MODIFIED TRANSMISSION LINE MODEL EQUATIONS FOR …microstrip antenna characteristics. The analytical...

Academy Journal of Science and Engineering 12 (1), 2018 15 - 128

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MODIFIED TRANSMISSION LINE MODEL EQUATIONS FOR

MICROSTRIP ANTENNA DESIGN

Nyitamen, Dominic S and Agbendeh, Simon T

Electrical Electronic Engineering Department, Nigerian Defence Academy, Kaduna

Abstract

Microstrip antennas are becoming more and more popular as the drive towards

miniaturization continues. Therefore, the need for accurate models is growing. Not

only accuracy is required, but also numerical efficiency, in order that the models are

suited for computer-aided-design (CAD) procedures involving optimization. The

transmission line model equations are used in the design of microstrip antennas.

However, the level of accuracy can be low and several iterations required in

optimization for better results. A modification of the dimensions obtained from TLM

method is modified before CAD application for higher accuracy. In this work the

transmission line model equations were modified by a factor and simulated.

Simulations were carried with the FDTD method of CST microwave Studio. Four

different substrates, namely FR-4 Rogers 5870 Roger RT 6010 Roger RT 5880 with

same thickness (1.6mm) but different dielectrics were tested experimentally with the

modified equations and compared with the conventional transmission line model at

1.75GHz. The three antenna parameters used for the studies were the return loss, S11,

the voltage standing wave ration VSWR and the radiation patterns. For the four

substrates used, the modification revealed improvements in the parameters of interest,

namely, the return loss, voltage standing wave ratio and radiation patterns. The

deviation in frequency (1.575GHz) was much less, hence better results.

Key words: antenna, microstrip patch, CAD, return loss, radiation pattern

1. Introduction

Various intricate techniques have been

proposed and used to analyze

microstrip antenna characteristics. The

analytical techniques include the

transmission line model, generalized

transmission line model, cavity model,

and multiport network model. The

Summerfield-type integral equations,

and the solutions of Maxwell’s

equations in the time domain form the

basis of microstrip antenna designs.

Numerical methods of analysis include

integral equation in the space domain,

or the finite-difference time-domain

(FDTD) approach. The methods based

on integral equation make one

important assumption: the dielectric

substrate and the ground plane are

infinite in extent. The solutions are

therefore more accurate when the

substrate and ground plane are several

wavelengths long [1,2]. The FDTD

technique is more efficient for finite-

sized antennas. The effect of the finite

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Modified Transmission Line Model……… Dominic S,Agbendeh, Simon T

Academy Journal of Science and Engineering 12 (1), 2018


size is less severe on impedance

behavior because microstrip antennas

are inherently resonant structures and

their impedance characteristics are

primarily determined by the patch. A

more accurate and numerically

efficient Transmission Line method

proposed microstrip patch antenna.

The radiation behavior, on the other

hand, is considerably influenced by the

finite size of the substrate primarily

due to launching of the surface waves

and their diffraction at the edge of the

substrate [3]. Consequently, the theory

of diffraction is occasionally used in

conjunction with other methods to

improve the predication of the

radiation pattern. The analytical

models were the first to be developed

for microstrip antennas [4]. They use

simplifying assumptions, but generally

offer simple and analytical solutions,

well suited for an understanding of the

physical phenomena and for antenna

CAD, in the analytical methods or

models, the fields associated with the

antenna are divided into an interior

region and an exterior region [5]. The

interior region is formed by the patch

conductor, the portion of the ground

plane under the patch, and the walls

formed by the projection of the patch

periphery onto the ground plane [6].

The fields in this region can be

modeled as a transmission line section

or a cavity giving rise to the

designations transmission line model

and cavity model. The exterior region

is the rest of the space. This includes

the remainder of the ground plane, the

remainder of the dielectric, and the top

of the patch conducting surface.

2. Conventional Transmission

Line Model

The transmission line model was the

first technique used to analyze a

rectangular microstrip antenna by

Munson in 1974 [7]. In this model, the

interior region of the patch antenna is

modeled as the section of transmission

line. It was indicated earlier that the

transmission-line model is the easiest

of all but it yields the least accurate

results and it lacks the versatility.

However, it does shed some physical

insight. Basically the transmission-line

model represents the microstrip

antenna by two slots, separated by a

low-impedance Zc transmission line of

length L.

a. Effective Dielectric

The dimensions of the patch are finite

along the length and width, the fields

at the edges of the patch undergo

fringing.The fringing and height are

calculated using the same equations

used for a matched transmission line.

This model assumes that some electric

field lines will pass out of the dielectric

and into empty space [8]. Because of

this, the permittivity will not strictly be

the relative permittivity of the material

it will instead have an effective

permittivity (𝜀𝑟𝑒𝑓𝑓). The effective

permittivity or reference permittivity is

affected by the width of the patch and

the height of the substrate. If it can be

assumed that the width is greater than

the height of the patch, then the

reference permittivity can be described

by equation (1) [8].

