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REPORT

COUPLED LINE BANDPASS FILTERS

S.SRINATH

AND

N.AJAY

Software Used : Agilent ADS 2011

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ACKNOWLEDGEMENTS

At the outset, We would like to express our gratitude for our institute – VelloreInstitute of Technology (V.I.T.) for providing us with the opportunity to undergoour undergraduate training, and assimilate knowledge and experience hithertounknown to us.

We would like to sincerely thank our teacher, Prof.Dr.Vijay Kumar for havingbelief in us when he allowed us to undertake the project work, for his constantsupport during the course of our activities. We will forever be obliged to him forhis assistance, encouragement and guidance.

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CONTENTS

CHAPTER 1: INTRODUCTION1.1BANDPASS FILTERS………………………………………………………….…..4

1.2 IMPEDANCE AND ADMITTANCE INVERTERS………………………..….5

1.3 COUPLED LINE FILTERS - INTRODUCTION………………………………..7

CHAPTER 2: COUPLED LINE FILTERS THEORY

3.COUPLED LINE FILTERS - THEORY.………….…………............................8

3.2 FILTER PROPERTIES OF A COUPLED LINE SECTION……………………..9

CHAPTER 3: BANDPASS FILTER THEORY

3.1 DESIGN OF COUPLED LINE B.P.F…………………………………………….…10

3.2 DEVELOPMENT OF EQUIVALENT CIRCUIT…………………………………13

CHAPTER 4: PROJECT DESIGN

4.1 DESIGN………………………………………………………………………………….…19

4.2 LINE CALC…………………………………………………………………….…………..23

CHAPTER 5: SIMULATION AND RESULT

5.1 SIMULATION………………………………………………….…………………………24

5.2 RESULT………………………….………………………………………………………….25

CHAPTER 6: CONCLUSIONS …………………….……………………………………………….…..26

CHAPTER 7: REFERENCES……………………………………………………………………………...27

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CHAPTER 1

Introduction :

1.1 Bandpass and Bandstop Filters

A useful form of bandpass and bandstop filter consists of λ/4 stubs connected byλ/4 transmission lines. Consider the bandpass filter here

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CHAPTER 1

Introduction :

1.1 Bandpass and Bandstop Filters

A useful form of bandpass and bandstop filter consists of λ/4 stubs connected byλ/4 transmission lines. Consider the bandpass filter here

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CHAPTER 1

Introduction :

1.1 Bandpass and Bandstop Filters

A useful form of bandpass and bandstop filter consists of λ/4 stubs connected byλ/4 transmission lines. Consider the bandpass filter here

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The quarter wave sections transform the center shunt parallel resonant circuitadmittance to a series impedance that is a series resonant circuit.

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The quarter wave sections transform the center shunt parallel resonant circuitadmittance to a series impedance that is a series resonant circuit.

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The quarter wave sections transform the center shunt parallel resonant circuitadmittance to a series impedance that is a series resonant circuit.

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1.2 Impedance and Admittance Inverters

Coupled Line Filters

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1.2 Impedance and Admittance Inverters

Coupled Line Filters

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1.2 Impedance and Admittance Inverters

Coupled Line Filters

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1.3 Coupled Line Filters - Introduction

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1.3 Coupled Line Filters - Introduction

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1.3 Coupled Line Filters - Introduction

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CHAPTER 2

Coupled Line Fliters - Thoery

2.1 Coupled Line Fliters - Thoery

The parallel coupled transmission lines can be used to construct many types offilters. Fabrication of multisection bandpass or bandstop coupled line filters isparticularly easy in microstrip or stripline form for bandwidths less than about20%.Wider bandwidth filters generally require very tightly coupled lines, whichare difficult to fabricate.

A two-port network can be formed from a coupled line section by terminatingtwo of the four ports with either open or short circuits, or by connecting twoends; there are 3 possible band-pass combinations,

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CHAPTER 2

Coupled Line Fliters - Thoery

2.1 Coupled Line Fliters - Thoery

The parallel coupled transmission lines can be used to construct many types offilters. Fabrication of multisection bandpass or bandstop coupled line filters isparticularly easy in microstrip or stripline form for bandwidths less than about20%.Wider bandwidth filters generally require very tightly coupled lines, whichare difficult to fabricate.

