SIMULATED AND EXPERIMENTAL TESTING OF IMPROVED WIDEBAND
MICROSTRIP BALUN CIRCUIT AT 5 GHz
Elizabeth Kelangi
B.E., Muffakham Jah College of Engineering, India, 2006
Danny H. Dang
B.S., California State University, Sacramento, 2001
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
2010
SIMULATED AND EXPERIMENTAL TESTING OF IMPROVED WIDEBAND
MICROSTRIP BALUN CIRCUIT AT 5 GHz
A Project
by
Elizabeth Kelangi
Danny H. Dang
Approved by:
__________________________________, Committee Chair
Preetham B. Kumar, Ph.D.
__________________________________, Second Reader
Fethi Belkhouche, Ph.D.
___________________________
Date
ii
Students: Elizabeth Kelangi
Danny H. Dang
This is to 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.
Department of Electrical and Electronic Engineering
iii
_________________
Date
Abstract
of
SIMULATED AND EXPERIMENTAL TESTING OF IMPROVED WIDEBAND
MICROSTRIP BALUN CIRCUIT AT 5 GHz
by
Elizabeth Kelangi
Danny H. Dang
The objectives of the project are to simulate and test a broadband microstrip balun to
operate at a center frequency of 5 GHz and 50% bandwidth. The balun design finds
extensive applications in the modern wireless communications particularly in
accomplishing frequency conversion mixers to make cellular phone and data transmission
networks possible. They are used to link symmetrical (balanced) circuit to asymmetrical
(unbalanced) circuit in design of mixers and push pull amplifiers. The simulation of the
circuit is done in Advanced Design System (ADS) software. The balun is designed to
convert signals from a single-ended, unbalanced mode to a balanced mode, having two
signals of equal balance impedance but shifted 180-degree in phase over the specified
frequency range with minimum loss and low voltage standing wave ratio (VSWR). The
goals of the design are to achieve high phase, amplitude balance and low VSWR with
good performance results.
, Committee Chair
Preetham B. Kumar, Ph.D.
_____________
Date
iv
ACKNOWLEDGEMENT
We are very appreciate to all those who gave us the possibility to complete this
project. We would like to thank the Department of Electrical and Electronic engineering
for the permission to work on this project. Special thanks go to Dr. Preetham Kumar,
Graduate Coordinator at Sac State, and my second reader Mr. Fethi Belkhouche, for their
time, guidance, patience and understanding. We would like to thank our professor Dr.
Kumar and our families who motivated us to complete the project.
We are grateful to all staffs and faculty members of College of Engineering and
Computer Science, California State University, Sacramento who contributed and helped
us to finish this work.
v
TABLE OF CONTENTS
Page
Acknowledgment… ............................................................................................................ v
List of Tables ................................................................................................................... .vii
List of Figures .................................................................................................................. viii
Chapter
1. INTRODUCTION ........................................................................................................ 1
2. DIRECTIONAL COUPLERS AND BALUNS............................................................ 3
2.1. Directional Coupler ....................................................................................... 3
2.2. Balun Design ................................................................................................. 5
3. IMPROVED MINIATURIZED WIDEBAND BALUN DESIGN AT 5
GHz. .............................................................................................................................. 9
3.1. Basic Topology of Balun Design. ................................................................. 9
3.2. Broadband Balun Design. ........................................................................... 11
4. SIMULATION STUDY OF BALUN DESIGN ......................................................... 14
4.1. Simulation Results of Balun Design. .......................................................... 14
5.
FABRICATION, TESTING, RESULTS AND DISCUSSION ................................ 17
6.
