How does the resonant length of a patch antenna relate to frequency?

A rectangular patch resonates when its length L is approximately half a guided wavelength: L is approximately equal to c / (2f times sqrt(epsilon_eff)), where epsilon_eff is the effective dielectric constant of the substrate, which accounts for the fringing fields that extend beyond the physical patch edges into the air above. The effective length is longer than the physical length by approximately 2 times delta_L, where delta_L accounts for the fringing extension at each radiating edge. For FR-4 (Er = 4.4) at 2.45 GHz: lambda_guided = 300 / (2.45 times sqrt(3.4)) = 66.3 mm. L = 66.3/2 = 33.2 mm minus fringing correction of approximately 2 mm = 31.2 mm. For Rogers 4003C (Er = 3.55): L = 33.9 mm. Higher Er substrates give smaller patches but narrower bandwidth.

Why do patch antennas have narrow bandwidth?

A patch antenna is essentially a resonant cavity between the patch and the ground plane. Like all high-Q resonators, it stores energy efficiently but releases it over a narrow frequency range. The bandwidth is approximately proportional to the substrate thickness h and inversely proportional to the dielectric constant: BW is approximately equal to (3.77 times (Er minus 1) / (Er squared)) times (h / lambda_0) times 100 percent. A patch on 1.6 mm FR-4 at 2.45 GHz has about 1.5 percent bandwidth (37 MHz). On 3.2 mm Rogers RT/duroid 5880 (Er = 2.2), bandwidth increases to 4 percent (98 MHz). Techniques to widen bandwidth include: thicker substrates (more volume for stored energy), stacked patches (dual resonances), U-slot patches (creating additional resonance modes), and aperture-coupled feeding (which adds a slot resonance).

How is circular polarization achieved with a patch?

Circular polarization requires two orthogonal modes with equal amplitude and 90-degree phase difference. Three common methods: First, a square patch fed at two points along orthogonal edges with a 90-degree hybrid coupler providing the phase shift. This gives the widest CP bandwidth (2 to 3 percent) but requires the coupler. Second, a nearly square patch (length differs from width by about 1 to 2 percent) fed at a single point on the diagonal. The slight dimension difference creates two degenerate modes with a natural 90-degree phase split at the center frequency. Simple but very narrowband (0.5 to 1 percent CP bandwidth). Third, truncated corners: cutting two diagonally opposite corners of a square patch perturbs the symmetry to create the two modes. Single-feed, moderate CP bandwidth (1 to 1.5 percent). GPS L1 antennas almost universally use right-hand circular polarization via one of these techniques.

Antenna Tech

Patch Antenna

The GPS antenna in a smartphone is a 25 × 25 mm ceramic patch, 4 mm thick, picking up −130 dBm signals from satellites 20,200 km away with right-hand circular polarization. The WiFi antenna in a ceiling-mounted access point is a 30 × 30 mm FR-4 patch providing 6 dBi broadside gain across 2.4 to 2.48 GHz. The 5G mmWave module in a base station is a 16 × 16 patch array on Rogers laminate, forming a 25 dBi beam that steers ±60°. All are patch antennas: a flat metallic rectangle on a grounded substrate, resonating at half a guided wavelength. Flat enough to embed in any product, simple enough to mass-produce on a PCB, and arrayable for phased array beamforming.

Category: Antenna Tech

Gain: 5 to 8 dBi (single element)

BW: 1 to 5% (basic), 10 to 30% (stacked)

Patch Antenna Substrate Comparison

Substrate	ε_r	Patch Size (2.45 GHz)	BW (1.6 mm)	Efficiency	Application
Air (foam-backed)	1.05	59 × 59 mm	5 to 8%	>95%	Wideband, lab
RT/duroid 5880	2.2	42 × 42 mm	3 to 4%	90 to 95%	Satcom, radar
RO4003C	3.55	34 × 34 mm	2 to 3%	85 to 90%	5G arrays, WiFi
FR-4	4.4	31 × 31 mm	1.5 to 2%	70 to 85%	GPS, IoT, low-cost
Ceramic (LTCC)	7 to 20	15 to 25 mm	0.5 to 1.5%	60 to 80%	Smartphone GPS

Resonant length (rectangular patch):
L ≈ c / (2f√ε_eff) − 2ΔL
ΔL = fringing extension at radiating edges

Impedance bandwidth (approximate):
BW ≈ 3.77 × [(ε_r−1)/ε_r²] × (h/λ₀) × 100%
FR-4, h=1.6mm, 2.45 GHz: BW ≈ 1.5%

Directivity (single element):
D ≈ 4πAe/λ² ≈ 5 to 8 dBi

Common Questions

Frequently Asked Questions

What sets the resonant frequency?

L ≈ λ_g/2, where λ_g = c/(f√ε_eff). Higher ε_r = smaller patch. FR-4 at 2.45 GHz: L = 31 mm. Ceramic at ε_r = 20: L = 15 mm. Fringing extends effective length by ~2ΔL.

Why narrow bandwidth?

Resonant cavity (patch over ground): high Q = narrow BW. BW ∝ h/λ and 1/ε_r. Thicker + lower ε_r = wider. Stacked patches, U-slots, and aperture coupling extend to 10 to 30%.

How to get circular polarization?

Dual-feed with 90° hybrid: widest CP BW (2 to 3%). Nearly-square single-feed: degenerate modes split, very narrow (0.5 to 1%). Truncated corners: moderate (1 to 1.5%). GPS L1 uses RHCP via one of these.

Related Terms

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Antenna Design

Patch Antenna Dimension Calculator

Enter operating frequency and substrate ε_r and thickness. Get the patch length, width, feed point location, and estimated bandwidth with fringing corrections.

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