustic Wave (SAW) devices, and also mechanical resonators etc.).

Active filter may contain transistor, FET and Op-amp.Filter

LPF BPFHPF

Active Passive Active Passive

6

INTRODUCTION

Types of Filters1. Low-pass Filter

Passes low freq

Rejects high freq

f1

f2

f1

2. High-pass Filter

Passes high freq

Rejects low freq

f1

f2

f2

7

INTRODUCTION

3. Band-pass Filter

Passes a small range of freq

Rejects all other freq

4.Band-stop Filter

Rejects a small range of freq

Passes all other freq

f1

f3

f2f1

f3

f1

f2 f2

f3

8

INTRODUCTION

Filter Parameters Pass bandwidth; BW(3dB) = fu(3dB) – fl(3dB)

Stop band attenuation and frequencies, Ripple difference between max and min of

amplitude response in passband Input and output impedances Return loss Insertion loss Group Delay, quality factor

9

INTRODUCTION

Low-pass filter (passive).

A Filter H()

V1() V2()ZL

A()/dB

0 c

3

10

20

30

40

50

1

21020A

V

VLognAttenuatio (1.1b)

1

2

V

VH (1.1a)

c

|H()|

1Transfer function

Arg(H())

10

INTRODUCTION

For impedance matched system, using s21 to observe the filter response is more convenient, as this can be easily measured using Vector Network Analyzer (VNA).

Zc

01

221

01

111

22

aa a

bs

a

bs

Transmission lineis optional

c

20log|s21()|

0dB

Arg(s21())

FilterZcZc

ZcVs

a1 b2

Complex value

11

INTRODUCTION

A()/dB

0 c

3

10

20

30

40

50

A Filter H()

V1() V2() ZL

Passband

Stopband

Transition band

Cut-off frequency (3dB)

Low pass filter response (cont)

12

INTRODUCTION

High Pass filter

A()/dB

0 c

3

10

20

30

40

50

c

|H()|

1

Transfer function

Stopband

Passband

13

INTRODUCTION

Band-pass filter (passive). Band-stop filter.

A()/dB

40

1

3

30

20

10

0 2o

1

|H()|

1 Transfer function

2o

A()/dB

40

1

3

30

20

10

0 2o

1

|H()|

1

Transfer function

2o

14

INTRODUCTION

6 8 10 12 14Frequency (GHz)

Filter Response

-50

-40

-30

-20

-10

0

12.124 GHz-3.0038 dB7.9024 GHz

-3.0057 dB

Input Return Loss

Insertion Loss

Figure 4.1: A 10 GHz Parallel Coupled Filter Response

Pass BW (3dB)

Stop band frequencies and attenuation

Q factor

Insertion Loss

15

FILTER DESIGN METHODS

Filter Design Methods

Two types of commonly used design methods:- Image Parameter Method- Insertion Loss Method

•Image parameter method yields a usable filter•However, no clear-cut way to improve the design i.e to control the filter response

16


Filter Design Methods•The insertion loss method (ILM) allows a systematic way to design and synthesize a filter with various frequency response.

•ILM method also allows filter performance to be improved in a straightforward manner, at the expense of a ‘higher order’ filter.

•A rational polynomial function is used to approximate the ideal |H()|, A() or |s21()|.

•Phase information is totally ignored.Ignoring phase simplified the actual synthesis method. An LC network is then derived that will produce this approximated response.

•Here we will use A() following [2]. The attenuation A() can be cast into power attenuation ratio, called the Power Loss Ratio, PLR, which is related to A()2.

17


211

12

11

Load todeliveredPower network source from availablePower

AP

AP

LoadPincP

LRP

PLR large, high attenuationPLR close to 1, low attenuationFor example, a low-passfilter response is shownbelow:

PLR large, high attenuationPLR close to 1, low attenuationFor example, a low-passfilter response is shownbelow:

ZLVs

Lossless2-port network

1

Zs

PAPin

PL

PLR(f)

Low-Pass filter PLRf

1

0

Low attenuation

Highattenuation

fc

(2.1a)

18

PLR and s21

In terms of incident and reflected waves, assuming ZL=Zs = ZC.