CONCLUSION .......................................................................................................... 27
References ......................................................................................................................... 29
vi
LIST OF TABLES
Page
1. Table 3.1 Dimension of the Microstrip Balun Circuit. ..................................................... 13
2. Table 5.1 Specifications of RT/DUROID Microwave Laminates .................................... 18
3. Table 5.2 The Power Reading Betweens the Design Simulation and the Actual Circuit . 23
4. Table 5.3 The Phase Betweens the Design Simulation and the Actual Circuit ................ 24
5. Table 5.4 The VSWR Betweens the Design Simulation and the Actual Circuit .............. 24
vii
LIST OF FIGURES
Page
1. Figure 2.1 Basic of Directional Coupler ............................................................................. 4
2. Figure 2.2 The Stripline Coupler ........................................................................................ 4
3. Figure 2.3 The Waveguide Coupler .................................................................................... 5
4. Figure 2.4 Diagram of a L-C Lumped Balun...................................................................... 6
5. Figure 2.5 Coaxial Balun .................................................................................................... 7
6. Figure 2.6 Simple Coupled Line Balun .............................................................................. 7
7. Figure 2.7 Simple Coupled Line Balun, using Broadside Coupler Structure ..................... 8
8. Figure 3.1 Center Tapped Transformer ............................................................................ 10
9. Figure 3.2 Design of Microstrip Wideband Balun ........................................................... 12
10. Figure 4.1 Plot of Frequency vs. Amplitude ..................................................................... 14
11. Figure 4.2 Plot of Frequency vs. Phase ............................................................................ 15
12. Figure 4.3 Plot of Frequency vs. VSWR .......................................................................... 16
13. Figure 5.1 Wideband Balun Circuit .................................................................................. 17
14. Figure 5.2 Wideband Balun Circuit with Soldering SMA Connectors (Front Side) ........ 19
15. Figure 5.3 Plot of Frequency vs. Amplitude ..................................................................... 20
16. Figure 5.4 Plot of Frequency vs. Phase ............................................................................ 21
17. Figure 5.5 Plot of Frequency vs. VSWR. ......................................................................... 22
viii
1
Chapter 1
INTRODUCTION
The function of a balun circuit is to convert 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 mixers, push-pull amplifiers. Baluns are
used to link a symmetrical (balance) circuit to an asymmetrical (unbalanced) circuit. The
ability of 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. 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 specific applications. Therefore, there is a need of
wideband matching structure for wideband applications. [1]
In this report, a design of broadband microstrip balun circuit will be simulated, fabricated
and tested. The test circuit operates at a center frequency of 5 GHz and 50% bandwidth.
2
The basic construction/design of a balun consists of two 90-degree phasing lines that
provide the required 180-degree split, and this involves the use of λ/4 and λ/2.
Chapter 1 of this report focuses on the introduction to the report. Chapter 2 explains
Microstrip Coupler, Directional Coupler Coupled Line Couplers and Wideband Balun
fundamentals. This chapter also explains the performance of standard coupler with a
coupling level of ~ -17 dB at one output port. The chapter then describes the goals of the
new designs and requirements that include small size and equal coupling levels at both
output ports and a phase balance of ~180 degrees in the frequency band of interest.
Chapter 3 of the report describes the model of balun design. Chapter 4 describes the
computer simulations and optimization needed to obtain the final form of the wideband
balun circuit. Chapter 5 describes the fabrication and comparison of simulated and tested
results of balun circuit using the HP 8720L Network Analyzer and the discussion of the
result.
Chapter 6 of the report 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 Directional Coupler
Directional couplers are four-port circuits where one port is isolated from the input port.
Directional couplers are passive reciprocal networks. 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 (scattering parameter S21=S12, S13=S31, etc.) For directional coupler, all
four ports are (ideally) matched, and the circuit is (ideally) lossless. 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, Bethe-hole coupler, hybrid
couplers and coupled line couplers. This design focused on coupled line couplers, since
the coupled line coupler provides higher bandwidth. [2]
The basic of directional coupler is as follows: as shown in Figure 2.1, it is a four port
device that samples the power flowing into port 1 coupled in to port 3 (the coupled port)
with the remainder of the power delivered to port 2 (the through port) and no power
delivered to the isolated port 4. It can be described respectively by Coupling (C),
Directivity (D) and Isolation (I). Coupling is the ratio of input power to the coupled
4
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 [4]
Figure 2.2 below shows the stripline coupler
Figure 2.2 The Stripline Coupler [4]
5
Figure 2.3 below shows the waveguide coupler.
