A 2.4 GHz Patch Antenna: RO4350B Geometry and Tuning Study
A first rectangular patch estimate for 2.400 GHz on an assumed RO4350B construction is W ≈ 40.92 mm and L ≈ 32.25 mm. This result uses a 1.524 mm dielectric height and εr = 3.66 in a simplified transmission-line model. It is a starting geometry for electromagnetic analysis, not a production antenna or a claim of measured resonance, gain or bandwidth.
This worked study extends the patch-antenna design overview. The deliverable is a reproducible seed and two small sensitivity sweeps. The feed, finite ground, enclosure and manufacturing details still need to be designed. RO4350B is one material candidate; its use does not by itself establish better system performance than an alternative construction.
Define the target before drawing copper
Here “2.4 GHz” means a single calculation frequency of 2.400 GHz. A product needs explicit lower and upper operating frequencies, polarization, coverage, impedance reference and mechanical limits. A resonance at 2.400 GHz does not establish coverage of a wider wireless band. Specify the actual system band and permitted mismatch before optimization.
The example assumes a single rectangular patch over a continuous ground plane, a thin homogeneous isotropic dielectric, zero conductor thickness and no soldermask. It approximates the dominant length resonance. It does not include a coaxial probe, inset feed, edge-feed transformer, dielectric loss, copper roughness, surface finish or radome. The real laminate is reinforced and the actual board is finite; those differences must be considered in the next model.
The Rogers RO4000 data sheet lists a RO4350B design Dk of 3.66 with an 8–40 GHz differential-phase-length characterization context. It separately lists process Dk 3.48 ± 0.05 at 10 GHz and 23°C. Using 3.66 at 2.4 GHz here is an explicit preliminary assumption, not a certified 2.4 GHz value or a tolerance limit. Confirm the construction-specific dielectric model with the material supplier and correlate a prototype.
Reproduce the initial dimensions
The starting equations follow the dimension-estimation approach shown in the MathWorks patch-array example. We calculate a single rectangular RO4350B candidate with our own assumptions; we do not reuse that example's FR4 array layout or performance results. Use consistent length units, f in Hz and c = 299,792,458 m/s:
- W = c/(2f) × √[2/(εr + 1)].
- εeff = (εr + 1)/2 + (εr − 1)/(2√[1 + 12h/W]).
- ΔL = 0.412h × [(εeff + 0.3)(W/h + 0.264)] / [(εeff − 0.258)(W/h + 0.8)].
- L = c/(2f√εeff) − 2ΔL.
With h = 1.524 mm, the calculation gives εeff ≈ 3.4357 and a fringing extension ΔL ≈ 0.7238 mm at each radiating end. The resulting physical length is about 1.448 mm shorter than the effective half-wave length. That distinction is why simply dividing a guided wavelength by two is not the finished patch dimension.
| Quantity | Value | Meaning |
|---|---|---|
| Patch width W | 40.917 mm | Transverse patch dimension; not the feed-line width |
| Patch length L | 32.248 mm | Physical resonant-direction dimension |
| Dielectric height h | 1.524 mm | Patch-to-ground separation, excluding copper |
| Fringing extension ΔL | 0.724 mm per end | Equivalent electrical extension, not extra drawn copper |
| Feed and ground dimensions | Not specified by this estimate | Must be selected and analyzed separately |
Length sweep: keep the other assumptions fixed
For each candidate length, estimate f ≈ c/[2(L + 2ΔL)√εeff]. Hold W, h and εr fixed. Reusing the same fringing correction is appropriate for this small, idealized length sweep; it is not a full-wave calculation. The table is a set of model predictions, not a measured S11 trace.
| Length change (mm) | Physical L (mm) | Predicted resonance (GHz) |
|---|---|---|
| -0.50 | 31.748 | 2.4361 |
| -0.25 | 31.998 | 2.4179 |
| 0.00 | 32.248 | 2.4000 |
| 0.25 | 32.498 | 2.3823 |
| 0.50 | 32.748 | 2.3649 |
A 0.25 mm increase in length moves this model's resonance downward by approximately 17.7 MHz; a 0.25 mm decrease moves it upward by about 17.9 MHz. These are chosen exploration increments, not claims about a fabricator's etching tolerance. Near the baseline, the fractional change is approximately −ΔLphysical/(L + 2ΔLfringing). Keep the two uses of “delta length” separate in the calculation sheet.