ZcVs

Lossless2-port network

Zc

PAPin

PL

a1

b1

b2

221

1

2

21

222

1

212

1

sLR

ba

b

a

LPAP

LR

P

P

(2.1b)

19

FILTER RESPONSES

Filter Responses

Several types filter responses:- Maximally flat (Butterworth)- Equal Ripple (Chebyshev)- Elliptic Function- Linear Phase

20

THE INSERTION LOSS METHOD

Practical filter response:

Maximally flat:- also called the binomial or Butterworth response,- is optimum in the sense that it provides the flattest possible passband response for a given filter complexity.- no ripple is permitted in its attenuation profile

N

cLR kP

21

[8.10]

– frequency of filter c – cutoff frequency of filterN – order of filter

21


Equal ripple- also known as Chebyshev.- sharper cutoff- the passband response will have ripples of amplitude 1 +k2

cNLR TkP

221 [8.11]

– frequency of filter c – cutoff frequency of filterN – order of filter

22


Figure 5.3: Maximally flat and equal-ripple low pass filter response.

23


Elliptic function:- have equal ripple responses in the passband and stopband.- maximum attenuation in the passband.- minimum attenuation in the stopband.

Linear phase:- linear phase characteristic in the passband- to avoid signal distortion- maximally flat function for the group delay.

24


Figure 5.4: Elliptic function low-pass filter response

25


Filter Specification

Low-pass Prototype

Design

Scaling & Conversion

Filter Implementation

Optimization & Tuning

Normally done using simulators

Figure 5.5: The process of the filter design by the insertion loss method.

26


Figure 5.6: Low pass filter prototype, N = 2

Low Pass Filter Prototype

27


Figure 5.7: Ladder circuit for low pass filter prototypes and their element definitions. (a) begin with shunt element. (b) begin with

series element.

Low Pass Filter Prototype – Ladder Circuit

28


g0 = generator resistance, generator conductance.

gk = inductance for series inductors, capacitance for shunt capacitors.(k=1 to N)

gN+1 = load resistance if gN is a shunt capacitor, load conductance if gN is a series inductor.

As a matter of practical design procedure, it will be necessary to determine the size, or order of the filter. This is usually dictated by a specification on the insertion loss at some frequency in the stopband of the filter.

29


Figure 4.8: Attenuation versus normalized frequency for maximally flat filter prototypes.

Low Pass Filter Prototype – Maximally Flat

30


Figure 4.9: Element values for maximally flat LPF prototypes

31


221 NLR TkP

For an equal ripple low pass filter with a cutoff frequency ωc = 1, The power loss ratio is:

1

0NT

[5.12]

Where 1 + k2 is the ripple level in the passband. Since the Chebyshev polynomials have the property that

[5.12] shows that the filter will have a unity power loss ratio at ω = 0 for N odd, but the power loss ratio of 1 + k2 at ω = 0 for N even.

Low Pass Filter Prototype – Equal Ripple

32


Figure 4.10: Attenuation versus normalized frequency for equal-ripple filter prototypes. (0.5 dB ripple level)

33


Figure 4.11: Element values for equal ripple LPF prototypes (0.5 dB ripple level)

34


Figure 4.12: Attenuation versus normalized frequency for equal-ripple filter prototypes (3.0 dB ripple level)

35


Figure 4.13: Element values for equal ripple LPF prototypes (3.0 dB ripple level).

36

FILTER TRANSFORMATIONS

LL

s

RRR

RR

R

CC

LRL

0'

0'

0

'

0'

[8.13a]

[8.13b]

[8.13c]

[8.13d]

Low Pass Filter Prototype – Impedance Scaling

37


'

'

kkc

k

kkc

k

CjCjjB

LjLjjX

The new element values of the prototype filter:

c

Frequency scaling for the low pass filter:

[8.14]

[8.15a]

[8.15b]

38


The new element values are given by:

c

kkk

c

kkk

R

CCC

LRLL

0

'

0'

[8.16a]

[8.16b]

39


c

Low pass to high pass transformation

The frequency substitution:

kck

kck

C

RL

LRC

0'

0

' 1

The new component values are given by:

[8.17]

[8.18a]

[8.18b]

40

BANDPASS & BANDSTOP TRANSFORMATIONS

0

0

0

012

0 1

0

12

210

Where,

The center frequency is:

[8.19]

[8.20]

[8.21]

Low pass to Bandpass transformation

41


kk

kk

LC

LL

0

'

0

'

The series inductor, Lk, is transformed to a series LC circuit with element values:

The shunt capacitor, Ck, is transformed to a shunt LC circuit with element values:

0

'

0

'

kk

kk

CC

CL

[8.22a]

[8.22b]

[8.23a]

[8.23b]

42


1

0

0

0

12

210

Where,

The center frequency is:

[8.24]

Low pass to Bandstop transformation

43


kk

kk

LC

LL

0

'

0

'

1

The series inductor, Lk, is transformed to a parallel LC circuit with element values:

The shunt capacitor, Ck, is transformed to a series LC circuit with element values:

0

'

0

' 1

kk

kk

CC

CL

[8.25a]

[8.25b]

[8.26a]

[8.26b]

44


45

EXAMPLE 5.1

Design a maximally flat low pass filter with a cutoff freq of 2 GHz, impedance of 50 Ω, and at least 15 dB insertion loss at 3 GHz. Compute and compare with an equal-ripple (3.0 dB ripple) having the same order.