Figure 2.3 The Waveguide Coupler [4]
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 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]
2.2 Balun Design
There are different types of balun designs: L-C balun, Transmission line and Microstrip
design.
6
1) L-C balun design as shown in Figure 2.4, 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 2.4 below shows the diagram of a L-C lumped balun
Figure 2.4 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.
2) Transmission line is used when the required for impedance transformation of 1:4 is
needed. Figure 2.5 shows a coaxial balun [4].
7
Figure 2.5 below shows the diagram of coaxial balun.
Figure 2.5 Coaxial Balun [10]
3) 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 2.7 shows a coupled line balun with broadside coupler structure.
Figure 2.6 below shows the simple coupled line balun[4].
Figure 2.6 Simple Coupled Line Balun [10]
8
Figure 2.7 below shows the simple coupled line balun using broadside coupler structure.
Figure 2.7 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 50%
9
Chapter 3
IMPROVED MINIATURIZED WIDEBAND BALUN DESIGN AT 5 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 8 GHz [1]. However, the earlier design did not have very flat
amplitude and phase balance and had very high VSWR 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].
10
Figure 3.1 below shows the diagram of center tapped transformer.
Figure 3.1 Center Tapped Transformer [9]
11
3.2 Broadband Balun Design
The final ADS schematic of the first balun circuit is shown in Figure 3.2, with current
dimensions as shown in Table 3.1. The circuit is designed with matching circuit at the
input port to get equal amplitude with low VSWR but with reasonably good phase
difference of 180 degrees.
12
Figure 3.2 below shows the design of microstrip wideband balun.
Figure 3.2 Design of Microstrip Wideband Balun
13
L1
50 mils
L2
50 mils
L3
50 mils
L4
50 mils
L5
50 mils
L6
50 mils
W1
35 mils
W2
30 mils
W3
25 mils
W4
25 mils
W5
30 mils
W6
35 mils
S1
14 mils
S2
18 mils
S3
22 mils
S4
22 mils
S5
18 mils
S6
14 mils
Table 3.1 Dimension of the Microstrip Balun Circuit
14
Chapter 4
SIMULATION STUDY OF BALUN DESIGN
The simulated results of wideband balun design are shown in Figures 4.1 to 4.6. The
design and simulations were run in Advanced Design System (ADS). 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 outputs for both ports are 14 dB.
0
m13
m1
m1
freq=5.000GHz
dB(S(3,1))=-14.370
dB(S(2,1))
dB(S(3,1))
-20
-40
m13
freq=5.000GHz
dB(S(3,1))=-14.370
-60
-80
0
2
4
6
8
10
12
14
16
18
20
freq, GHz
Figure 4.1 Plot of Frequency vs. Amplitude
15
Figure 4.2 below shows phase balance at the two output ports and frequency. The center
phase(S(2,1))-phase(S(3,1))
frequency is 5 GHz and the phase difference between port 2 and 3 is 110 degree.
400
200
m2
0
m2
freq=5.000GHz
phase(S(2,1))-phase(S(3,1))=110.029
-200
-400
0
2
4
6
8
10
12
14
16
18
20
freq, GHz
Figure 4.2 Plot of Frequency vs. Phase
Figure 4.3: below shows the VSWR at the input port S (1, 1) and output ports S (2, 2) and
S (3, 3). While the VSWR at the two output ports is ~1.5. The input VSWR is 33.7. The
curve for input VSWR which needs to be improved is not as flat as we expected.
vswr(S(3,3))
vswr(S(2,2))
vswr(S(1,1))
16
100
90
80
70
60
50
40
30
20
10
0
m7
freq=5.000GHz
vswr(S(3,3))=1.578
m5
freq=5.000GHz
vswr(S(1,1))=33.767
m5
m7
m6
0
2
4
6
8
10 12 14 16 18 20
m6
freq=5.000GHz
vswr(S(2,2))=1.464
freq, GHz
Figure 4.3 Plot of Frequency vs. VSWR
17
Chapter 5
FABRICATION, TESTING, RESULTS AND DISCUSSION
The layout was produced from previously fabricated circuit from “Design, Simulation
and Fabrication of Improved Wideband Microstrip Balun Circuit at 5 GHz” by Jizhen
Tang [9].
