Calculator
Formula used
Rectangular width:
W = c / (2fᵣ) × √(2 / (εᵣ + 1))Effective dielectric constant:
εeff = (εᵣ + 1)/2 + (εᵣ − 1)/2 × (1 + 12h/W)⁻¹ᐟ²Fringing extension:
ΔL/h = 0.412 × ((εeff + 0.3)(W/h + 0.264)) / ((εeff − 0.258)(W/h + 0.8))Physical rectangular length:
L = c / (2fᵣ√εeff) − 2ΔLCoaxial feed resistance model:
Rin(y₀) = Redge × cos²(πy₀/L)
y₀ = (L/π) × arccos(√(Ztarget/Redge))Minimum practical ground estimate:
Lg = L + 6h
Wg = W + 6hApproximate VSWR ≤ 2 fractional bandwidth:
BW ≈ 3.771 × |(εᵣ − 1)/εᵣ²| × (h/λ₀) × (W/L)Closed-form equations provide initial dimensions. A coaxial probe, connector body, solder pad, finite ground plane, enclosure, fabrication stack-up, and nearby objects can shift resonance and matching.
How to use this calculator
- Select rectangular, square, or circular geometry.
- Choose design mode for new dimensions or analysis mode for an existing patch.
- Enter frequency, substrate permittivity, substrate height, and conductor properties.
- Select automatic coaxial matching or enter a manual feed position.
- Choose automatic or custom ground-plane dimensions.
- Set a frequency sweep and fabrication tolerances when needed.
- Calculate, inspect warnings, and review the live geometry diagram.
- Export results to CSV or use the PDF and print button.
Example data
| Application | Frequency | Substrate | εr | Height | Target feed |
|---|---|---|---|---|---|
| Wi-Fi patch | 2.45 GHz | FR-4 | 4.4 | 1.6 mm | 50 Ω |
| ISM telemetry | 915 MHz | Rogers RO4003C | 3.55 | 1.524 mm | 50 Ω |
| GPS L1 patch | 1.57542 GHz | Rogers 6010 | 10.2 | 1.27 mm | 50 Ω |
| 5.8 GHz link | 5.8 GHz | Rogers 5880 | 2.2 | 0.787 mm | 50 Ω |
| Sub-6 GHz study | 3.5 GHz | Rogers RO4350B | 3.48 | 0.762 mm | 50 Ω |
Coaxial-fed patch antenna design
A coaxial-fed patch antenna uses a conducting patch above a continuous ground plane. A dielectric substrate separates both conductors and sets the guided wavelength. The inner coaxial conductor passes through the ground and connects to the patch.
Patch size primarily controls resonance, while feed position controls input resistance. The radiating edges usually show higher resistance than the patch center. Moving the probe inward therefore provides a practical impedance-matching method for common transmission lines.
Relative dielectric constant strongly affects physical dimensions and field confinement. High-permittivity substrates reduce size but often increase stored energy and sensitivity. Lower-permittivity laminates generally support better efficiency, wider bandwidth, and less severe surface-wave behavior.
Substrate height creates another important tradeoff in antenna development. A thicker substrate can improve bandwidth and radiation resistance. Excessive height can increase probe inductance, unwanted modes, surface waves, and spurious feed radiation.
The rectangular calculation applies a transmission-line approximation with fringing correction. Its dominant length is near one-half guided wavelength after edge extension. Circular patches use a cavity-model radius equation with a substrate-height correction for fringing fields.
Analytical impedance estimates are useful for selecting an initial probe location. They cannot reproduce every detail of a real connector transition. Probe diameter, solder volume, antipad geometry, ground size, housing, and manufacturing variation may alter measured results.
Bandwidth, directivity, gain, and efficiency values on this page are screening estimates. They help compare substrates and identify obviously difficult designs. They should not replace a full-wave solver when performance, compliance, polarization, or production repeatability matters.
After calculating, create the model in an electromagnetic simulator with actual stack-up data. Sweep feed position, patch dimensions, connector geometry, and ground size. Fabricate, measure, compare, then tune the final dimensions carefully.
Frequently asked questions
Why does the physical patch length differ from half wavelength?
Fringing fields make the patch electrically longer than its copper length. The calculator subtracts two edge extensions from the effective resonant length.
Where should a 50-ohm coaxial feed be placed?
The probe is usually placed on the patch centerline and moved inward from a radiating edge until the estimated input resistance approaches 50 ohms.
Can I use FR-4 at microwave frequencies?
FR-4 is common and inexpensive, but its dielectric tolerance and loss can reduce repeatability and efficiency. Verify the actual laminate data and frequency behavior.
Why is the bandwidth estimate narrow?
Single-layer microstrip patches naturally store substantial reactive energy. Thin substrates and high dielectric constants usually increase quality factor and reduce fractional bandwidth.
Does the calculator include probe inductance?
It provides a simple probe-inductance estimate based on substrate height and probe diameter. Complex connector and antipad fields still require simulation.
What ground-plane size should I begin with?
A common starting estimate adds about three substrate heights around every patch edge. Larger finite grounds can change pattern, gain, and resonance.
Can this calculator design circular polarization?
It estimates basic rectangular, square, and circular resonators. Circular polarization normally requires perturbations, dual feeds, slots, truncations, or stacked elements not fully modeled here.
Why can simulation and measurements disagree?
Material tolerances, copper roughness, connector geometry, solder, finite grounds, nearby structures, and calibration errors can each shift impedance and resonance.
Is the result ready for fabrication?
Treat it as an initial engineering design. Validate the complete structure in a full-wave solver and confirm the prototype using calibrated RF measurements.