Page 116




𝜀𝑟𝑒𝑓𝑓 =𝜀𝑟+1

2+

𝜀𝑟−1

2[1 + 12

ℎ

𝑊]

−1

2 1

b. Effective Length

The length of the patch looks

electrically slightly larger than the

usual length of the design, because of

the fringing field along the patch

width, the dimensions of the patch

along its length have been extended on

each end by a distance Δ𝐿, which is a

function of the effective dielectric

constant 𝜀𝑟𝑒𝑓𝑓and the width-to-height

ratio (W/h). A very popular and

practical approximate relation for the

normalized extension of the length is

[4]. this parameter can be calculated by

using Equation 2:

∆𝐿 = 0.412ℎ(𝜀𝑟𝑒𝑓𝑓+0.3)(

𝑊

ℎ+0.264)

(𝜀𝑟𝑒𝑓𝑓−0.258)(𝑊

ℎ+0.8)

2

After the calculation of each of

effective and extended lengths of the

patch, the actual value of the patch

length (L) is calculated by using

Equation 3:

𝐿 = 𝐿𝑒𝑓𝑓 − 2∆𝐿 3

c. Effective Width

For an efficient radiator, a practical

width that leads to good radiation

efficiencies is given by the following

formula equation 4:

𝑊 =𝑐

2𝑓𝑟√

2

𝜀𝑟+1 4

d. Resonant Frequency

For the dominant TM010 mode, the

resonant frequency of the microstrip

antenna is a function of its length.

Usually it is given by equation 5:

𝑓 =𝑐

2𝐿√𝜀𝑟 5

3. Materials and Methodology

The microstrip antenna is made up of a

dielectric substrate and conducting

patches. The choice of substrates and

their dimensions are critical factors at

the desired frequency of operation.

Through numerical computations and

simulation, certain factor was obtained

to modify the conventional equations.

The FDTD method of CST microwave

Studio is used for simulations. Four

different substrates were chosen with

same thickness for experimentation at

a fixed frequency of 1.575GHz used by

GPS. The four variants of the

microstrip antenna designs were

carried out using the conventional

TLM and tested for results. The same

designs were modified by introducing

a numerical factor, k and the tested for

results. These results were then

compared for the four cases

(substrates) against return loss, voltage

standing wave ratio and antenna

patterns. The factor k is obtained

numerically through series of

simulations.

Modified Equations for the microstrip

antenna dimensions

Page 117




A half wavelength variation in surface

current is observed during simulation

along the patch boundary (L + W).

[𝐿+𝑊]

𝐾=

𝜆𝑔

2 6

where k is an empirically derived

parameter that includes the effect of

the substrate, and 𝜆𝑔 is the wavelength

in the dielectric that is computed from

the free space wavelength 𝜆0 as:

𝜆𝑔 =𝜆0

√𝜀𝑒𝑓𝑓 7

and 𝜀𝑒𝑓𝑓 is the effective permittivity of

the substrate.

Based on this, design equations are

derived relating to the geometry and

operating frequency band of the

proposed antenna. The design

procedure can be framed as follows:

For a design involving a 50Ω

transmission line on a substrate with

permittivity 𝜀𝑟 and thickness h. The

calculation of wavelength in the

dielectric, 𝜆𝑔 is carried out using

Equation 7.

The design dimensions of the patch are

found as

𝐿 = 𝑊 = 0.47𝜆𝑔 and

The design the dimensions of the

ground using

𝐿𝑔 = 𝑊𝑔 = 0.64𝜆𝑔

For any given specification of the

patch antenna, the patch and the

ground plane dimensions are modified

by k, which is given in equation 6.

This modification is verified

experimentally.

4. Experimental Results and

Discussions

The numerical value of was found and

used to modify the design before

simulation to compare with the direct

TLM design. The validity of the

modified equations proposed is

highlighted by comparing the results of

the reflection coefficient, the VSWR

and radiation pattern. Simulations were

performed using conventional

transmission line model (TLM) and

modified equations for four substrate

materials at the GPS resonate

frequency of 1.575 GHz. The results

were compared. Figure 1 shows a

rectangular microstrip antenna fed by a

50Ωcoaxial probe. The following

parameters in Table 1 were used in

evaluating the proposed factor

introduced.

Page 118




Figure 1. Rectangular Microstrip antenna fed by 50 ohms coaxial probe.

Table 1: Antenna Description at frequency of 1.575 GHz

Antenna 1 Antenna 2 Antenna 3 Antenna 4

Substrate FR-4 Rogers 5870 Roger RT 6010 Roger RT 5880

h (mm) 1.6 1.6 1.6 1.6

𝜀𝑟 4.4 2.32 10.2 2.2

𝜀𝑒𝑓𝑓 4.08 2.25 9.52 2.13

𝑥𝑓 6.85 9.28 4.47 9.52

k 4.08 2.25 9.52 2.13

Antenna 1 using FR4 at the Resonate

Frequency of 1.575 GHz

Figure 2 is the return loss plot of

Antenna 1 whose parameters are

shown in Table 1, using FR4 substrate

at the resonate frequency of 1.575

GHz. The plot with marker 1

represents the simulation of the

antenna using the conventional TLM,

while marker 2 represents the

simulation of the antenna using the

modified equations. The modified

equations gave better results as

compared with the conventional TLM.