The final wideband balun circuit is shown in Figure 5.1.
Figure 5.1 Wideband Balun Circuit
18
For the real circuit after fabricated, the copper site is on the top and dielectric substrate
under it. When fabricated the wideband microstrip balun circuit was choose RT/DUROID
microwave laminates RO4003 with properties as shown in Table 5.1
5870
6002
6006
RO 4003
RO 4003
QLAM
Dielectric
Constant
2.33
2.94
6.15
3.38
3.38
1
1
1
1
1
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
115 (3)
95 (2.4)
95 (2.4)
75 (1.9)
95 (2.4)
r
Mur
Dielectric
Thickness
H (mils)
RMS (mm)
Table 5.1 Specifications of RT/DUROID Microwave Laminates
19
The input and two output ports of the fabricated circuit were soldered with three SMA
connectors. The circuit then hooked up and tested on the HP 8720 L network analyzer to
validate the design. The figure 5.2 below shows the ports three ports 1, 2 and 3.
port1
port 3
port 2
Figure 5.2 Wideband Balun Circuit with Soldering SMA Connectors (Front Side)
20
5.1 Measured test results:
Figure 5.3 below shows the plot of frequency versus amplitude of port 2 and port 3. The
amplitude for port 2 is 14.7 dB and for port 3 is 15.0 dB.
0
-10
m3
m4
-20
m3
freq=5.050GHz
dB(balun_ports12..S(2,1))=-14.705
dB(balun_ports13..S(2,1))
dB(balun_ports12..S(2,1))
-30
-40
-50
m4
freq=5.050GHz
dB(balun_ports13..S(2,1))=-15.085
-60
-70
-80
-90
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
freq, GHz
Figure 5.3 Plot of Frequency vs. Amplitude
16
17
18
19
20
21
21
Figure 5.3 below shows the plot of frequency versus phase. The phase difference between
two output ports is 168 degree. Ideally, it should be 180 degree.
350
300
250
phase(balun_ports12..S(2,1))-phase(balun_ports13..S(2,1))
200
150
100
50
0
-50
m8
f req=5.050GHz
phase(balun_ports12..S(2,1))-phase(balun_ports13..S(2,1))=-168.069
-100
-150
m8
-200
-250
-300
-350
0
2
4
6
8
10
12
14
16
18
freq, GHz
Figure 5.4 Plot of Frequency vs. Phase
20
22
Figure 5.4 below shows the plot of frequency versus VSWR. The VSWR for two output
port 2 and 3 is 2.2 and the input port is 13.5.
100
90
m9
f req=5.050GHz
v swr(balun_ports12..S(1,1))=13.590
80
vswr(balun_ports13..S(2,2))
vswr(balun_ports12..S(2,2))
vswr(balun_ports12..S(1,1))
70
m10
f req=5.050GHz
v swr(balun_ports12..S(2,2))=2.252
60
50
m11
f req=5.050GHz
v swr(balun_ports13..S(2,2))=2.376
40
30
20
m9
10
m10
m11
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
freq, GHz
Figure 5.5 Plot of Frequency vs. VSWR
20
21
23
5.2 Summary of results:
For the power readings, the design simulation and the actual circuit values are very close.
The values are given in Table 5.2:
Port:
dB reading from design
dB reading from the actual
simulation:
circuit:
S(2,1)
-14.370
-14.705
S(3,1)
-14.370
-15.085
Table 5.2 The Power Readings Betweens the Design Simulation and the Actual Circuit.
The powers output for port 2 & 3 of the actual circuit are close to the design simulation
values but these numbers are high compare to the design target which is equal to 1. If the
current design is being used, an additional circuit would be needed at the output ports to
help bring the power outputs of port 2 and 3 close to the input power of port 1.
For the phase angle, the design simulation result was 110 degree difference
between two ports. The actual circuit has the phase reading is 168 degree. The goal of the
design is 180 degree. The new design is needed to improve the phase angle between two
output ports.
