DESIGN, SIMULATION, FABRICATION AND TESTING OF IMPROVED WIDEBAND MICROSTRIP BALUN CIRCUIT OPERATING FROM 1-12 GHz

Chandra Anusha Kotagiri B.Tech, J N T University, India, 2008

Navya Harika Nimmagadda B.Tech, J N T University, India, 2008

PROJECT

Submitted in partial satisfaction of the requirements for the degree of

MASTER OF SCIENCE

in

ELECTRICAL AND ELECTRONIC ENGINEERING

at

CALIFORNIA STATE UNIVERSITY, SACRAMENTO

FALL 2011

ii

DESIGN, SIMULATION, FABRICATION AND TESTING OF IMPROVED WIDEBAND MICROSTRIP BALUN CIRCUIT OPERATING FROM 1-12 GHz

A Project

by

Chandra Anusha Kotagiri

and

Navya Harika Nimmagadda

Approved by: __________________________________, Committee Chair Preetham B. Kumar, Ph.D. __________________________________, Second Reader Russell L. Tatro, M.S. ___________________________ Date

iii

Students: Chandra Anusha Kotagiri Navya Harika Nimmagadda

I certify that these students have met the requirements for format contained in the

University format manual, and that this project is suitable for shelving in the Library and

credit is to be awarded for the project.

___________________, Graduate Coordinator _________________ Preetham B. Kumar, Ph.D. Date

Department of Electrical and Electronic Engineering

iv

Abstract

of

DESIGN, SIMULATION, FABRICATION AND TESTING OF IMPROVED WIDEBAND MICROSTRIP BALUN CIRCUIT OPERATING FROM 1-12 GHz

by

Chandra Anusha Kotagiri Navya Harika Nimmagadda

The objective of the project is to design, fabricate and test a broadband micro strip balun

to operate at a center frequency of 5 GHz and with a bandwidth range of 1-12 GHz. A

balun circuit is used in commercial applications such as cellular telephones, high

definition television and other circuits, which receives a single-ended input signal to

generate an amplified differential signal with 180° of phase difference, with low VSWR

at the input and output ports. The simulation of the design was done using the Agilent

Advanced Design System (ADS) software. The circuit was then fabricated in microstrip,

and the simulated results demonstrate high amplitude, phase balance, and low VSWR

over the operating frequency range. The measured results also demonstrate good

amplitude and phase balance, thought the VSWR values are on the high side, and future

work will focus on further improvement in performance

, Committee Chair Preetham B. Kumar, Ph.D. ______________________, Date

v

ACKNOWLEDGEMENTS

We wish to express sincere gratitude to all those who gave us the possibility to complete

this project.

Firstly we would like to thank our advisor, committee chair and graduate coordinator Dr.

Preetham Kumar, for his eminent guidance, valuable help and encouragement throughout

this project.

We sincerely thank Mr. Russell Tatro our second reader, for reviewing this work and for

his time, guidance, patience and understanding.

We would also like to thank Mr. R.K. Ravuri for helping us in the fabrication of the

circuit.

We would also like to take the opportunity to thank all the staff and faculty members of

College of Engineering and Computer Science, California State University, Sacramento

who contributed and helped us throughout our curriculum.

At the end we would like to thank our parents for their constant encouragement.

vi

TABLE OF CONTENTS

Page

Acknowledgement .............................................................................................................. v

List of Tables .................................................................................................................... vii

List of Figures .................................................................................................................. viii

Chapter

1. INTRODUCTION ...........................................................................................................1

2. DIRECTIONAL COUPLERS AND BALUNS.............................................................. 3

2.1 Directional Couplers ................................................................................................. 3

2.2 Balun Design ............................................................................................................. 6

3. IMPROVED MINIATURIZED WIDEBAND BALUN DESIGN OPERATING FROM 1-12 GHZ .......................................................................................................... 10

