Modeling Multiple Printed Antennas
Embedded in Stratified Uniaxial
Anisotropic Dielectrics
Ph.D. Candidate:
Benjamin D. Braaten
Electrical and Computer Engineering
North Dakota State University
February 6th, 2009
Topics
 Introduction
 The printed antenna.
 Properties and applications.
 Proposed research
 Derivation of the new spectral domain immittance
functions.
 Solving the new spectral domain immittance functions.
 Numerical results and measurements.
 Future work.
 Conclusion.
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Introduction
 In 1953 Deschamps
formally introduced
the microstrip
antenna [1].
 Many uses:







Radar
Cellular comm.
Satellite comm.
Wireless networks
Wireless sensors
Biomedical devices
RFID …
[1] G. A. Deschamps, “Microstrip Microwave Antennas,” 3rd USAF Symposium on Antennas, 1953.
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Introduction
 Advantages:
 Disadvantages:
 Low profile
 Many designs have a
narrow bandwidth
 Lightweight
 Radiate into a half space
 Low cost
 Able to achieve UWB  Poor endfire radiation
(in some cases)
 Poor isolation between
the feed an radiating
 Dual frequency
elements
capabilities
 Possible surface waves
 Simple to fabricate
(power loss)
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Introduction
 Region between
plates act like the
region between a
transmission line and
a ground plane with
both ends open.
 Results in a standing
wave.
 Fringing fields are
responsible for
radiation.
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Introduction
 Properties of interest include:
 Input impedance
 Current distribution
 Radiation patterns
 Bandwidth
 Feed techniques
 Mutual coupling with other
elements
 Conducting patch layout
 … etc.
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Introduction
Many different types of layouts
exist:
[2]
[3]
[2] Anthony Lai and Tatsou Itoh, “Composite Right/Left Handed Transmission Line Metamaterials,”
IEEE Magazine, September 2004.
[3] H. Wang, X. B. Huang and D. G. Fang, “A single layer wideband U-slot microstrip patch antenna
array,” IEEE Antennas and Wireless Propagation Letters, vol. 7, 2008, pp. 9-12.
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Proposed Research
Consider:
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Proposed Research
RESEARCH QUESTIONS:
What is the input impedance of a driven element in the
layered anisotropic structure in the presence of
other conducting patches defined on arbitrary
anisotropic layers in the same structure?
and
 What is the mutual impedance between a driven
element in the layered anisotropic structure and
other conducting patches defined on arbitrary
anisotropic layers in the same structure?
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Proposed Research
The previous two questions are very significant in
many fields.
 Microstrip antenna arrays [4].
 Frequency Selective Structures (FSS) [5]
 Radio Frequency Identification (RFID) [6]
 IC based antennas
 Radar …
[4] David M. Pozar and Daniel H. Schaubert, “Microstrip Antennas: The analysis and Design of
Microstrip Antennas and Arrays”, IEEE Press, Piscataway, NJ, 1995.
[5] A.L.P.S. Campos an A.G. d'Assuncao, “Scattering paramters of a frequnecy selective surface
between anisotropic dielectric layers for incidnet co-polarized plane waves,” IEEE Antennas and
Propagation Society International Symposium, 2001, Vol. 4, July 8-13, 2001, p. 382-385.
[6] K. Finkenzeller, RFID Handbook:Fundamentals and Applications in Contactless Smart Cards and
Identification, John Wiley and Sons, West Sussex, England, 2003.
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The new spectral domain immittance
functions
Start with the following Hertz vector potentials:
Electric Hertz
potential
and
Magnetic Hertz
potential
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The new spectral domain immittance
functions
 Next, only the y-direction of the Hertz vector
potential is needed.
and
 This is because the optical axis is in the ydirection
and
 this component satisfies the higher order TE
and TM tangential boundary conditions.
