transmission line model sanjeev

8/2/2019 Transmission Line Model Sanjeev

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Transmission Line model

Sanjeev Yadav


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3/11/2012 [email protected]


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Transmission line model

The rectangular patch antenna is very probably the

most popular Microstrip antenna design implemented

by designers.

Fig-1 shows the geometry of this antenna type A rectangular metal patch of width W=a and length

l=b is separated by a dielectric material from a

ground plane by a distance h.

The two ends of the antenna (located at 0 and b) can

be viewed as radiating due to fringing field along

each edge of width W(=a).



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The two radiated edges are separated by a distance

l(=b).

The two edges along the sides of length l are often

referred to as non-radiating edges. The two analysis methods for rectangular Microstrip

antennas which are most popular for CAD

implementation are transmission line model and the

cavity model.



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The transmission line model provides a very lucid

conceptual picture of the simple implementation of

rectangular Microstrip patch antenna .

In this model the rectangular Microstrip antennas

consists of a Microstrip transmission line with a pair

of loads at either end.

As presented in fig-2-2a the resistive loads at each

end of the transmission line represent loss due to

radiation .

At resonance, the imaginary components of the inputimpedance seen at the driving point cancel, and

therefore becomes exclusively real.



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The driving point or feed point of an antenna is the location on an

antenna is the location on an antenna where a transmission line is

attached to provide the antenna with a source of microwave power. The impedance measured at the point where the antenna is connected

to the transmission line is called the driving point impedance or input

impedance.

The driving point Zdrv at any point along the center line of a rectangular

micro strip antenna can be computed using transmission line model .

The transmission line model is most easily represented mathematically

using the transmission line equation written in term of admittances as

presented in equation.

)tan(

)tan(

LjYY

LjYYYY

Lo

oL

oin



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Yin is the input admittance at the end of a transmission line of

length L(=b),where has a characteristic admittance of Yo ,and a

phase constant of terminated with a complex load admittance

Y.

In other words ,the Microstrip antenna is modeled as a

Microstrip transmission line of width W(=a),which determines

the characteristic admittance ,and of physical length L(=b) and

loaded at both ends by an edge admittance Ye which models

the radiation loss. This is shown in fig-2.2(a).



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Using the eq-1, the driving point admittance Ydrv=1/Zdrv at a

driving point between two radiating edges is expressed as:

Ye is the complex admittance at each radiating edge which

consist of a edge conductance and edge susceptance Be inthe eqn given below.

Ye = Ge +j Be3/11/2012 [email protected]


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Approximate values of Ge and Be are



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The fringing field extension normalized to the

substrate thickness h is

)8.0/)(258.0(

)264.0/)(3.0(412.0

hW

hW

h

l

e

e



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Fig-present four common methods used to directly feed aMicrostrip antenna.

The first method is often called coaxial probe feed fig-3(a) the outershield of a coaxial transmission line is connected to the groundplane of Microstrip antenna.

Metal is removed from the ground plane which is generally thesame radius as the inside of coaxial shield .

The coaxial center conductor then passes through the dielectricsubstrate of patch antenna and connects to patch .

Feeding the antenna in the center(i.e. at a/2) suppresses theexcitation of a mode along the width of the antenna .

This feed symmetry enforces the purest linear polarization alongthe length of patch which can be achieved with a single direct feed.



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The second feed method shown in fig- 3(b) drives the

antenna with a Microstrip transmission line along a

non-radiating edge. This feed method is modeled in an identical manner

to the coaxial probe feed when using the transmission

line model ;in practice , it can often to excite a mode

along the width of patch when a=b and cause antennato elliptical polarization.

The advantage of this feed method is that it allows

one to use a 50 micro strip transmission line

connected directly to a 50 driving point impedance

which eliminates the need for impedance matching.



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The third feed method of fig-3(c)is to derive the antenna at one

of its radiating edges with a Microstrip transmission line.

This disturbs the field distribution along one radiating edge

which causes slight changes in the radiation pattern. The impedance of a typical resonant rectangular (a


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A fourth feed method illustrated in fig-2.3(d) is to cut a

narrow notch out of a radiating edge far enough into patch

to locate a 50 driving point impedance .

The removal of the notch perturbs the patch fields slightly

,but the transmission line model generally predicts a drivingpoint location which is close to measurement.

One can increase the patch width, which increases the edge

conductance ,until at resonance ,the edge impedance is 50

Microstrip line at a radiating edge.

The patch width is large enough in this case to increase the

antenna gain considerably.



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Methods of Analysis The MSA generally has a two-dimensional radiating patch on a thin dielectric

substrate and therefore may be categorized as a two-dimensional planar

component for analysis purposes. The analysis methods for MSAs can be

broadly divided into two groups.

In the first group, the methods are based on equivalent magnetic current

distribution around the patch edges (similar to slot antennas). There are

three popular analytical techniques:

The transmission line model;

The cavity model;

The MNM.

In the second group, the methods are based on the electric current

distribution on the patch conductor and the ground plane (similar to dipole

antennas, used in conjunction with full-wave simulation/numerical analysis

methods). Some of the numerical methods for analyzing MSAs are listed as

follows:



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The method of moments (MoM);

The finite-element method (FEM);

The spectral domain technique (SDT);

The finite-difference time domain (FDTD)

method.

This section briefly describes these methods. 1.4.1



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transmission line model sanjeev

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