3.1 Basic Topology Of A Balun Design ....................................................................... 10

3.2 Broadband Balun Design ........................................................................................ 11

3.3 Some Of The Special Features Of The Balun…………...………………………...14

4. SIMULATION STUDY OF WIDEBAND BALUN DESIGN .................................... 15

5. LAYOUT AND FABRICATION OF WIDEBAND BALUN CIRCUIT .................... 18

6. MEASURED RESULTS FOR AMPLITUDE BALANCE, PHASE BALANCE AND VSWR VALUES……………………………………………………………...………25

7. CONCLUSION AND SCOPE FOR FUTURE WORK ................................................29

References ..........................................................................................................................30

vii

LIST OF TABLES Page

1. Table 3.1 Dimensions Of The Microstrip Balun Circuit……………………………13

2. Table 5.1 Specifications Of RT/DUROID Microwave Laminates………………….22 3. Table 6.1 Simulated Vs Measured results…………………………………………...27

viii

LIST OF FIGURES

Page

1. Figure 2.1 Basic schematic of directional coupler ........................................................ 4

2. Figure 2.2 Typical coaxial coupler ............................................................................... 5

3. Figure 2.3 Typical stripline coupler .............................................................................. 5

4. Figure 2.4 Typical waveguide coupler ........................................................................... 6

5. Figure 2.5 Diagram of a L-C lumped balun .................................................................. 7

6. Figure 2.6 Coaxial balun ............................................................................................... 8

7. Figure 2.7 Simple coupled line balun ........................................................................... 8

8. Figure 2.8 Simple coupled line balun, using broadside coupler structure ................... 9

9. Figure 3.1 Center tapped trasformer ........................................................................... 11

10. Figure 3.2 Design of microstrip wideband balun ...................................................... 12

11. Figure 4.1 Amplitude balance at output ports ............................................................ 15

12. Figure 4.2 Phase balance at the output ports.............................................................. 16

13. Figure 4.3 VSWR performance at input port and output ports .................................. 17

14. Figure 5.1 Layout of wideband balun circuit ............................................................. 18

15. Figure 5.2 Layout of wideband balun circuit in Gerber file………………………....19

16. Figure 5.3 Wideband balun without resistors………………………………………..20

17. Figure 5.4 Photograph of the router machine………………………………………..21

18. Figure 5.5 Wideband balun circuit with soldered resistors………………………….22

ix

19. Figure 5.6 Wideband balun circuit with soldering SMA connectors……………….23

20. Figure 5.7 HP/Agilent 8510C Network Analyzer…………………………………..23

21. Figure 6.1 Plot of Frequency vs Amplitude………………………………………...24

22. Figure 6.2 Plot of Frequency vs Phase………………………………………………25

23. Figure 6.3 Plot of Frequency vs VSWR…………………………………………….26

1

Chapter 1

INTRODUCTION

A balun circuit converts signals from a single-ended, unbalanced mode to a

balanced mode, having two signals of equal balance impedance but shifted 180 degrees in

phase over the specified frequency range with minimum loss and low voltage standing

wave ratio (VSWR). The circuit has one input port and two output ports. The main

application of this circuit is in the design of frequency conversion mixers to make cellular

phone and data transmission networks possible, and are also used in push-pull amplifiers.

Baluns are used to link a symmetrical (balance) circuit to an asymmetrical (unbalanced)

circuit. [1-7]

A balanced circuit is a circuit where the two sides have identical transmission

characteristics in all respects. An unbalanced circuit is the one in which voltages on the

two conductors are unequal with respect to ground. The ability of a balun to

electromagnetically couple an unbalanced input and produce a balanced output is

generally to achieve compatibility between systems, and as such, finds extensive

application in modern communications, particularly in realizing frequency conversion

mixers to make cellular phone and data transmission networks possible. They are also

used to convert a carrier signal from coaxial cable to Category five cable types designed

for high signal integrity [1-7].

Planar baluns are used as they have low insertion loss and wide bandwidth as

compared to other types of balun. Most of the current balun structures are narrowband for

2

specific applications. Therefore, there is a need of wideband matching structure for

wideband applications such as the rapidly developing area of Ultra Wideband (UWB)

systems. [4-7]

In this project, a broadband microstrip balun circuit was designed, simulated,

fabricated and tested in the Microwave Laboratory at CSUS. Earlier reports [8,9,11]

detail similar baluns, however, these designs lacked at least one of the fundamental

requirements of amplitude balance, phase balance or low VSWR. The current design

matched the requirements of amplitude/phase balance and low VSWR over a broadband

range of 1-12 GHz in simulation, however, while the measured amplitude and phase

balance showed good response, VSWR still requires some improvement.

The report is organized as follows: Chapter 1 is an introduction. Chapter 2

explains directional coupler and balun fundamentals. This chapter then describes

different types of directional couplers and later describes about balun design and its

applications.