A two-port network can be formed from a coupled line section by terminatingtwo of the four ports with either open or short circuits, or by connecting twoends; there are 3 possible band-pass combinations,

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CHAPTER 2

Coupled Line Fliters - Thoery

2.1 Coupled Line Fliters - Thoery

The parallel coupled transmission lines can be used to construct many types offilters. Fabrication of multisection bandpass or bandstop coupled line filters isparticularly easy in microstrip or stripline form for bandwidths less than about20%.Wider bandwidth filters generally require very tightly coupled lines, whichare difficult to fabricate.

A two-port network can be formed from a coupled line section by terminatingtwo of the four ports with either open or short circuits, or by connecting twoends; there are 3 possible band-pass combinations,

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2.2 Filter Properties of a Coupled Line Section

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2.2 Filter Properties of a Coupled Line Section

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2.2 Filter Properties of a Coupled Line Section

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CHAPTER 3

Coupled Line Bandpass Filters

3.1 Design of Coupled Line Bandpass Filters

Narrowband bandpass filters can be made with cascaded coupled line sections ofthe form shown in Figure.

A two-port coupled line section having a bandpass response.

To derive the design equations for filters of this type, a single coupled linesection can be approximately modeled by the equivalent circuit shown in Figure.

Equivalent circuit of the coupled line section of above figure

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CHAPTER 3

Coupled Line Bandpass Filters

3.1 Design of Coupled Line Bandpass Filters

Narrowband bandpass filters can be made with cascaded coupled line sections ofthe form shown in Figure.

A two-port coupled line section having a bandpass response.

To derive the design equations for filters of this type, a single coupled linesection can be approximately modeled by the equivalent circuit shown in Figure.

Equivalent circuit of the coupled line section of above figure

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CHAPTER 3

Coupled Line Bandpass Filters

3.1 Design of Coupled Line Bandpass Filters

Narrowband bandpass filters can be made with cascaded coupled line sections ofthe form shown in Figure.

A two-port coupled line section having a bandpass response.

To derive the design equations for filters of this type, a single coupled linesection can be approximately modeled by the equivalent circuit shown in Figure.

Equivalent circuit of the coupled line section of above figure

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We will do this by calculating the image impedance and propagationconstant of the equivalent circuit and showing that they are approximately equalto those of the coupled line section for θ = π/2, which will correspond to thecenter frequency of the bandpass response.

ABCD Parameters of Some Useful Two-Port Circuits

Table 3.1

The ABCD parameters of the equivalent circuit can be computed using the ABCDmatrices for transmission lines from Table:

The ABCD parameters of the admittance inverter were obtained by considering itas a quarter-wave length of transmission of characteristic impedance, 1/J .

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We will do this by calculating the image impedance and propagationconstant of the equivalent circuit and showing that they are approximately equalto those of the coupled line section for θ = π/2, which will correspond to thecenter frequency of the bandpass response.

ABCD Parameters of Some Useful Two-Port Circuits

Table 3.1

The ABCD parameters of the equivalent circuit can be computed using the ABCDmatrices for transmission lines from Table:

The ABCD parameters of the admittance inverter were obtained by considering itas a quarter-wave length of transmission of characteristic impedance, 1/J .

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We will do this by calculating the image impedance and propagationconstant of the equivalent circuit and showing that they are approximately equalto those of the coupled line section for θ = π/2, which will correspond to thecenter frequency of the bandpass response.

ABCD Parameters of Some Useful Two-Port Circuits

Table 3.1

The ABCD parameters of the equivalent circuit can be computed using the ABCDmatrices for transmission lines from Table:

The ABCD parameters of the admittance inverter were obtained by considering itas a quarter-wave length of transmission of characteristic impedance, 1/J .

