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SMG-8306 Transmission Lines & Waveguides
1
Abstract—Microstripline is a planar waveguide fabricated in
the integrated circuits and can be realized in the printed circuit
boards. With their miniaturized formation, these waveguides
are used in the modern day high frequency communication
systems. They are highly cost effective compared to their larger
counterparts such as rectangular waveguides. Different
microwave components such as antennas, couplers, filters,
dividers can be formed via microstrip lines.
Index Terms—Microstrip lines, COMSOL, Simulation
I. INTRODUCTION
ICROSTRIPLINES are the planar waveguides that can
be realized in smaller scale enough to fit in the
integrated circuits and can also be fabricated with printed
electronics[1]. The geometry of the Microstripline is simple
and easily conceivable. Microstrip is just a thin conductor
laid on the dielectric surface or the substrate.
Figure 1: Microstrip Structure [1]
The nature of propagation of waves through the waveguide
depends upon the substrate height, width of the microstrip
line and the dielectric constant of the substrate. The
thickness of the microstrip itself is considered to be nominal.
COMSOL Multiphysics 3.5a® has been used here to
describe the cross section of the structure in 2-D.
II THEORY
We can approximate the following parameters of the
microstrip lines:
Characteristic Impedance
Effective Dielectric Constant of the substrate
For the analysis, the structure specified in Figure 1 will be
referred. Assumptions made for the analytical solution are:
Sidewalls at the sides of substrate are conducting.
Dielectric substrate is electrically thin (h<<λ)
Also the waves realized in microstrip lines are not
perfect TEM but quasi TEM waves.
With the dimensions of the basic Microstripline structure
given, we can define the characteristic impedance of the line
as:
Where the effective dielectric constant of the microstrip line
is given by:
Effective Dielectric Constant here has been used to
calculate the characteristic impedance and has not been
included in the result table.
The characteristic impedance of the stripline can be
expressed in terms of its inductance and capacitance as in
Eq. 3. The equation relates characteristic impedance with the
capacitance in the medium and in the air.
A coupled coplanar Microstripline includes two identical
striplines within the substrate. S is the new parameter which
denotes the separation between the two coplanar striplines. If
the equal potentials are supplied for both of the strips, then it
is called an even mode and odd mode when the potential is
opposite. In this report, only the even mode has been
focused. The characteristic impedance is given by [3]
Radio Frequency Electronics, Tampere University of Technology
Properties of Microstripline Prabhat Man Sainju, Rohit Ahuja
M
SMG-8306 Transmission Lines & Waveguides
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Where
And
III RESULTS & OBSERVATIONS
A. Stripline for different substrate materials
In this case we have used the different substrate materials
over the same geometry for basic stripline configuration. The
electric energy density of the configuration has been shown
in figure 2. The Table I shows the different values of
characteristic impedances for different substrate materials.
W is the width of the metallic strip and h represents the
height of the strip from the ground plane of the substrate
(refer Figure 1). From the COMSOL, we get the Capacitance
of the stripline for the particular substrate (C in the TABLE
I) and for the air medium (Ca in the TABLE I). The substrate
materials have been varied depending upon its relative
permittivity.
The characteristic impedance can be calculated from these
simulated values (Zc,s in the TABLE I) as per the equation 2.
This value has been compared to the analytical solution (Zc,a
in the TABLE I) as obtained from Equation 1.
Figure 2: Electric Potential of basic stripline
TABLE I
CHARACTERISTIC IMPEDANCE FOR DIFFERENT SUBSTRATES
W cm h cm Er C
pF/m
Ca
pF/m Zc,s Ω Zc,a Ω
0.2 0.5 3.25 98.5 30.3 61.05 62.163
0.2 0.5 4.5 136 30.3 51.884 52.828
0.2 0.5 12.1 367 30.3 31.640 32.216
As the relative permittivity of the substrate is increased, the
capacitance of the stripline increases. On the other hand, the
characteristic impedance of the stripline decreases.
B. Stripline with different dimensions
In this section, we deal with the same Microstripline but with
different dimensions (variations in Width to Height ratio).
The relative permittivity of the test stripline has been set to
3.25. TABLE II
CHARACTERISTIC IMPEDANCE FOR DIFFERENT DIMENSIONS
W
cm h cm Er
C
pF/m
Ca
pF/m Zc,s Ω Zc,a Ω
0.2 0.5 3.25 98.5 30.3 61.05 62.163
0.1 0.5 3.25 86.4 26.6 69.624 70.791
0.07 0.5 3.25 66.6 20.5 90.335 90.88
As the Width of the stripline is decreased, the surface area
associated with the capacitance of the system decreases. This
effect is also seen in the Ca values for the air medium. Since
the capacitance is decreased, the characteristic impedance
increases. This can be verified with the analytical solution
Zc,a in TABLE II which has been derived from the equation
1. The results match with the simulation outputs.
C. Comparison with Coupled stripline with Coplanar
Strip
The coupled stripline with coplanar strip includes two
identical metallic strips placed inside the substrate. The
strips are aligned in the same plane separated by a distance.
Figure 3: Electric Potential of Coupled Coplanar Stripline
TABLE III
CHARACTERISTIC IMPEDANCE FOR COPLANAR STRIP
W cm h cm S cm C
pF/m
L
μH/m Zc,s Ω Zc,a Ω
0.1 0.5 0.1 118.5 0.778 81.35 81.72
0.175 0.5 0.1 151.8 0.655 65.69 65.1
0.175 0.5 0.2 163 0.724 66.68 66.714
The tabular result above now includes the separation
between the strips as a new parameter. Capacitance and
inductance of the stripline was generated from the COMSOL
SMG-8306 Transmission Lines & Waveguides
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and the characteristic impedance Zc,s is the result of equation
3. The analytical solution was obtained from the equation 4.
As the separation of the stripline was increased, the
capacitance as well as inductance increased. Hence, in reality
the characteristic impedance has also increased.
IV. CONCLUSION
Microstriplines are basically used as the antenna feeds,
dividers and couplers and hence it becomes pretty much
necessary to match its impedance with the connecting port.
COMSOL was used to simulate the Microstripline with the
various field patterns to obtain its parameters such as
capacitance and inductance. The results were compared to
the set of analytical formulas provided in the standard text
materials. It was observed that the simulated results were
close to the analytical solution. However, steps involved in
COMSOL for the simulation have not been included in the
report.
The impedance equation 3 with the capacitance in the air
medium was not applicable for different coupled
Microstripline configurations. Hence, the COMSOL
simulation was divided into electrostatics and magnetostatics
simulation. Electrostatic simulation resulted in the
capacitance of the line and magnetostatics simulation
resulted in the inductance.
Hence, it was found that the analytical calculations can be
useful for the prediction of properties of the Microstripline.
Similarly, COMSOL was observed to be a very useful tool
for the simulation of Microstripline behavior.
REFERENCE [1] Microwave Engineering, D. Pozar, 3rd edition
[2] COMSOL Tutorials -ACDC_Module/Tutorial_Models/microstrip
[3] Foundations for Microwave Engineering (2nd Edition), Collin, Robert
E.