Chapter 3 of the report describes the model of balun design with a center

frequency of 5GHz. Chapter 4 describes the computer simulations and optimization

needed to obtain the final form of the wideband balun circuit. Chapter 5 of the report

shows the design layout of the wideband balun circuit. Chapter 6 describes the measured

results of the wideband balun, and Chapter 6 describes the conclusions of the project and

the direction of future work. Finally the report gives list of relevant references.

3

Chapter 2

DIRECTIONAL COUPLERS AND BALUNS

2.1 Direction Coupler

Directional couplers are four-port circuits where one port is isolated from the

input port. All four ports are (ideally) matched, and the circuit is (ideally) lossless and

[2]. Directional couplers separate signals based on the direction of signal propagation.

These devices are used to unequally split the signal flowing in the mainline and to fully

pass the signal flowing in the opposite direction. Directional couplers are passive

reciprocal networks used in the field of radio technology by using two transmission lines

set close enough together so that energy passing through is coupled to the other. [2] . A

passive network contains no source that could add energy to the input signal and

reciprocal network is one in which the power losses are the same between any two ports

regardless of direction of propagation. Directional couplers can be realized in microstrip,

stripline, coax and waveguide. Directional couplers generally use distributed properties of

microwave circuits, the coupling feature is generally a quarter (or multiple) quarter-

wavelengths. [2]

There are different types of direction couplers, for example, hybrid couplers,

Bethe-hole coupler and coupled line couplers. This design focused on coupled line

couplers because of its ability to provide higher bandwidth. [2]

The basic function of directional coupler is to sample the forward and reverse

travelling waves through a transmission line or a waveguide. The common use of this

4

element is to measure the power level of a transmitted or received signal. The coupler is a

four port device. The forward travelling wave goes into port 1 and exit from port 2. A

small fraction of it goes out through port 4. In a perfect coupler no signal appears in port

4. Since the coupler is a lossless passive element, the sum of the signals power at ports 1

and 2 equals to the input signal power. The reverse travelling wave goes into port 2 and

out of port 1. A small fraction of it goes out through port 3. In a perfect coupler no signal

appears in port 4[14]. It can be described respectively by Coupling (C), Directivity (D)

and Isolation (I). Coupling is the ratio of input power to the coupled power. Directivity

(D) is the ratio of coupled power to the power at the isolated port. Isolation (I) is the ratio

of input power to power out of the isolated port. [4]

Figure 2.1 below shows the basic of directional coupler.

Figure 2.1 Basic of directional coupler [2]

Hybrid couplers are the special case of a four-port directional coupler that is

designed for a 3-dB (equal) power split. Hybrids come in two types, 90 degree or

5

quadrature hybrids, and 180 degree hybrids (such as rat-races and magic tees). 90 degree

hybrid coupler has a 90 degree phase shift between port 2 and 3 when fed from port 1.

And the magic-T hybrid or rat-race hybrid has a 180 degree phase shift between port 2

and 3 when fed from port 4. [2]

Fig 2.2 below shows a typical coaxial coupler

Fig 2.2 Typical coaxial coupler [13]

Figure 2.3 below shows a typical stripline coupler

Figure 2.3 Typical stripline coupler [4]

6

Figure 2.4 below shows a typical waveguide coupler.

Figure 2.4 Typical waveguide coupler [4]

2.2 Balun Design

A balun is a passive electronic device that translates between balanced and

unbalanced electrical signals and changes impedance. It can take many forms and their

presence is not always obvious. They always hold some form of electromagnetic coupling. A

balun’s function is to achieve compatibility between systems, and has wide applications in

modern communications. It helps in realizing frequency conversion mixers to make cellular

phone and data transmission networks possible. It is used in radio, video and audio

applications. They are used in for push-pull amplifier, balanced mixers and antenna feeds.

[9].

7

There are different types of balun designs: L-C balun, Transmission line and

Microstrip design.

• L-C balun design as shown in Figure 2.5 is also known as a “lattice-type” balun. It

is essentially a bridge. It has two capacitors and two inductors, which produce the

+/- 90 degree phase shifts.

Figure 2.5 below shows the diagram of a L-C lumped balun

Figure 2.5 Diagram of a L-C lumped balun [10]

The main application for this circuit is on the output of a push-pull amplifier,

which provides a balanced signal and with the need of convert to a single un-balanced

output.