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FROM FILTER DESIGN BY THE IMAGE PARAMETERMETHOD :

From the above equations the image impedance of the equivalent circuit is

which reduces to the following value at the center frequency, θ = π/2:

We also have that

The propagation constant is

Equating the image impedances , and the propagation constants, yields thefollowing equations:

where we have assumed sinθ _ 1 for θ near π/2. These equations can be solvedfor the even- and odd-mode line impedances to give

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FROM FILTER DESIGN BY THE IMAGE PARAMETERMETHOD :

From the above equations the image impedance of the equivalent circuit is

which reduces to the following value at the center frequency, θ = π/2:

We also have that

The propagation constant is

Equating the image impedances , and the propagation constants, yields thefollowing equations:

where we have assumed sinθ _ 1 for θ near π/2. These equations can be solvedfor the even- and odd-mode line impedances to give

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FROM FILTER DESIGN BY THE IMAGE PARAMETERMETHOD :

From the above equations the image impedance of the equivalent circuit is

which reduces to the following value at the center frequency, θ = π/2:

We also have that

The propagation constant is

Equating the image impedances , and the propagation constants, yields thefollowing equations:

where we have assumed sinθ _ 1 for θ near π/2. These equations can be solvedfor the even- and odd-mode line impedances to give

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3.2 Development of an equivalent circuit for derivation of designequations for a coupled line bandpass filter for N=2.

(a) Layout of an (N + 1)-section coupled line bandpass filter.

(b) Using the equivalent circuit of Figure for each coupled line section.

(c) Equivalent circuit for transmission lines of length 2θ.

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3.2 Development of an equivalent circuit for derivation of designequations for a coupled line bandpass filter for N=2.

(a) Layout of an (N + 1)-section coupled line bandpass filter.

(b) Using the equivalent circuit of Figure for each coupled line section.

(c) Equivalent circuit for transmission lines of length 2θ.

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3.2 Development of an equivalent circuit for derivation of designequations for a coupled line bandpass filter for N=2.

(a) Layout of an (N + 1)-section coupled line bandpass filter.

(b) Using the equivalent circuit of Figure for each coupled line section.

(c) Equivalent circuit for transmission lines of length 2θ.

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(d) Equivalent circuit of the admittance inverters.

(e) Using results of (c) and (d) for the N = 2 case.

(f) Lumped-element circuit for a bandpass filter for N = 2.

Now consider a bandpass filter composed of a cascade of N + 1 coupled linesections, as shown in Figure a. The sections are numbered from left to right, withthe load on the right, but the filter can be reversed without affecting the response.Since each coupled line section has an equivalent circuit of the form shown inFigure 2.2, the equivalent circuit of the cascade is as shown in Figure b. Betweenany two consecutive inverters we have a transmission line section that iseffectively 2θ in length. This line is approximately λ/2 long in the vicinity of thebandpass region of the filter, and has an approximate equivalentcircuit that consists of a shunt parallel LC resonator, as in Figure c.

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(d) Equivalent circuit of the admittance inverters.

(e) Using results of (c) and (d) for the N = 2 case.

(f) Lumped-element circuit for a bandpass filter for N = 2.

Now consider a bandpass filter composed of a cascade of N + 1 coupled linesections, as shown in Figure a. The sections are numbered from left to right, withthe load on the right, but the filter can be reversed without affecting the response.Since each coupled line section has an equivalent circuit of the form shown inFigure 2.2, the equivalent circuit of the cascade is as shown in Figure b. Betweenany two consecutive inverters we have a transmission line section that iseffectively 2θ in length. This line is approximately λ/2 long in the vicinity of thebandpass region of the filter, and has an approximate equivalentcircuit that consists of a shunt parallel LC resonator, as in Figure c.

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(d) Equivalent circuit of the admittance inverters.

(e) Using results of (c) and (d) for the N = 2 case.

(f) Lumped-element circuit for a bandpass filter for N = 2.

Now consider a bandpass filter composed of a cascade of N + 1 coupled linesections, as shown in Figure a. The sections are numbered from left to right, withthe load on the right, but the filter can be reversed without affecting the response.Since each coupled line section has an equivalent circuit of the form shown inFigure 2.2, the equivalent circuit of the cascade is as shown in Figure b. Betweenany two consecutive inverters we have a transmission line section that iseffectively 2θ in length. This line is approximately λ/2 long in the vicinity of thebandpass region of the filter, and has an approximate equivalentcircuit that consists of a shunt parallel LC resonator, as in Figure c.