Dielectric sensitivity: vary the model, not the artwork
In the next sweep the drawn W and L remain at their baseline values. Recalculate εeff and the fringing extension for each assumed εr. The ±0.10 range is an illustrative sensitivity bracket selected for this study. It is not a Rogers specification and must not be confused with the process-Dk tolerance.
| Assumed εr | Predicted resonance (GHz) |
|---|---|
| 3.56 | 2.4322 |
| 3.66 | 2.4000 |
| 3.76 | 2.3691 |
This gives an approximate shift of +32.2 MHz or −30.9 MHz around the baseline. It shows why retuning copper against an uncertain dielectric model can give a misleading sense of precision. Do not add the length and dielectric shifts as independent worst cases without defining correlations and the actual process ranges. Replace the illustrative bracket with agreed material data before deciding prototype variants.
Turn the seed into a useful tuning experiment
| Stage | Controlled inputs | What to inspect | Decision |
|---|---|---|---|
| Complete geometry | Finite ground, board outline, feed topology, copper, mask and housing | Port definition and mesh convergence | Fix the model boundary before comparing variants |
| Length sweep | Feed geometry and width held constant initially | Mode location, input reactance and S11 across the band | Select a length neighborhood, not just a single deep notch |
| Feed sweep | Candidate length held constant | Input impedance and matching sensitivity | Choose feed location or matching geometry with adequate margin |
| Construction corners | Agreed height, Dk and etched geometry ranges | Band-edge mismatch and radiation changes | Reject nominal-only solutions |
| Installed prototype | Known fixture and enclosure configuration | Impedance, pattern, efficiency and repeatability | Correlate before releasing production artwork |
Length and feed adjustments interact, so the staged sweep organizes the work rather than proving that the parameters are independent. For an inset feed, the notch itself modifies geometry. For a probe feed, include the probe transition and ground connection. Do not transfer a feed offset from another substrate and assume that it remains a 50 Ω match.
A practical prototype set can use the baseline and two neighboring lengths while keeping the other geometry identical. Label each board with its artwork revision and record the as-built dimensions. Use simulation to choose the neighboring increments; the ±0.25 mm values above merely demonstrate the arithmetic. Keep an unmodified control board before attempting irreversible copper trimming.
Measure the installed antenna and separate the conclusions
Texas Instruments AN058, Antenna Selection Guide, treats impedance/bandwidth measurements and over-the-air characterization separately. Its measurement guidance also addresses calibration, cable mounting and device placement. Apply those distinctions to the patch: a good input match alone does not establish a useful radiation pattern or efficiency.
For each prototype, record the VNA reference plane, calibration method, sweep settings, connector and cable arrangement, enclosure state and ambient conditions. Keep cables and nearby objects consistent between variants. For radiation testing, state the polarization, angular coverage, reference antenna or calibration method and uncertainty. Report measured values only after those tests exist; this article supplies no gain, efficiency or bandwidth claim.
If the predicted length trend appears in simulation but not on hardware, first check the dielectric height, unit conversion, feed construction and measurement plane. If bare-board matching changes when the cover is installed, retune the installed model. For arrays, do not copy this element into a grid without checking coupling and the feed network; use the phase-matching guide and our antenna validation workflow to structure the next review.
What to send for an antenna PCB quotation
Provide the operating band, polarization and coverage goals, patch or array drawings, feed stackup, ground and mechanical boundaries, quantity, material candidates, copper and mask requirements, and required test scope. Identify which dimensions are preliminary and which are approved. If substitutions are acceptable, ask for their proposed dielectric height and material model before approving new artwork. A lower-frequency control board or a different millimeter-wave antenna may need a different material decision.
Original calculations and HTML tables; no third-party figures reproduced. Source roles: Rogers for laminate definitions, MathWorks for the starting dimension equations, and Texas Instruments for antenna measurement distinctions. All numerical sweeps here are idealized analytical results, not full-wave simulations or laboratory measurements.