Fourier-Based Transmission Line Ultra-wideband Wilkinson Power Divider for
EARS Applications
ByK. Shamaileh, M. Almalkawi,
V. Devabhaktuni, N. Dib, B. Henin, A. Abbosh
NSF EARS Award 1247946Program Director George Haddad
1
Outline• Motivation and Challenges• Research on Power Dividers• Wilkinson Power Divider Design
• Conventional Vs Proposed Ultra-wideband Schematics
• Simulation and Experimental Results• Summary• Acknowledgment
2
Motivation and Challenges• Most of the frequency spectrum is allocated to different
wireless services
• Typically, some of these assigned bands remain idlesome of the time
• Cognitive Radios (CRs) are gaining attention as anattractive solution to maximizing bandwidth utilizationand channel capacity
3
Motivation and Challenges• In CR, the temporarily unallocated frequencies are loaned to
secondary users as long as the “legitimate/primary” usersare not receiving/transmitting data
• The concept of CR enhances access to the radio spectrum
However
• To bring this concept to reality, we require front-endmicrowave components that support CR operation overwide frequency range (e.g. spectrum sensing)
4
CR Framework
Cognitive Radio
Front-end components
DSP/internetworking
Input/output interface
FiltersDividersAntennas
...
5
Examples of Front-end Components
Antenna array
Power divider
6
Ultra-wideband Spectrum• The frequency spectrum ranges between 3.1 GHz and
10.6 GHz• Approved for commercial applications (FCC, 2002)• Most widely used in medical treatments, tactical and
strategic communication, through-the-wall imaging,high data rate transmission, etc.
Different approaches have been recently reported:
7
Research on Power Dividers
Multilayer substrate Stubs based
Increasedfabrication cost
Largercircuit area
Larger circuit area,difficulty in cascading
Tapered lines
Each uniform impedance branch in the power divider is replaced bya single non-uniform transmission line (NTL) transformer
Proposed UWB Wilkinson Power Divider
8
Single Frequency Proposed UWB
9
Design Objectives
• Objective 1: NTL that matches a source impedance Zs
to a load impedance Zl
Even Mode Analysis
• Objective 2: Achieve optimum output ports isolationand matching conditions
Odd Mode Analysis
Even Mode Analysis
10
32R2
2R1
2R
deinZ• Accomplished by enforcing
the magnitude of thereflection coefficient |Γ| tobe zero (or close to zero)over UWB frequency range
• |Γ| at the input port can beexpressed in terms of Ze
in
• Zein is calculated from ABCD parameters of NTL
• B and C values are calculated in terms of a truncated Fourier series
• Optimum values of the Fourier coefficients are obtained by minimizing anerror function in MATLAB
where
1 1
1 1,i i K K
i i K K
A B A B A BA BC D C D C DC D
1, 2, ...i K
01
( ) 2 2ln cos sinN
n nc n
Z z nz nza bZ d d
c
in in inin 1
Error max( , ... ... )f f fj mE E E
j je ljin
j jl
A f Z B fZ f
C f Z D f
2in
jinf jE f
ej sin
jin ej sin
Z f Zf
Z f Z
11
Even Mode Analysis
• ABCD matrix of the network is calculated as follows:
• Carried out to obtain theresistor values R1, R2 and R3
for achieving the optimumoutput ports isolation andmatching conditions
3 2Total2 2
12
1st Section
2nd Section 3rd Section
.
.
. .
.
R R
R
ABCD ABCD ABCD ABCD
ABCD ABCD ABCD
12
32R2
2R1
2R
3d
3d
3d
oinZ
Odd Mode Analysis
• Finally, we have:
• Setting V2 to zero, and solving for , we obtain:
• For perfect output ports matching over the UWB range, the below errorneeds to be minimized over the R1, R2, R3 design space
1 2
1 2Total
V VA BI IC D
11
VI
11
oin
V BZ
I D
out out outout 1
Error max( , ... ... ),f f fj mE E E 2out
joutf jE f
13
Odd Mode Analysis
Simulation and Experimental Results
• Characteristic impedance of 50Ω
• Rogers RO4003C substrate withrelative permittivity of 3.55,thickness of 0.813 mm, and losstangent of 0.0027 is employed
• Length of each NTL arm of theproposed WPD is set to 10 mm
14
• Input and output ports matching parameters S11 and S22, respectively, andthe isolation parameter S23 are below -10 dB over the UWB range.
• S21 is in the range -3.2 dB to -4.2 dB over the UWB frequency range.
3 4 5 6 7 8 9 10 11-50
-40
-30
-20
-10
0
Frequency (GHz)
S-P
aram
eter
s (d
B)
S11: Simulated
S11: Measured
S21: Simulated
S21: Measured
S22: Simulated
S22: Measured
S23: Simulated
S23: Measured
15
S-Parameters
• The measured phase imbalance is less than ± 10o over the entire designfrequency range
• The obtained amplitude imbalance is around ± 0.1 dB over the entireUWB range
-0.5
-0.25
0
0.25
0.5
|S21
| - |S
31| (
dB)
3 4 5 6 7 8 9 10 11-30
-20
-10
0
10
20
30
Frequency (GHz)
S
21 -
S31
(Deg
ree)
16
Imbalance
Simulated and measured group delay are: Almost flat over the UWB range Less than 0.2 ns
3 4 5 6 7 8 9 10 110
0.1
0.2
0.3
0.4
Frequency (GHz)
Gro
up D
elay
(ns)
SimulatedMeasured
17
Group Delay
3-D IIR Digital Beam Filters for Space-Time White Space Detection in Cognitive Radio
• Four sub-systems areproposed for space-timewhite space detection (Univ.of Akron Contribution)
• A power divider is essentialin feeding the antenna arrayin S-1! (Univ. of ToledoContribution)
18
• After S-4, an algorithm to solve the link scheduling androuting problem efficiently utilizing 3D sensinginformation is required (Univ. of Norfolk Contribution)
Summary• For the first time, a CAD method for the design of an
UWB WPD based on Fourier impedance profiles hasbeen presented.
• The design optimizes both cost and real estate!
• The proposed WPD has been fabricated. There is aclose match between simulations and measurements.
• The proposed WPD can serve as a front-end modulein realizing EARS hardware.
19
Acknowledgment
• This research is supported in part by NSF EARS Award 1247946(Collaborators – Norfolk State, Ohio Northern, University of Akron)
• The authors gratefully acknowledge the motivation and support fromNSF EARS Program Director Dr. George Haddad
Thank You
