Modified TransmissionLine Model for Rectangular Patch Antenna Design Using Mathematica

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INSTITUTO TECNOLÓGICO DE AERONÁUTICA DIVISÃO DE
ENGENHARIA ELETRÔNICA DEPARTAMENTO DE
TELECOMUNICAÇÕES LABORATÓRIO DE ANTENAS E
PROPAGAÇÃO http//www.ele.ita.br/lap
Modified Transmission-Line Model for Rectangular
Patch Antenna Design Using Mathematica
D.C. Nascimento danielcnascimento_at_gmail.com
A.F. Tinoco S. atinoco_at_ita.br
J.C. da S. Lacava lacava_at_ita.br
IMS 2008, 9th International Mathematica
Symposium June 20 24, 2008
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Modified Transmission-Line Model for Rectangular

• Contents
• The Microstip Antennas
• Classical Accurate Transmission-Line Model (CATL)
• Modified Classical Accurate Transmission-Line
  Model (MCATL)
• New approach for designing rectangular patch
  antennas
• Conclusions

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• Microstrip Antennas.

Some examples of the Microstrip antennas,
The main features of these antennas are light
weight, low profile and conformability on non
planar surfaces.
These radiators are widely applied in
high-performance aircraft, spacecraft, and
satellites.
Analysis can be performed using empirical,
semi-empirical, or full-wave techniques
What is the most proper teaching approach to
cover this type of antenna for undergraduate
courses?
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Classical Accurate Transmission-Line Model (CATL)
Based on a typical geometry of the
microstrip antenna, which is composed of a
metallic patch printed on grounded dielectric
substrate, Pues and Van de Capelle suggested the
CATL model in 1984.
For a rectangular patch it was assumed that -
The patch can be modeled by two main slots. -
Each slot can be modeled by a voltage-dependent
current source and a self-admittance Ys. -
And, the section below the patch can be modeled
as a low impedance transmission line.
- Schematic representation of Classical Accurate
Transmission Line Model
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Classical Accurate Transmission-Line model (CATL)
To verify the accuracy of the model it was
designed a rectangular microstrip antenna with
linear polarization, and operating at 2 GHz.
A typical microwave laminate was used and a
Mathematica notebook was written to aid the
design.
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Classical Accurate Transmission-Line model (CATL)
The dimensions of the rectangular patch
These dimensions were validated with commercials
software. IE3D ? Zeland Software Inc. HFSS ?
Ansoft Corporation.
Mathematica notebook
Antenna input impedance graphics
From these graphics we note that a) The real and
imaginary parts of the antenna input impedance
are lower than the values obtained with the
commercial software. b) The antenna resonance
frequency was shifted up
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Modified Classical Accurate Transmission-Line
Model (MCATL)
To increase the accuracy of the Van de Capelles
model we proposed two modifications.
First modification. In order to shift the
antenna resonance frequency down we relocated the
slot admittance and the voltage-dependent current
source to the center of the slot
With this modification the schematic of the
transmission-line model changes to
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Modified Classical Accurate Transmission-Line
model (MCATL)
Second modification. To increase the
real part of the antenna input impedance,
ReZin, we used the length b instead of beff
to calculate the self-admittance of the slot, Ys,
and the mutual admittance, Ym.
In this case, the code can be rewritten in easy
way in the Mathematica notebook. That is, only
the following change is needed
Original Van de Capelles model
Our modification
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Modified Classical Accurate Transmission-Line
model (MCATL)
Using the classical model dimensions
Antenna input impedance
a 46.20 mm, b 60.06 mm, p 13.70 mm
Now we observe a very well agreement among the
MCATL model and the results obtained using
commercials software.
Running the modified code
We can also note that the resonance frequency is
out of the operation frequency.
Consequently, we need to redesign the antenna to
work properly at 2 GHz
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Modified Classical Accurate Transmission-Line
model (MCATL)
The inductive component of the input impedance
affect the symmetrical bandwidth, as seen from
the return loss graphics
Antenna input impedance at 2 GHz
We note that the resonance frequency of the
antenna was tuned to 2 GHz and the input
impedance has a strong inductive component at
this frequency. Zin f2GHz 49.97 j12.81 ?
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New approach for designing rectangular patch
antennas
According to the standard design procedure, the
maximum of the input impedance occurs at the
operating frequency.
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New approach for the design Electrical
parameter of the antenna
Other electrical parameters that can be
calculated using our Mathematica notebook are
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New approach for the design Electrical
parameter of the antenna
An additional aspect of the transmission line
model
Based on this model (CATL or MCATL) we find
an equivalent lumped network
Using the circuit theory we can obtain a
series lumped circuit representation
Equivalent lumped network
Now, from the definition of the quality
factor for a series circuit we can estimate the
quality factor of the antenna. For this case Q
48.7
The Q factor calculated using the
transmission line model is Q 49.1, that is
closed to 48.7
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Conclusions

• This paper reports a simple but accurate new
  approach for the analysis and design of thin
  rectangular microstrip antennas.
• After modifications we have introduced in the
  classical accurate transmission line model, the
  antenna electrical parameters agree very well
  with simulations performed using commercial
  software.
• Designing the patch to operate at the Xin  0
  condition the symmetrical bandwidth was improved.
  
• This new approach is suitable for
  computer-aided-design procedures and is clearly
  adequate for undergraduate courses. Students can
  implement it in a simple way by using mathematics
  software such as Mathematica?.

Acknowledgments. This work was partially
supported by FINEP projects RHODES and SINAV.
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Classical Accurate Transmission-Line model (CATL)
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Classical Accurate Transmission-Line Model (CATL)
- Proposed by Pues and Van de Capelle (1984)
microwave laminate (loss tangent 0.0022, ?r
2.55, thickness 1.524 mm)