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Equilateral Triangular Microstrip Antenna -A New Design Formula Based on
Bhatnagar's Postulate
Article · June 2019
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SKIT RESEARCH JOURNAL VOLUME 5; ISSUE 1: 2015
Equilateral Triangular Microstrip Antenna - A New
Design Formula Based on Bhatnagar's Postulate
Swati Swami, S.K. Bhatnagar, Abhijat Vats, Monika Mathur
Department of Electronics and Communication Engineering
Swami Keshvanand Institute of Technology Management & Gramothan, Jaipur, India
Email- szoya2010@gmail.com
Received 11 February 2015, received in revised from 9 April 2015, accepted 9 April 2015
Abstract: Triangular microstrip antenna is commonly used in Fig. 1. Shows a typical geometry of an equilateral triangular
wireless communication. Several approximate formulae for its patch antenna with inset feeding. The resonant frequency of
design are in use. This paper presents a new design formulae for such an antenna is given by [2].
equilateral triangular patch antenna. This is based on Bhatnagar's
Postulate. The postulate is extended and validated for equilateral
triangular patch antenna. Thus a new thinking for estimating
physical side length of a triangular microstrip antenna has been
presented. The 'H' concept has been used here to put forward a Where mn refers to TMmn modes (For equilateral triangle,
new formula for estimating the physical side length of the m+n+l = 0)
triangular patch. It has been postulated that “Extension in
physical side length of the patch is directly proportional to the
normalized thickness of the antenna substrate and the electrical
side length of the patch. The constant of proportionality is
independent of the resonant frequency, thickness and Dielectric However, the electrical length is larger than the physical length
Constant of the substrate”. For a triangular patch also its value is of the radiating side due to the fringing fields.
unity.
Key Words: Microstrip Antenna, dielectric constant, electric
length, fringing fields, triangular patch, Bhatnagar’s postulate.
1. INTRODUCTION
An electrically conducting patch suspended over a ground
plane acts as an antenna if it is fed with electromagnetic energy. Different researchers have used different formulae and
This function depends critically on the field at the fringes of the different notations for these three quantities. A good
patch. These are called “fringing fields”. The fringing fields description of these is given in [3]. Some of them are
extend beyond the radiating edge of the patch. Electrically the
patch is considered to be extended beyond its physical size. This
extension in physical length affects the resonant frequency of
the patch [1]. Estimation of its value is therefore necessary for
designing an antenna patch. This paper presents a new formula
for this estimation for an equilateral triangular patch antenna.
The antenna is designed for the given operating frequency (fr),
dielectric constant of substrate (εr) and height of dielectric
substrate (h).
Fig 1: Equilateral triangular patch antenna with inset feeding
40
SKIT RESEARCH JOURNAL VOLUME 5; ISSUE 1: 2015
Large number of antennas were designed using the new
formulae. FR4 epoxy substrate (dielectric constant 4.4) of
thickness 1.6 mm was used. The resonant frequency was varied
from 1 to 8 GHz. Parameter H was varied from 0.011 to 0.089.
where the effective dielectric constant of the substrate is given
by [5]
2. BHATNAGAR’S POSTULATE AND ITS
EXTENSION
Bhatnagar’s Postulate was originally stated for a rectangular
microstrip antenna [7, 8]. According to this postulate, the Fig 2: Top view of the Triangular Microstrip patch antenna in HFSS
extension in physical length of the radiating side is The HFSS (High Frequency Structure Simulator) software was
proportional to its electrical length i.e.
used for simulation of triangular microstrip patch antenna. Fig.
2. Shows the antenna design in HFSS. Some typical results are
shown in figures 3, 4, 5 and 6.
Fig 3: Simulated result: Resonant frequency- designed = 1 GHz,
Simulated = 1.002 GHz
Where Se is the electrical side-length.
H and β have same meaning and β = 1
3. DESIGN, SIMULATION AND VALIDATION
Combining (2) and (11) gives a new design formula for
equilateral triangular patch antenna. Physical length of
radiating side of the triangular patch is given by
Fig 4: Simulated result: Resonant frequency--- designed = 3 GHz,
simulated = 3.028 GHz
41
SKIT RESEARCH JOURNAL VOLUME 5; ISSUE 1: 2015
4. CONCLUSION
Bhatnagar's Postulate for extension in length of the radiating
side has been successfully extended for equilateral triangular
patch antenna. This extension is due to fringing fields. Thus a
new thinking for estimating physical side length of a triangular
microstrip antenna has been presented. The 'H' concept has
been used here to put forward a new formula for estimating the
physical side length of the triangular patch. It has been
postulated that “Extension in physical side length of the patch is
directly proportional to the normalized thickness of the antenna
substrate and the electrical side length of the patch. The
constant of proportionality is independent of the resonant
frequency, thickness and Dielectric Constant of the substrate”.
For a triangular patch also its value is unity. New design
formulae have been validated. These formulae are simple and
Freq [GHz] straight forward. These do not contain empirical values. They
Fig 5: Simulated result: Resonant frequency--- designed = 6 GHz, are perhaps more relevant as the extension in length has been
simulated = 6.111 GHz
directly related with the electrical length of the radiating edge.
5. ACKNOWLEDGMENT
The authors would like to thank Director (Academics) and the
Management of SKIT for permission to carry out this work and
to publish it.
REFERENCES
[1] Ramesh Garg et al, “Microstrip Antenna Design Handbook” Artech
House Inc, Boston, 2001.
[2] Swati, T. Kumar, A. K. Aggarwal, “Dual band Equilateral Triangular
Patch Antenna,” IJCEM, vol.15, pp. 77-79, Sept. 2012.
[3] S. H. Al-Charchafchi, W .K. Wan Ali, M. R. Ibrahim, S. R. Barnes,
“Design of a Dual Patch Triangular Microstrip Antenna,” Applied
Microwave & Wireless, pp. 60-67, March 1998.
[4] S. R. Chowdhury, Dr. S.Basu, “Miniaturization of Equilateral Triangular
Microstrip Patch Antenna using Parallel Slotting Technique,” IJECT,
Freq [GHz] vol. 3, pp. 106-109, Jan.-March 2012.
Fig 6: Simulated result: Resonant frequency--- designed = 8 GHz, [5] Constantine A. Balanis, “Antenna Theory: Analysis and Design”, Third
simulated = 8.170 GHz Edition, John Wiley & Sons, Inc., Publication, New Jersey.
New formulae proposed in this paper were used to design [6] J. L. Volakis, “Antenna Engineering Handbook.” McGraw Hill, 2007.
antennas for simulation. The results have been summarized in [7] D. Mathur, S. K. Bhatnagar, V. Sahula, “Quick estimation of rectangular
patch antenna dimensions based on equivalent design concept,” IEEE
table 1. It can be seen that the resonant frequency of the
Antennas and Wireless Propagation Letter, vol. 13, pp. 1469 - 1472, July
designed structure matches very well with the corresponding 2014.
designed value. This is validation of the proposed theory and [8] S. K. Bhatnagar, “A new approach for designing rectangular microstrip
formulae. antenna,” in Proc. Of National Conference on Recent Trends in
Table 1: Simulated results Microwave Techniques and Applications, Microwave-2012. University
of Rajasthan, 30 July - 1 Aug. 2012.
Resonant Frequency (GHz)
Designed Simulated
1 1.002
2 2.016
3 3.028
4 4.038
5 5.044
6 6.111
7 7.2
8 8.17
42
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