Microstrip Patch Antenna 2.45 GHz Benchmark: circular, F-shaped, triangular, square, hexagonal

Which patch shape performs best at 2.45 GHz, the ISM band powering Wi-Fi, Bluetooth, ZigBee, RFID, and medical telemetry? Five geometries (circular, F-shaped, triangular, square, hexagonal): designed, simulated in CST Studio Suite, fabricated on FR-4, measured on a Rohde & Schwarz VNA. The circular patch wins in both simulation and measurement.

Results

Simulation (CST Studio Suite)

Geometry	S11 (dB)	VSWR	Bandwidth (%)	Main Lobe (dB)	Side Lobe (dB)
Circular	−53.08	1.004	3.12	5.54	−3.7
F-shaped	−30.02	1.065	2.98	4.11	−1.6
Triangular	−18.86	1.257	2.45	4.51	−0.6
Square	−16.38	1.357	2.41	3.00	−6.7
Hexagonal	−14.78	1.446	2.12	5.54	−7.0

Main Lobe (dB) is CST's far-field main-lobe magnitude; circular and hexagonal genuinely tie at 5.54 dB.

Measurement (VNA)

Geometry	S11 (dB)	VSWR
Circular	−31.99	1.125
F-shaped	−16.98	1.167
Triangular	−15.37	1.368
Square	−14.46	1.536
Hexagonal	−13.93	1.694

Simulation vs. Measurement

Geometry	S11 sim (dB)	S11 meas (dB)	ΔS11 (dB)	VSWR sim	VSWR meas	ΔVSWR
Circular	−53.08	−31.99	+21.09	1.004	1.125	+0.121
F-shaped	−30.02	−16.98	+13.04	1.065	1.167	+0.102
Triangular	−18.86	−15.37	+3.49	1.257	1.368	+0.111
Square	−16.38	−14.46	+1.92	1.357	1.536	+0.179
Hexagonal	−14.78	−13.93	+0.85	1.446	1.694	+0.248

• Same ranking in both; all five clear S11 < −10 dB
• Circular sits closest to 2.45 GHz with the deepest null
• Deltas: SMA parasitics, FR-4 εr spread, etching, solder

Figure of Merit

Different footprints, so normalise:

Geometry	Footprint (mm²)	Main Lobe (dB)	Gain ÷ area (cm⁻²)	Gain × BW
Circular	908	5.54	0.394	0.112
F-shaped	635	4.11	0.406	0.077
Triangular	552	4.51	0.511	0.069
Square	863	3.00	0.231	0.048
Hexagonal	751	5.54	0.477	0.076

• Link budget and bandwidth: circular. Tight board area: triangular or hexagonal.

Fabricated Antennas

Two samples per design (one measured), photolithography on FR-4, SMA-fed:

Circular (best performer)	F-shaped	Triangular
Square	Hexagonal

Design Parameters

Common

Parameter	Value
Operating frequency	2.45 GHz
Substrate	FR-4 (εr ≈ 4.4, tan δ = 0.02)
Substrate height (Hs)	1.4 mm
Conductor height (Ht)	0.036 mm
Ground plane (Wg × Lg)	75.20 × 58.76 mm
Feed line width (Fw)	2.7 mm (50 Ω)
Feed-patch gap (Gpf)	1 mm

Geometry-Specific

Geometry	Dimensions
Circular	R = 17.0 mm
Square	S = 29.38 mm
Triangular	Tb = 37.60 mm, Th = 29.38 mm
Hexagonal	Ha = 17.0 mm
F-shaped	W = 37.60, L = 29.38, Vw = 10.0, Bh = 8.0, Sh = 3.0, Mw = 25.0 mm

Simulation

Set PatchShape in Main and run: patch-antenna.bas builds substrate, ground plane, patch, feed, waveguide port, monitors, and solver from scratch.