Table 5.3 below compares the phase results of the design simulation and the
actual circuit.
24
Phase difference from
Phase difference from the
design simulation:
actual circuit:
110 degree
168 degree
Table 5.3 The Phase Betweens the Design Simulation and the Actual Circuit.
For the VSWR, the design simulation yielded better results on port 2 and port 3 and not
so good on port 1. The result readings for three ports of the actual circuit achieved the
similar affects. The reading for port 2 and 3 are closer to the design target and port 1 is
still high.
Port:
VSWR value from design
VSWR value from the
simulation:
actual circuit:
S(1,1)
33.767
13.590
S(2,2)
1.464
2.252
S(3,3)
1.578
2.376
Table 5.4 The VSWR Betweens the Design Simulation and the Actual Circuit.
The VSWR readings for all three ports for this design are high, especially port 1. Ideally,
with a perfect 1:1 VSWR there would be no reflected power. The voltage and the current
25
will be constant over the whole length of the feed line. In this design, the return loss is
low for port 1 and high for port 2 and 3. The good news is the design is going to the right
direction but the goal value has not been achieved (VSWR = 1, return loss (dB) = α, %
power/voltage loss = 0/0, reflection coefficient = 0, mismatch loss (dB) = 0). The
followings equations can be used to verify the design:
Formulas to calculate VSWR:
VSWR =
𝐸𝑚𝑎𝑥
(𝐸𝑓𝑟𝑑+𝐸𝑟𝑒𝑓)
= (𝐸𝑓𝑟𝑑−𝐸𝑟𝑒𝑓) ,
𝐸𝑚𝑖𝑛
(5.1)
where:
Emax = maximum voltage on the standing wave
Emin = minimum voltage on the standing wave
Efrd = incident voltage wave amplitude
Eref = reflected voltage wave amplitude
VSWR =
(1+ 𝜌)
(1−𝜌)
,
(5.2)
where 𝜌 is the reflection coefficient of the antenna (absolute value of voltage
reflection)
Return loss = 10 log
𝑃𝑟
𝑃𝑖
= 20 log
𝐸𝑟
𝐸𝑖
,
(5.3)
26
During the test, there may be some sources of error that contributed to the test results.
Since the test was running at very high frequency and the circuit was not shielded, some
outside signal sources (room light source, noise from other machines) may interfere with
the test results. However, these sources of error should not make a big impact on the test
results.
27
Chapter 6
CONCLUSION
The microstrip balun design used in this project is aimed for better amplitude close to 1
and phase of 180 degree with low VSWR at a center frequency of 5 GHz and bandwidth
range of 1-10 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 coupled line design was used. There was lot of changes made to this design for
attaining precise phase shift and amplitude over the specified bandwidth. The simulation
results showed that both balun designs maintained a roughly flat equal amplitude balance
of ~14 dB at the two output ports, with a phase difference of ~110 degrees over the
frequency range of 1-10 GHz. The VSWR at the two output ports are significantly lower
at around 1 and higher at input port around 33. The widths between two transmission
lines were matched for better results.
The design can be further improved in the future. Since the phase angle difference
between port 2 and 3 for this design is only 168 degree. The future design needs to bring
it close to 180 degree. The power reading for port S(2,1) and port S(3,1) is -14 dB. We
want the power readings close to 1 as much as possible. If the current design is being
used, an additional circuit is needed to help bring the output at port 2 and 3 equal to port
1. Ideally the VSWR for all three ports should be close to 1. With the current design, the
28
gain for port 2 and 3 are at 2 but port 1 is 13. The new design can improve on port 3 to
make it close to 1. Overall, the current design is on the right track to achieve the designed
results but further work is needed to bring it to the target goal.
29
REFERENCES
1. Jaidev Sharma, “Design of Miniaturized Microstrip Balun at 2.45 GHz”, California
State University, Sacramento, 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, California State
University, Sacramento, Fall 2008
9. Jizhen Tang, Design, Simulation and Fabrication of Improved Wideband Microstrip
Balun Circuit at 5 GHz, California State University, Sacramento, Fall 2009
30
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.p
df