• Transmission line is used when the required for impedance transformation of 1:4 is

needed. Figure 2.6 shows a coaxial balun [4].

8

Figure 2.6 below shows the diagram of coaxial balun.

Figure 2.6 Coaxial balun [10]

• Microstrip design is the main focus for this project. There is a wide-range of

printed/micro-strip balun topologies they have the advantage of being inexpensive,

realized as they are on the Printed Circuit board (PCB) or Microwave Integrated

Circuit (MIC) substrate. An example of simple coupled line balun is shown in

Figure 2.6 while Figure 2.8 shows a coupled line balun with broadside coupler

structure.

Figure 2.7 below shows the simple coupled line balun.

Figure 2.7 Simple coupled line balun [10]

9

Figure 2.8 below shows the simple coupled line balun using broadside coupler

structure.

Figure 2.8 Simple coupled line balun, using broadside coupler structure [10]

The next chapter describes the changes and the steps that were taken to design

miniaturized broadband balun to operate at a center frequency of 5 GHz and with a

bandwidth range of 1-12 GHz.

10

Chapter 3

IMPROVED MINIATURIZED WIDEBAND BALUN DESIGN OPERATING FROM 1-12 GHz

3.1 Basic Topology of Balun Design

In the previous chapters, we have covered the concept of direction couples and

baluns. This chapter will focus on improved balun design that works over a broadband

frequency range, and gives flat equal amplitude with 180 degrees of precise phase shift,

which is the main goal of this project. This work is based on earlier project design of

balun for wideband frequency at 5 GHz [8][9][11]. However, the earlier design did not

have very flat amplitude and phase balance at the input port. The aim of the two balun

designs reported in the work is centered at the operating frequency of 5 GHz with 50%

bandwidth and phase shift of 180. This design is simpler than earlier design which helps

in fabrication, and also reduces size and cost of fabrication. [1]

The central principle behind a standard balun design is the center-tapped

transformer as shown in Figure 3.1. It uses the coupling element for a balanced output

and taps are used for coupling of the signals to generate balun outputs [9].

11

Figure 3.1 below shows the diagram of center tapped transformer.

Figure 3.1 Center tapped transformer [9]

3.2 Broadband Balun Design:

The final ADS schematic of the balun circuit is shown in Figure 3.2, with current

dimensions as shown in Table 3.1. The circuit is improvement of previous design with

matching circuit at the input port to get equal amplitude with low VSWR but with

reasonably good phase difference of 180 degrees. [11]

Figure 3.2 below shows the design of microstrip wideband balun.

12

Figure 3.2 Design of microstrip wideband balun

The dimensions of the balun circuit are shown below.

13

Table 3.1 Dimensions Of The Microstrip Balun Circuit

L1 80 mils

L2 50 mils

L3 50 mils

L4 50 mils

X 50 mils

X2 40 mils

Taper3,5,6,7_W1 X

Taper4_W1 45 mils

Taper3,4,5,6_W2 35 mils

Taper7_W2 45 mils

Taper5,6_L L3

Taper3_L 60 mils

Taper4,7_L 125 mils

Corn5,6,9,10,12_W X

Corn1,2,3,4_W 35 mils

Corn11_W 45 mils

TL24,25,26,27_W X

TL24,25,26,27_L 14 mils

TL1,2_W X

TL1,2_L L2

14

TL28_W X

TL28_L 100 mils

3.3 Some Of The Special Features Of The Balun are:

• The through port on the input side is terminated with a 50 ohm resistor.

• The input coupled line has a 50 ohm termination at the center of the input coupled line.

• The output coupled line is terminated with an open-circuit microstrip line of 100 mils length.

15

Chapter 4

SIMULATION STUDY OF WIDEBAND BALUN DESIGN

The simulated results of improved wideband balun design are shown in Figures

4.1 to 4.6. The design and simulations were run in Agilent Advanced Design System

(ADS) software. The optimized design is shown in Figure 4.1 after designing several

different circuit using different components.

4.1 Simulation Results of Balun Design

This section gives the simulated results for balun design. The amplitude balance,

phase response and VSWR of design are shown in Figures 4.1 to 4.3 respectively. Figure

4.1 shows amplitude balance at both output ports and frequency. The center of the

frequency is 5 GHz. The power output for port S(2,1) is ~-15 dB and the power output

for port S(3,1) is -17dB.