Page 119




Figure 2 The Return Loss of Antenna 1 of the conventional TLM and the Modified

Equations

The simulated VSWR of Antenna 1

using the conventional TLM and

modified equations is as shown in

Figure 3. The modified equations

“marker 2” gave better results close to

the desired frequency as compared

with the conventional TLM “marker

1”.

Figure 3 The VSWR of Antenna 1 of the conventional TLM and the Modified

Equations

Figure 4 is the plot of the simulated

radiation pattern of Antenna 1. As seen

from the plot, the modified equations

gave wider angle of the main lobe as

compared with the conventional TLM.

Page 120




Figure 4 The Radiation Pattern of Antenna 1 of the conventional TLM and the

Modified Equations

Antenna 2 using Rogers 5870 at the

Resonate Frequency of 1.575 GHz

Figure 5 is a return loss plot of

Antenna 2 using Rogers RT 5870

substrate (Table 1) at the resonate

frequency of 1.575GHz. The plot with

marker 1 represents the simulation of

the antenna using the conventional

TLM, while marker 2 represents the


modified equations. It is clear that the

modified equations gave better results

as compared with the conventional

TLM


Equations

Page 121






modified equations is as shown in


“marker 2” gave a VSWR of 1.03 at a

frequency of 1.582 GHz as compared

with the conventional TLM “marker 1”

with VSWR of 1.05 at 1.526 GHz.


Equations

Figure 7 below is the simulated

radiation pattern plot of Antenna 2. As

seen from the plot, the modified

equations wider angle of the main lobe

and smaller back lobe as compared

with the conventional TLM


Modified Equations

Page 122




Antenna 3 using Rogers RT 6010 at

the Resonate Frequency of 1.575 GHz

Figure 8 presents the return loss plot of

Antenna 3 using Rogers RT 6010

substrate at the resonate frequency of

1.575 GHz. The plot with marker 1








TLM


Equations



modified equations is as presented in





1”.


Equations

Page 123




Figure 10 shows the simulated

radiation pattern plot of Antenna 2 and

from the plot, the modified equations

gave a slight narrow angle of the main

lobe and back lobe as compared with

the conventional TLM, this is as a

result of the effect of a high dielectric

constant of the substrate material.


Modified Equations

Antenna 4 using Rogers RT 5880 at

the Resonate Frequency of 1.575 GHz

Figure11 presents the return loss plot

of Antenna 4 using Rogers RT 5880

substrate at the resonate frequency of

1.575 GHz. The plot with marker 1








TLM


Equations

Page 124






modified equations is as presented in





1”.


Equations

Figure 13 is the simulated radiation

pattern plot of Antenna 2, and from the

plot, the modified equations provide

wider angle of the main lobe and

smaller back lobe as compared with

the conventional TLM

.


Modified Equations

Page 125




5. Conclusion

In this paper, a modified and

computation-efficient transmission line

model is developed to analyze the

microstrip antenna. The results so far

show that the modified equations can

be successfully used to design the

microstrip antenna and even though the

model is conceptually simple, it still

produces better results in a relatively

short period of computing time. The

results obtained highlight an excellent

agreement between the modified

equations and the FDTD method of

CST microwave Studio. A comparison

of the results produced by the final

model with the FDTD data showed the

validity of the proposed model. This

allows the analysis of different

substrate materials and frequencies for

linear polarization. Based on these

characteristics, the modified equations

can be useful for microstrip antenna

designs.

References

[1] Makwana, G.D, Ghodgaonkar

and Gupta, S "Investigation of a

new radiating mode in

rectangular dielectric resonator

antenna:Experimental validation"

International Journal of

Microwave and Optical

Technology 9(4):309-316 · Jan.

2014

[2] Budhaditya Majumdar and Karu

Essell "Extended Transmission-

Line Modelling of Inset-Fed

Reconfigurable Rectangular

Microstrip Antennas" Progress

In Electromagnetics

Research B, Vol. 68, 123–140,

2016

[3] Z. N. Chen and M. Y. W. Chia

,“Broadband Planar Antennas

Design and Applications”, John

Wiley and Sons, Ltd, England,

2006.

[4] D. M. Pozar, "Microstrip

antennas," in Proceedings of the

IEEE, vol. 80, no. 1, pp. 79-91,

Jan. 1992

[5] Carver, K.R., and E. L. Coffey,

“Theoretical Investigation of the

Microstrip Antenna,” Tech.

Report PT-00929, Physical

Science Laboratory, New

Mexico State University, Las

Cruces, NM, 1979

[6] Garg, I. Bahl, A. Ittipiboon, and

P. Bhartia, Microstrip Antenna

Design Handbook, Artech

House, London, 1980

[7] M.R. Chaharmir, J. Shaker, and

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6

https://www.researchgate.net/journal/1553-0396_International_Journal_of_Microwave_and_Optical_Technology



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