46

EXAMPLE 5.1 (Cont)

Solution: First find the order of the maximally flat filter to satisfy the insertion loss specification at 3 GHz.

618.0

618.1

0.2

618.1

618.0

5

4

3

2

1

g

g

g

g

g

We can find the normalized freq by using: 5.012

31

c

47

EXAMPLE 5.1 (Cont)

The ladder diagram of the LPF prototype to be used is as follow:

LL

s

RRR

RR

R

CC

LRL

0'

0'

0

'

0'

C3 C5

L2 L4

C1

cR

gC

0

11

c

gRL

20

2

cR

gC

0

33

c

gRL

40

4

cR

gC

0

55

48

EXAMPLE 5.1 (Cont)

984.0102250

618.09

0

11

cR

gC

438.61022

618.1509

202

c

gRL

183.3102250

00.29

0

33

cR

gC

438.61022

618.1509

404

c

gRL

984.0102250

618.09

0

55

cR

gC

pF

nH

pF

nH

pF

LPF prototype for maximally flat filter

49

EXAMPLE 5.1 (Cont)

541.5102250

4817.39

0

11

cR

gC

031.31022

7618.0509

202

c

gRL

223.7102250

5381.49

0

33

cR

gC

031.31022

7618.0509

404

c

gRL

541.5102250

4817.39

0

55

cR

gC

pF

nH

pF

nH

pF

4817.3

7618.0

5381.4

7618.0

4817.3

5

4

3

2

1

g

g

g

g

g

LPF prototype for equal ripple filter:

50


Filter Specification

Low-pass Prototype

Design

Scaling & Conversion

Filter Implementation

Optimization & Tuning

Normally done using simulators

51

SUMMARY OF STEPS IN FILTER DESIGN

A. Filter Specification

1. Max Flat/Equal Ripple,

2. If equal ripple, how much pass band ripple allowed? If max

flat filter is to be designed, cont to next step

3. Low Pass/High Pass/Band Pass/Band Stop

4. Desired freq of operation

5. Pass band & stop band range

6. Max allowed attenuation (for Equal Ripple)

52

SUMMARY OF STEPS IN FILTER DESIGN (cont)

B. Low Pass Prototype Design

1. Min Insertion Loss level, No of Filter

Order/Elements by using IL values

2. Determine whether shunt cap model or series

inductance model to use

3. Draw the low-pass prototype ladder diagram

4. Determine elements’ values from Prototype Table

53


C. Scaling and Conversion

1. Determine whether if any modification to the

prototype table is required (for high pass, band

pass and band stop)

2. Scale elements to obtain the real element values

54


D. Filter Implementation

1. Put in the elements and values calculated from

the previous step

2. Implement the lumped element filter onto a

simulator to get the attenuation vs frequency

response

55

EXAMPLE 5.2

Design a band pass filter having a 0.5 dB equal-ripple response, with N = 3. The center frequency is 1 GHz, the bandwidth is 10%, and the impedance is 50 Ω.

56

EXAMPLE 5.2 (Cont)

Solution: The low pass filter (LPF) prototype ladder diagram is shown as follow:

= 0.1 N = 3 = 1 GHz

CAPID=C1C=5.15 pF

INDID=L1L=15.91 nH

INDID=L2L=4.918 nH

ACCSID=I1Mag=1 mAAng=0 DegOffset=0 mADCVal=0 mA

RESID=R1R=1 Ohm

RESID=R2R=1 Ohm

RSL1 L3

C2 RL

57

EXAMPLE 5.2 (Cont)

From the equal ripple filter table (with 0.5 dB ripple), the filter elements are as follow;

LRg

Lg

Cg

Lg

000.1

5963.1

0967.1

5963.1

4

33

2

1

2

1

58

EXAMPLE 5.2 (Cont)