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Numerical results and measurements
The TEM, TM and TE modes
TEM mode
TM and TE modes
[9]
[9] http://www.ibiblio.org/kuphaldt/electricCircuits/AC/02407.png
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The new spectral domain immittance
functions
Now define the following expression for the magnetic
and electric field:
where the Hertzian vector potentials are solutions to
the following wave equations:
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The new spectral domain immittance
functions
and
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The new spectral domain immittance
functions
To simplify evaluating the previous expressions, we
define the following Fourier transform:
This results in the following relations:
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The new spectral domain immittance
functions
This results in the following simplified expressions:
where
and
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The new spectral domain immittance
functions
Similarly for
and
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The new spectral domain immittance
functions
Single layer problem
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The new spectral domain immittance
functions
Single layer problem
Now use these expressions
to enforce the boundary
conditions:
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The new spectral domain immittance
functions
Single layer problem
After extensive factoring and manipulation, the following
spectral domain immittance functions are derived:
and
(typical
expression –
spectral
domain
Green’s
function)
where
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The new spectral domain immittance
functions
Double (d3 = 0) and Triple layer problems
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The new spectral domain immittance
functions
Double and Triple layer problems
After extensive factoring and manipulation, the following
spectral domain immittance functions are derived:
and
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Solving the new expressions
 The spectral domain
moment method was
used to solve for the
unknown current.
 PWS functions were
used as expansion and
basis functions.
 A delta source was
used to drive the
problem.
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Numerical results and measurements
The problem chosen to validate newly derived spectral
domain immittance functions was the printed dipole.
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Numerical results and measurements
The first step was to
validate the numerical
results with experimental
measurements.

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Radius a = 0.4 mm
Length L = 60 mm
FR-4: εr = 4.35
Printed strip W = 4a
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Numerical results and measurements
Picture of measured monopole.
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Numerical results and measurements
This resulted in the following measured resonant
frequencies:(Epsilam-10:
and
,
Rogers 5880:
)
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Numerical results and measurements
Single layer results
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Numerical results and measurements
Single layer results
L = 15 mm
W = 0.5 mm
d1 = 1.58 mm
Notice the ycomponent has the
most effect on the
resonant frequency
(TM0 mode).
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Numerical results and measurements
Single layer results The TEM, TM and TE mode reminder
A quick illustration
of the TM0 mode.
TM and TE modes
[9]
[9] http://www.ibiblio.org/kuphaldt/electricCircuits/AC/02407.png
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Numerical results and measurements
Single layer results
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Numerical results and measurements
Single layer results
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Numerical results and measurements
Single layer results
L = 15 mm
W = 0.5 mm
f = 500 MHz
d1 = 1.58 mm
Notice:TM0 has
the most effect
(i.e. y-compontent
of the permittivity
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Numerical results and measurements
Double layer results
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Numerical results and measurements
Double layer results
L = 15 mm
W = 0.5 mm
d1 = 1.58 mm
d2 = 1.58 mm
ε1= 2.55
Notice: εx2 affects
the resonant
frequency the
most.
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Numerical results and measurements
Double layer results
The field lines:
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Numerical results and measurements
Double layer results
L = 15 mm
W =0 .5 mm
d1 = 1.58 mm
ε1= 2.55
region 2: anisotropic
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Numerical results and measurements
Double layer results
L = 15 mm
W = 0.5 mm
f = 500 MHz
d1 = 1.58 mm
d2 = 1.58 mm
ε1= 3.25.
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Numerical results and measurements
Double layer results
(Single layer results)
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Numerical results and measurements
Double layer results
L = 15 mm
W = 0.5 mm
f = 500 MHz
d1 = 1.58 mm
d2 = 1.58 mm
ε1= 3.25.
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Numerical results and measurements
Double layer results
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Numerical results and measurements
Triple layer results
L = 15 mm
W = 0.5 mm
f = 500 MHz
d1 = 1.58 mm
d2 = 1.58 mm
d3 = 1.58 mm
ε1= ε2= 3.25.
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Numerical results and measurements
Triple layer results
(Double layer results)
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Conclusion
 New spectral domain immittance functions
have been derived.
 The new spectral domain immittance
functions have been validated with
measurements, published literature and
commercial software.
 One, two and three layer problems have
been investigated.
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Conclusion
 The following has been shown:
 The permittivity in the direction of the optical axis
below the printed dipole has the most impact on
the resonant frequency.
 The layer thickness values eventually have little
effect on the resonant frequency.
 The permittivity in the direction of the optical axis
above printed dipoles has little or no effect on the
mutual coupling.
 The permittivity in the direction orthogonal to the
optical axis in the layers above the dipoles can be
used to control the mutual coupling.
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Conclusion
 Future work
 Investigate coupling between rectangular
microstrip antennas in layered anisotropic diel.
 Investigate coupling between UWB antennas in
layered anisotropic diel.
 Investigate how anisotropic materials could be
used to control coupling between RFID tags
 IC based antennas
 Metamaterial based designs
 Mathematical aspects
 poles
 surface wave modes
 convergence
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Questions
Thank you for listening
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