1. UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE, ECE DEPARTMENT, ECGR 4121/5121 PROJECT II 1
Design of Microstrip Rectangular-Patch Antenna
Operating in the 2.4 GHz Band
Joshua S. LaPlant
Abstract—This document encapsulates the design procedure of
a microstrip Rectangular-Patch antenna that operates in the 2.4
GHz band. Through investigative analysis, a variety of methods
for achieving a resonance of 2.4 GHz by the means of iterative
simulations have been included herein.
I. INTRODUCTION
Fig. 1. Physical and Effective Lengths of Rectangular Microstrip Patch [1]
In order to design a Microstip Rectangular Patch antenna,
the following parameters, in reference to Fig. 1, are defined as:
L = length of patch
W = width of patch
∆L = extended length due to fringing
r = dielectric constant of substrate
h = height of substrate
Where r and h are 4.4 and 1.6 mm, respectively.
II. THEORY
A. Hand Calculations
The initial design of the rectangular patch antenna involved
estimating the physical parameters by applying a series of
design equations for an operating frequency (fr) of 2.4 GHz.
First the width of the patch was designed by applying Eqn. 1,
W =
1
2fr
√
µo o
2
1 + r
(1)
Joshua S. LaPlant is an undergraduate Electrical Engineer in the Depart-
ment of Electrical and Computer Engineering, University of North Carolina
Charlotte, Charlotte, North Carolina (e-mail: jlaplant@uncc.edu).
resulting in a width of approximately 38.01037 mm. Next the
effective dielectric constant ( e) was calculated to be 4.0857
using Eqn. 2.
e =
r + 1
2
+
r − 1
2
1
1 + 12 h
W
(2)
With this, the extended length due to fringing (∆L) could be
calculated with Eqn. 3.
∆L = 0.412h
( e + 0.3)(W
h )
( e − 0.258)(W
h )
(3)
∆L was found to be 0.7388 mm, then applied to Eqn. 4 to
calculate the length of the patch.
L =
1
2fr
√
µo o
− 2∆L (4)
The length of the patch was calculated to be 29.4219 mm.
Generally, it is undesirable to have a width greater than the
length. A simple way to overcome this is to scale the width
by an optimal factor (investigated in Section II.B), resulting
in a new width. With this new width, the design parameter
calculations could be recomputed accordingly, thus resulting
in a new length. This would be considered a ”traditional”
approach; however, for the purposes of this design, alternative
methods were investigated and documented in Section II.B.
B. Design by Simulation
From this point forward, the remainder of the design process
was carried out using HFSS to optimize the resonant frequency
of the antenna to 2.4 GHz. Rather than recalculating the length
(L) based off of the scaled width, the original length was held
constant. With the original length still applied to the design,
a parametric sweep was run to determine the optimal scaling
factor of the width (LF) using the relationship shown below
in Eqn. 5.
Wnew = L(LF) (5)
The new width was swept for scaling factors (LF) from 0.6
to 0.95 with a step size of 0.05, as seen below in Fig. 2.
From Fig. 2, it was determined that the optimal width factor
was LF = 0.65, subsequently resulting in an adjusted Wnew
of 19.124 mm. This placed the zero-crossing at approximately
2.385 GHz, still requiring an additional shift to place the zero-
crossing closer to the desired resonant frequency of 2.4 GHz.
Subsequently, the overall size of the patch was then adjusted
by increasing and decreasing the width and length by a

2. UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE, ECE DEPARTMENT, ECGR 4121/5121 PROJECT II 2
Fig. 2. Parametric Sweep of Recalculated Widths for LF = 0.6-0.95(Input
Impedance)
percentage of it’s size. This relationship is modeled below in
Eqn.’s 6 and 7, where S is the percentage scaling factor.
Ws = Wnew + (S)Wnew (6)
Ls = L + (S)L (7)
Similar to before, a parametric sweep was performed for S
with percentage increases from 0.1% to 5% (S = 0.001 to
0.05), producing results that shifted the zero-crossing to lower
frequencies. In light of this, a second parametric sweep was
run for a decreasing S from -0.1% to -0.7% (S = -0.001 to
-0.007). From these results, the percent scaling factor that
shifted the point of resonance closest to 2.4 GHz was S =
0.0035, or 0.35%, which can be observed in Fig.3. The scaled
Fig. 3. Input Impedance for LF = 0.65 and Scaled Width and Length of S
= -0.0035 (-0.35% Decrease in Overall Size)
length (Ls) was found to be 29.3189 mm, whereas the scaled
width (Ws) was found to be 19.0573 mm (seen in Fig. ). It was
observed that the slightest change with regards to S resulted
in drastic shifts in frequency for the imaginary zero-crossing.
Additionally, as the width is scaled up and down, the input
impedance was increased, furthering the need for a quarter-
wave transformer to match the impedance to 50 Ω.
C. Quarter-Wave Transformer Design
To reduce the input impedance for a better match, a single-
section quarter-wave transformer was implemented by first
Fig. 4. HFSS Design Model for LF = 0.65 and Scaled Width and Length of S
= -0.0035 (-0.35% Decrease in Overall Size) before Quarter-wave Transformer
making note of the peak resistance (RL = 321.0446 Ω) at the
new imaginary zero-crossing frequency (2.395 GHz). Using
the realized peak input resistance and characteristic impedance
value (Zc) of 50 Ω in accordance with Eqn. 8, the value of
the impedance Zo was calculated for further use in Eqn. 9.
Zo = ZcRL (8)
Zo was calculated to be 126.697 Ω and applied to Eqn. 9 to
calculate the value of A as 3.6303.
A =
Zo
60
r + 1
2
+
r − 1
r + 1
(0.23 +
0.11
r
) (9)
The resulting value of A was applied to Eqn. 10 to solve for
ratio of the width of the transformer trace to the height of the
substrate.
Wt
h
=
8eA
e2A − 2
(10)
From Eqn. 10, the width of the single-section transformer trace
(Wt) was approximately 0.3398 mm.
Once the width of the trace was found, the length of the
trace could then be calculated by finding the effective dielectric
constant , e,t, using the same equation as Eqn. 2, resulting in
e = 2.9242. Finally the length of the trace (Lt) was calculated
to be 18.2746 mm by making use of Eqn. 11.
Lt =
λt
4
=
vp
4fr
√
t
(11)
The resulting peak input resistance dropped down to just
over 50 Ω’s, a suitable match for this design. Unfortunately,
this shifted the input impedance’s imaginary zero-crossing
frequency closer to 2.38 GHz, requiring further adjustments
to the design parameters.
D. Final Design Adjustments
Now that the peak input resistance was in the ballpark of
a 50 Ω match, the imaginary zero-crossing frequency could
then be shifted once more to acquire a resonant frequency
of 2.4 GHz. Like the previous steps, a parametric sweep was
performed to decrease the length by a certain percentage (T)

3. UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE, ECE DEPARTMENT, ECGR 4121/5121 PROJECT II 3
by applying Eqn. 12), ensuring the width of the patch remain
unchanged as to not disturb the matched impedance.
Lfinal = Ls + (T)Ls (12)
The sweep for the varying percentage decreases of the length
involving scaling factor T was performed for T = -0.0004
to -0.0008 (-0.04% to -0.08%). With respect to Fig. 5, it
Fig. 5. Parametric Sweep of Length Scaling Factor for T Values from -0.0004
to -0.0008 (-0.04% to -0.08% Decrease in Length) for Input Impedance
was observed that the majority of Values of T resulted in a
frequency close to 2.4 GHz. Therefore, the decision for which
scaling factor T rested upon whichever value resulted in the
lowest dip on the Return Loss (S11) plot shown in Fig. 6.
Conclusively, a scaling factor of T = -0.0006 was determined
Fig. 6. Parametric Sweep of Length Scaling Factor for T Values from -0.0004
to -0.0008 (-0.04% to -0.08% Decrease in Length) for Return Loss
to be the best fit, producing an absolute minimum Return Loss
at -30 dB. The final adjustment to the length (Lf inal) was
approximately 29.30128 mm, which can also be seen applied
to the final design model, with the addition of the quarter-wave
transformer, in Fig.7
III. SIMULATION
A. Return Loss (S11)
B. Input Impedance
C. Gain
D. E-Plane Field Patterns
IV. REFERENCES
REFERENCES
[1] C.A. Balanis, ”Rectangular Patch,” in Antenna Theory Analysis and
Design, Third edition, Hoboken, NJ, USA, Wiley, 2005, ch.14, sec.2,
Fig. 7. Final HFSS Design Model of the Rectangular Patch Antenna with a
Quarter-wave Transformer
Fig. 8. Return Loss (S11)
Fig. 9. Input Impedance (S11)
pp. 816-820.

4. UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE, ECE DEPARTMENT, ECGR 4121/5121 PROJECT II 4
Fig. 10. 3-Dimensional Polar Plot of the Gain
Fig. 11. 3-Dimensional Polar Plot of Gain in dB
Fig. 12. 3-Dimensional Polar Plot of the E-Plane
Fig. 13. E-Plane Radiation Pattern