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The first step in establishing this equivalence is to find the parameters for theTequivalent and ideal transformer circuit of Figure c (an exact equivalent). TheABCD matrix for this circuit can be calculated for a T-circuit and anideal transformer:

Equating this result to the ABCD parameters for a transmission line of length 2θand characteristic impedance Z0 gives the parameters of the equivalent circuit as

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The first step in establishing this equivalence is to find the parameters for theTequivalent and ideal transformer circuit of Figure c (an exact equivalent). TheABCD matrix for this circuit can be calculated for a T-circuit and anideal transformer:

Equating this result to the ABCD parameters for a transmission line of length 2θand characteristic impedance Z0 gives the parameters of the equivalent circuit as

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The first step in establishing this equivalence is to find the parameters for theTequivalent and ideal transformer circuit of Figure c (an exact equivalent). TheABCD matrix for this circuit can be calculated for a T-circuit and anideal transformer:

Equating this result to the ABCD parameters for a transmission line of length 2θand characteristic impedance Z0 gives the parameters of the equivalent circuit as

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The end sections of the circuit of Figure b require a different treatment. The linesof length θ on either end of the filter are matched to Z0 and so can be ignored.The end inverters, J1 and JN+1, can each be represented as a transformerfollowed by a λ/4 section of line, as shown in Figure d. The ABCD matrix of atransformer with a turns ratio N in cascade with a quarter-wave line is

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The end sections of the circuit of Figure b require a different treatment. The linesof length θ on either end of the filter are matched to Z0 and so can be ignored.The end inverters, J1 and JN+1, can each be represented as a transformerfollowed by a λ/4 section of line, as shown in Figure d. The ABCD matrix of atransformer with a turns ratio N in cascade with a quarter-wave line is

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The end sections of the circuit of Figure b require a different treatment. The linesof length θ on either end of the filter are matched to Z0 and so can be ignored.The end inverters, J1 and JN+1, can each be represented as a transformerfollowed by a λ/4 section of line, as shown in Figure d. The ABCD matrix of atransformer with a turns ratio N in cascade with a quarter-wave line is

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CHAPTER 4

Project Design

4.1Design – ADS Simulation

The order of the filter was calculated assuming an equi-ripple (Chebyshev type1) response with an attenuation of 20dB at the center frequency of 5.85 Ghz andthe pass band ripple amplitude (G) of 0.5dB.

Using the standard Chebyshev model:

This gives us n=3. Now, we get the low pass prototype values from the standardChebyshev table:

The elements values obtained are g0=g4=1, g1=g3=1.5963,and g2=1.0967. Thelow-pass prototype elements values obtained can be represented as shown

Low-pass filter prototype

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CHAPTER 4

Project Design

4.1Design – ADS Simulation

The order of the filter was calculated assuming an equi-ripple (Chebyshev type1) response with an attenuation of 20dB at the center frequency of 5.85 Ghz andthe pass band ripple amplitude (G) of 0.5dB.

Using the standard Chebyshev model:

This gives us n=3. Now, we get the low pass prototype values from the standardChebyshev table:

The elements values obtained are g0=g4=1, g1=g3=1.5963,and g2=1.0967. Thelow-pass prototype elements values obtained can be represented as shown

Low-pass filter prototype

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CHAPTER 4

Project Design

4.1Design – ADS Simulation

The order of the filter was calculated assuming an equi-ripple (Chebyshev type1) response with an attenuation of 20dB at the center frequency of 5.85 Ghz andthe pass band ripple amplitude (G) of 0.5dB.

Using the standard Chebyshev model:

This gives us n=3. Now, we get the low pass prototype values from the standardChebyshev table:

The elements values obtained are g0=g4=1, g1=g3=1.5963,and g2=1.0967. Thelow-pass prototype elements values obtained can be represented as shown

Low-pass filter prototype

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• The low-pass filter consists of series and parallel branch.