Figure 4.1 Amplitude balance at output ports

16

Figure 4.2 below shows phase balance at the two output ports and frequency. The

center frequency is 5 GHz and the phase difference between ports 2 and 3 is 186 degree.

Figure 4.2 Phase balance at the output ports

Figure 4.3: below shows the VSWR at the input port 1 and output ports 2 and 3.

While the VSWR at the two output ports is ~1.1, the input VSWR is 2.65. The curve for

input and output VSWRs are improved and as flat as we expected.

17

Figure 4.3 VSWR performance at input port and output ports

There is an excellent amplitude balance between the output ports. There is a

flat 183 degrees phase difference over the frequency band between the output ports.

The VSWR at the input and the two output ports is close to 1.

18

Chapter 5

LAYOUT AND FABRICATION OF WIDEBAND BALUN CIRCUIT

The layout was produced from the current circuit design. The wideband balun

circuit laid out in ADS is as shown:

.

Figure 5.1 Layout of wideband balun circuit

19

In order to obtain the layout, we exported the layout file as a Gerber file which is

generated in the project directory.

Figure 5.2 shows the layout of the wideband balun circuit in Gerber file.

Figure 5.2 Layout of wideband balun circuit in Gerber file

Then we used IsoPro 2.7 T-Tech to import Gerber file. The first step was to isolate the

traces of the balun design. The green layer around the blue traces is the new isolation

layer. The second step was to create a contour, the outer boundary of the PC board. Then

we created tabs in the contour to help the board stay in place while the board was being

20

routed. The third step was to perform a rubout of the excess area. The red layer is the area

where we wanted to do the rubout as is shown in the figure 5.3. [9]

The wideband balun circuit is shown in IsoPro 2.7 as follows:

Figure 5.3 Wideband balun without resistors

The fabrication was done on the T-Tech Quick Circuit router machine in the Microwave

Laboratory at CSUS. Figure 5.4 below shows a photograph of the router machine used in

the fabrication.

21

Figure 5.4 Photograph of the router machine

After the T-Tech machine is turned on, the first step was to route the isolation layer and

then rubout layer. The second step was to run contour layer and break the taps by using a

chisel.

For the actual circuit after fabrication, the copper site is on the top and dielectric

substrate is under it. While fabricating the wideband microstrip balun circuit we chose

RT/DUROID microwave laminate RO4003 with properties as shown in Table 5.1. [11]

22

5870 6002 6006 RO 4003 RO 4003

QLAM

Dielectric

Constant

εr

2.33

2.94

6.15

3.38

3.38

Mur 1 1 1 1 1

Dielectric

Thickness

H (mils)

20

50

50

32

16

Hu 3.9* 1034 3.9* 1034 3.9* 1034 3.9* 1034 3.9* 1034

Conductivity 5.8*107 5.8*107 5.8*107 5.8*107 5.8*107

TanD 0.0012 0.0012 0.0027 0.0027 0.0027

Rough

RMS (mm)

115 (3) 95 (2.4) 95 (2.4)

75 (1.9) 95 (2.4)

Table 5.1 Specifications Of RT/DUROID Microwave Laminates

The final fabricated circuit, with the required shorts and resistors is shown in Figure 5.6

below, while the measurement setup on the HP/Agilent 8510 C Network Analyzer is

shown in Figure 5.7.

23

Figure 5.6 Wideband balun circuit with soldering SMA connectors

Figure 5.7 Network Analyzer

24

Chapter 6

MEASURED RESULTS FOR AMPLITUDE BALANCE, PHASE BALANCE AND VSWR VALUES

6.1 Measured test results:

Figure 6.1 below shows the plot of amplitude balance at port 2 and port 3. The

coupling amplitude at port 2 is -16 dB and at port 3 is -32 dB, at the center frequency of 5

GHz.

Figure 6.1 Plot of Frequency vs Amplitude

25

Figure 6.2 below shows the plot of phase balance, or the difference in phase

between the two output ports. The phase difference between the two output ports is -200

degrees at the center frequency of 5 GHz; ideally, it should be 180 degrees.

Figure 6.2 Plot of Frequency vs Phase

Figure 6.3 below shows the plot of VSWR at the input port and two output ports.