Transforming the LPF prototype to the BPF prototype

INDID=L2L=1 nH

CAPID=C1C=1 pF

CAPID=C2C=1 pF

ACCSNID=I1Mag=10 mAAng=0 DegF=1 GHzTone=2Offset=0 mADCVal=0 mA

RESID=R1R=1 Ohm RES

ID=R2R=1 Ohm

INDID=L1L=1 nH

INDID=L3L=1 nH

CAPID=C3C=1 pF

RS

RL

C1

C2

C3L1

L2

L3

59

EXAMPLE 5.2 (Cont)

pFLZ

C 199.05963.1102250

1.09

1001

nHZL

L 0.1271.01012

505963.19

0

1

1

0

pFZ

CC 91.34

50)1.0(1012

0967.19

00

22

nHC

ZL 726.0

0967.11012

501.09

20

02

60

EXAMPLE 5.2 (Cont)

pFLZ

C 199.05963.1102250

1.09

3003

nHZL

L 0.1271.01012

505963.19

0

3 0

3

61

EXAMPLE 5.3

Design a five-section high pass lumped element filter with 3 dB equal-ripple response, a cutoff frequency of 1 GHz, and an impedance of 50 Ω. What is the resulting attenuation at 0.6 GHz?

62

EXAMPLE 5.3 (Cont)

Solution: The high pass filter (HPF) prototype ladder diagram is shown as follow:

N = 5 = 1 GHz

At c = 0.6 GHz, ; referring back to Fig 4.12

The attenuation for N = 5, is about 41 dB

INDID=L1L=1 nH

INDID=L2L=1 nH

INDID=L3L=1 nH

CAPID=C1C=1 pF

CAPID=C2C=1 pF

ACCSNID=I1Mag=10 mAAng=0 DegF=1 GHzTone=2Offset=0 mADCVal=0 mA

RESID=R1R=1 Ohm

RESID=R2R=1 Ohm

RS

RLL1 L3 L5

C2 C3

667.016.0

11

c

63

EXAMPLE 5.3 (Cont)

From the equal ripple filter table (with 3.0 dB ripple), the filter elements are as follow;

LRg

Lg

Cg

Lg

Cg

Lg

000.1

4817.3

7618.0

5381.4

7618.0

4817.3

6

55

44

33

2

1

2

1

64

EXAMPLE 5.3 (Cont)

pFCZ

Cc

18.47618.0101250

11'

920

2

nHL

ZL

c

28.24817.31012

50'

91

1

0

nHL

ZL

c

754.15381.41012

50'

93

03

Impedance and frequency scaling:

65

EXAMPLE 5.3 (Cont)

pFCZ

Cc

18.47618.0101250

11'

940

4

nHL

ZL

c

754.15381.41012

50'

95

05

66

EXAMPLE 5.4

Design a 4th order Butterworth Low-Pass Filter. Rs = RL= 50Ohm, fc = 1.5GHz.

L1=0.7654H L2=1.8478H

C1=1.8478F C2=0.7654FRL= 1g0= 1

L1=4.061nH L2=9.803nH

C1=3.921pF C2=1.624pFRL= 50g0=1/50

noRZR

c

no

LZL

co

n

Z

CC

50Z

rad/s 104248.95.12

o

9

GHzc

Step 1&2: LPP

Step 3: Frequency scalingand impedance denormalization

67

EXAMPLE 5.5

Design a 4th order Chebyshev Low-Pass Filter, 0.5dB ripple factor. Rs = 50Ohm, fc = 1.5GHz.

L1=1.6703H L2=2.3661H

C1=1.1926F C2=0.8419FRL= 1.9841

g0= 1

L1=8.861nH L2=12.55nH

C1=2.531pF C2=1.787pFRL= 99.2

g0=1/50

noRZR

c

no

LZL

co

n

Z

CC

50Z

rad/s 104248.95.12

o

9

GHzc

Step 1&2: LPP


68

EXAMPLE 5.6

Design a bandpass filter with Butterworth (maximally flat) response.

N = 3. Center frequency fo = 1.5GHz.

3dB Bandwidth = 200MHz or f1=1.4GHz, f2=1.6GHz.

69

EXAMPLE 5.6 (cont)

From table, design the Low-Pass prototype (LPP) for 3rd order Butterworth response, c=1.

Zo=1

g1 1.000F

g3 1.000F

g2 2.000H

g4

12<0o

Hz 1592.0

12

21

c

cc

f

f

Step 1&2: LPP

70

EXAMPLE 5.6 (cont) LPP to bandpass transformation. Impedance denormalization.

133.0

497.1

6.12

4.12

12

21

2

1

o

GHzfff

GHz

GHz

o

50

Vs15.916pF

0.1414pF79.58nH

0.7072nH 0.7072nH15.916pF50

RL

o

oLZ

ooLZ oo Z

C

C

Z

o

o


chp4-microwave filters_withexamples

Documents

passive filter

filter passive

active filter

filter hpf

filter lpf

filter performance

r filter response

goal of filter design