• J-inverter is used to convert low-pass filter to bandpass filter

Bandpass filter prototype

Now, we use the following design equations to get the inverter constants for acoupled line filter with N+ 1 sections:

Based on the filter application in system design, the fractional bandwidth(FBW) is calculated using equation below:

where, ω1 and ω2 denote the edges of the passband frequency.

FBW = (6.5Ghz – 5.3Ghz)/5.85Ghz = 205MHz

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• The low-pass filter consists of series and parallel branch.

• J-inverter is used to convert low-pass filter to bandpass filter

Bandpass filter prototype

Now, we use the following design equations to get the inverter constants for acoupled line filter with N+ 1 sections:

Based on the filter application in system design, the fractional bandwidth(FBW) is calculated using equation below:

where, ω1 and ω2 denote the edges of the passband frequency.

FBW = (6.5Ghz – 5.3Ghz)/5.85Ghz = 205MHz

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• The low-pass filter consists of series and parallel branch.

• J-inverter is used to convert low-pass filter to bandpass filter

Bandpass filter prototype

Now, we use the following design equations to get the inverter constants for acoupled line filter with N+ 1 sections:

Based on the filter application in system design, the fractional bandwidth(FBW) is calculated using equation below:

where, ω1 and ω2 denote the edges of the passband frequency.

FBW = (6.5Ghz – 5.3Ghz)/5.85Ghz = 205MHz

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• Then the odd and even resistance calculated by using equation

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• Then the odd and even resistance calculated by using equation

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• Then the odd and even resistance calculated by using equation

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Now, the even and odd mode impedances can be calculated as follows:

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Now, the even and odd mode impedances can be calculated as follows:

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Now, the even and odd mode impedances can be calculated as follows:

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4.2 ADS Simulation – Line Calc

ADS Simulation – Line Calc-Coupled Line 1 & 4

ADS Simulation – Line Calc-Coupled Line 2 & 3

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4.2 ADS Simulation – Line Calc

ADS Simulation – Line Calc-Coupled Line 1 & 4

ADS Simulation – Line Calc-Coupled Line 2 & 3

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4.2 ADS Simulation – Line Calc

ADS Simulation – Line Calc-Coupled Line 1 & 4

ADS Simulation – Line Calc-Coupled Line 2 & 3

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CHAPTER 5

ADS Simulation

5.1 ADS Simulation – 3rd Order Filter

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CHAPTER 5

ADS Simulation

5.1 ADS Simulation – 3rd Order Filter

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CHAPTER 5

ADS Simulation

5.1 ADS Simulation – 3rd Order Filter

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5.2ADS Simulation – Result

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5.2ADS Simulation – Result

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5.2ADS Simulation – Result

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CHAPTER 6

Conclusion

6.1 ADS Simulation – Conclusion

On a substrate with a dielectric constant of 3.38, the centerfrequency of 5.85 GHz was selected, the bandwidth is 200MHz, the minimum attenuation amounts to -20 dB and thepass-band ripple is obtained equal to 0.5 dB.

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CHAPTER 7

References

7.1 References

1. Design and Optimization of Parallel Coupled MicrostripBandpass Filter for FM Wireless Applications -Salima Seghier,Nadia Benabdallah, Nasreddine Benahmed,Fethi TarikBendimerad and Kamila Aliane.

2. MICROWAVE FILTER DESIGN: COUPLED LINE FILTER - Michael S.Flanner

H. Karimi zarajabad and S. Nikmehr, “A Novel Fractal Geometry forHarmonic Suppression in Parallel Coupled- Line MicrostripBandPass Filter”, IEEE 2008.

Miguel Bacaicoa, David Benito, Maria J. Garde, Mario Sorolla andMarco Guglielmi, “New Microstrip Wiggly-Line Filters withSpurious Pass-band Suppression”, IEEE Transactions on microwavetheory and techniques, vol. 49, no. 9, September 2001.

Hong, J.S., M.J, “Microstrip Filter for RF/Microwave Applications”,A Wiley- Interscience Publication, Canada, 2001.

D. M. Pozar, “Microwave Engineering”, John Wiley & Sons Inc.,1998