The VSWR at the input port is 200, and at the output port 2 and 3 is 68 and 67

respectively

26

Figure 6.3 Plot of Frequency vs VSWR

27

Table 6.1 below shows the comparison between the simulated results and the

measured results at the center frequency of ~ 6 GHz.

Simulated Data Measured Data

Amplitude balance for

port2

-15 -16

Amplitude balance for

port 3

-17 -32

Phase Balance 186 200

VSWR at input port 1 2.65 200

VSWR at output port 2 1.1 68

VSWR at output port 3 1.1 67

Table 6.1 Simulated vs Measured results

The simulated and actual measurements show good agreement in amplitude and phase at

the center frequency, and also over the operating range of the device. The VSWR at input

and output ports needs to be improved, and the deviation in the values is due to the

following reasons:

28

• Use of chip resistances which are added to obtain good stability in amplitude and

phase.

• Losses occurred in the microstrip lines.

• Losses occurred due to the use of resistances.

29

Chapter 7

CONCLUSION AND SCOPE FOR FUTURE WORK

The microstrip balun design used in this project is aimed at good amplitude and

phase balance, with low VSWR at a center frequency of 6 GHz and bandwidth range of

1-12 GHz. The wide band width at input port and equal amplitudes at output ports was

achieved by matching circuits and changing the size of microstrip transmission lines.

The basic multi-coupled line design was used. There were a lot of modifications

made to this design for attaining precise phase shift and amplitude over the specified

bandwidth. The simulation results showed that both balun designs maintained amplitude

balance of ~ -15 dB and -17 dB at the two output ports respectively, with a phase

difference of ~187 degrees over the frequency range of 1-12 GHz. The VSWR at the two

output ports are significantly lower at around 1 and at input port around 2.65. However,

the measured results, while showing good amplitude and phase balance, showed

relatively high VSWR values. Future work will focus on the improvement of VSWR

performance by use of enhanced matching networks, and low-loss transmission lines.

30

REFERENCES

[1] Jaidev Sharma, “Design of Miniaturized Microstrip Balun at 2.45 GHz”, California

State University, Sacramento, M.S. report, Summer 2008.

[2] Peter A. Rizzi, “Microwave Engineering”, Prentice Hall - 2001

[3] Wikipedia, Transmission line. Retrieved 10 September, 2010 from World Wide Web: http://en.wikipedia.org/wiki/Transmission_line

[4] Guillermo Gonzalez, “Microwave transistor amplifiers analysis and design”

.Prentice Hall – 2000.

[5] Microwave encyclopedia, Retrieved 22 July, 2010 from World Wide Web:

http://www.microwaves101.com/encyclopedia/coupled_line_couplers.cfm

[6] Wikipedia, Balun. Retrieved 5 September, 2010 from World Wide Web:

http://en.wikipedia.org/wiki/Balun [7] Microwave encyclopedia, Retrieved 7 August, 2010 from World Wide Web:

http://www.microwaves101.com/encyclopedia/baluns.cfm

[8] Khushboo Gandhi and Vinothkumar Radhakrishnan, Design and Simulation of

Improved Wideband Microstrip Balun Circuits at 8 GHz, M.S. Thesis, California

State University, Sacramento, Fall 2008

[9] Jizhen Tang, Design, Simulation and Fabrication of Improved Wideband Microstrip

Balun Circuit at 5 GHz, M.S. Thesis, California State University, Sacramento, Fall

2009

31

[10] RF, RFIC & Microwave Theory, Design, Retrieved 21 November, 2010 from

World Wide Web:

http://www.odyseus.nildram.co.uk/RFMicrowave_Circuits_Files/Balun%20Design.

pdf

[11] Elizabeth Kelangi and Danny H.Dang, “Simulated and experimental testing of

improved wideband microstrip balun circuit 5 GHz ", M.S. Thesis, California State

University, Sacramento, fall 2010.

[12] http://www.rfmd.com/directional-coupler.aspx [RF Micro Devices, 26 July 2011]

[13] http://www.df6na.de/df6na/surplus/Directional_Coupler_0143.jpg [Directional

Coupler, 26 July 2011]

[14]http://www.hit.ac.il/web/upload/file/maabadot_handasa/microwaves/experiment_5__

coupler_design.pdf [Coupler Design, 27 July 2011]