PatchShape	Patch construction
"circular"	Cylinder, R = 17.0 mm
"square"	Brick, S = 29.38 mm
"triangular"	Extruded isosceles triangle, base 37.60 mm, height 29.38 mm
"hexagonal"	Extruded regular hexagon, side 17.0 mm
"fshaped"	Boolean union of vertical bar + two horizontal bars

• Annealed-copper conductors; Eps exposed for FR-4 tolerance sweeps
• Hex mesh, adaptive refinement, open boundaries, 6·Hs port
• Two feed expressions per shape: Ey (edge) and Fx (centre)
• Exports the solved sweep to s11.s1p for antenna ingest

Fabrication and Measurement

Full process in fabrication-and-measurement.pdf:

• CorelDraw mask → laminated photoresist FR-4 → ~2 min UV exposure → NaOH developer → chemical etch
• SMA soldered to the 50 Ω feed; S-parameters on a Rohde & Schwarz ZVH

VNA (Smith chart)	Laminator	UV exposure unit

UV exposure (closed)	Etching machine

Blank FR-4 substrate	Circular patch in NaOH developer bath

Figures

Return loss: simulation vs measurement	CST S11 sweep: circular patch

• Left: measured S11 tracks the simulated ranking, all five below −10 dB
• Right: the winner's simulated S11 shows a −53.08 dB null at 2.434 GHz (Fig 4.2)
• Full CST outputs for all five shapes in simulation-and-results.pdf

Analysis Toolkit

Module	What it does
metrics.py	Exact S11, reflection coefficient, and VSWR identities; bandwidth from band edges
design.py	Shape-correct resonance equations (Balanis, Garg) and patch footprint areas
fom.py	Area-normalised gain and gain-bandwidth product
check.py	Physics validator wired into CI
tables.py	Renders and injects every README table between marker comments
touchstone.py	Minimal .s1p reader (DB, MA, RI) for VNA and CST sweeps
plots.py	Publication-ready charts from the canonical data

Applications

#	Application	Why 2.45 GHz patches fit
1	Wi-Fi (802.11 b/g/n) access points and clients	Low profile, direct PCB integration
2	Bluetooth and BLE modules	Compact footprint on standard FR-4
3	ZigBee / IEEE 802.15.4 sensor networks	Cheap to mass-produce with node hardware
4	RFID readers (2.45 GHz ISM band)	Directional pattern suits gate and portal readers
5	Wireless medical telemetry	Conformal, lightweight, body-worn friendly
6	ISM-band industrial telemetry and microwave power transfer	Etchable, low cost, easily arrayed for higher gain

Tech Stack

Layer	Tool
EM simulation	CST Studio Suite (VBA macro, time-domain solver)
Model scripting	CST VBA
Analysis toolkit	Python 3.9+ (standard library core; matplotlib optional)
Testing	pytest (21 tests)
Mask design	CorelDraw
Fabrication	Photolithography: laminator, UV exposure, NaOH developer, chemical etching
Measurement	Rohde & Schwarz ZVH vector network analyzer
Substrate	FR-4, 1.4 mm, 0.036 mm copper

Documentation

Document	Contents
methodology.pdf	Design parameters, substrate specs, VNA calibration
simulation-and-results.pdf	CST results: S11, VSWR, radiation patterns, gain
fabrication-and-measurement.pdf	Step-by-step fabrication, VNA measurements

References

1. C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed. Hoboken, NJ: Wiley, 2016. Chapters 14.2-14.4: transmission-line and cavity models for rectangular and circular patches.
2. R. Garg, P. Bhartia, I. Bahl, and A. Ittipiboon, Microstrip Antenna Design Handbook. Norwood, MA: Artech House, 2001. Design curves and impedance matching for varied patch geometries.
3. D. M. Pozar, "Microstrip Antennas," Proc. IEEE, vol. 80, no. 1, pp. 79-91, Jan. 1992. Survey of microstrip theory, design methods, and feeding techniques.
4. K. F. Lee and K. M. Luk, Microstrip Patch Antennas. London: Imperial College Press, 2011. Geometry-specific analysis of triangular, circular, and polygonal patches.

License

MIT