Mutual Coupling Between Broadside Printed Dipoles Embedded in Stratified Anisotropic Dielectrics

1
Mutual Coupling Between Broadside Printed Dipoles
Embedded in Stratified Anisotropic Dielectrics

• Benjamin D. Braaten
• Robert M. Nelson
• David A. Rogers

North Dakota State University
2
Topics

• Problem Definition
• Spectral domain immittance functions
• Results
• Discussion
• Conclusion

North Dakota State University
3
Problem Definition

• Consider

North Dakota State University
4
Interests

• The previous problem is of interest 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 parameters of a
frequency selective surface between anisotropic
dielectric layers for incident 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
HandbookFundamentals and Applications in
Contactless Smart Cards and Identification, John
Wiley and Sons, West Sussex, England, 2003.
North Dakota State University
5
The new spectral domain immittance functions
Start with the following Hertz vector potentials
Electric Hertz potential
and
Magnetic Hertz potential
North Dakota State University
6
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
  y-direction
• and
• this component satisfies the higher order TE and
  TM tangential boundary conditions.

North Dakota State University
7
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
North Dakota State University
8
The new spectral domain immittance functions
and
North Dakota State University
9
The new spectral domain immittance functions
To simplify evaluating the previous expressions,
we define the following Fourier transform
This results in the following relations
North Dakota State University
10
The new spectral domain immittance functions
This results in the following simplified
expressions
where
and
North Dakota State University
11
The new spectral domain immittance functions
Similarly for
and
North Dakota State University
12
The new spectral domain immittance functions
Double layer problem
North Dakota State University
13
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
North Dakota State University
14
The new spectral domain immittance functions
An example of a spectral domain immittance
function
North Dakota State University
15
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.

North Dakota State University
16
Dipole Results
Consider
North Dakota State University
17
Dipole Results
A single anisotropic substrate (d1 1.58 mm)
North Dakota State University
18
Dipole Results
A single anisotropic cover (d1 1.58 mm d2
1.58 mm)
North Dakota State University
19
Dipole Results
Separated by a single anisotropic layer (d1
1.58 mm d2 1.58 mm)
North Dakota State University
20
Conclusion

• New multi-conductor spectral domain immittance
  functions have been summarized.
• Broadside printed dipoles on a single anisotropic
  substrate have been investigated.
• It is shown that the permittivity in the
  y-direction (direction of the optical axis) has
  the largest impact on the mutual coupling.
• Broadside printed dipole with a single
  anisotropic superstrate have been investigated.
• It is shown that the mutual coupling is
  unaffected by the permittivity in the y-direction
  (direction of the optical axis).

North Dakota State University
21
Conclusion

• Broadside printed dipoles separated by a single
  anisotropic superstrate have been investigated.
• It is shown that both components of the
  permittivity affect the mutual coupling.

North Dakota State University
22
Questions

• Thank you for listening

North Dakota State University