Microstrip Patch Antenna Calculator sizes a rectangular patch from frequency, dielectric constant and substrate thickness. It also returns the inset feed depth, bandwidth and gain.
Enter the laminate's design Dk, not its process Dk. Rogers lists 3.66 for RO4350B, not 3.48.
Feed and Substrate Loss
Picking a substrate above fills its loss tangent here. Copper loss is always included.
Same Design on Other Substrates
| Substrate | Patch L × W | Bandwidth | Efficiency |
|---|---|---|---|
| FR-4 (typ.) | 29.42 × 38.01 mm | 62.5 MHz | 39% |
| RO4350B | 32.22 × 40.92 mm | 37.3 MHz | 72% |
| RO4003C | 32.71 × 41.41 mm | 36.0 MHz | 76% |
| RT/duroid 5880 | 41.32 × 49.38 mm | 37.5 MHz | 88% |
| Air | 60.18 × 62.46 mm | 35.6 MHz | 96% |
Using the Microstrip Patch Antenna Calculator
The Microstrip Patch Antenna Calculator works in two directions. Size from Frequency turns a target frequency into a patch length and width. Frequency from Size takes copper you already have and returns the frequency it resonates at.
Both modes need the dielectric constant and the substrate thickness, in millimeters, mils or inches. Picking a laminate preset also fills its loss tangent. That loss figure drives the efficiency, bandwidth and gain cards.
Enter the design Dk of the laminate in the Microstrip Patch Antenna Calculator, not the process Dk. Rogers lists RO4350B at 3.48 for process control and 3.66 for circuit design. RO4003C is 3.38 and 3.55 in the same table.
The gap matters. A 2.4 GHz patch sized with 3.48 comes out 33.03 mm long. If the board behaves at 3.66, that copper resonates near 2.343 GHz. It lands 57 MHz low on an antenna with about 36 MHz of bandwidth.
Patch Length and Width Formulas
The patch width is set first, and it depends only on the resonant frequency and the dielectric constant. This width is chosen for good radiation, which is why it comes out larger than the length.
Part of the field runs through the air above the board. The patch therefore sees an effective dielectric constant below the laminate value, and the difference grows as the board gets thicker against the patch width.
Fringing fields at the two radiating edges make the patch act longer than its copper. Hammerstad's expression gives that extension per end, and it usually lands near half the substrate thickness.
The physical length is a half wavelength in the effective dielectric, less the extension at both ends. Length alone sets the resonance, so it is the dimension to trim on a prototype.
In these equations c is the speed of light, fr is the resonant frequency and h is the substrate thickness. The fringing and effective dielectric expressions match David Jackson's microstrip antenna notes from the University of Houston, with the length written in the Balanis form. Frequency from Size runs the same set backward from L and W.
Microstrip Patch Antenna Design at 2.4 GHz
With its default entries the Microstrip Patch Antenna Calculator sizes a 2.4 GHz patch on FR-4, using a dielectric constant of 4.4 and a 1.6 mm board. The width comes to 38.01 mm and the effective dielectric constant to 4.086.
A half wave in that dielectric is 30.90 mm. The fringing extension is 0.739 mm per end, so 1.478 mm comes off. The finished patch is 29.42 mm long by 38.01 mm wide, the figure shown in the result header.
The first card adds a tolerance figure. Each 0.1 mm of length error moves the resonance by 7.77 MHz. An over-etched board that loses 0.2 mm of length sits about 16 MHz high before any other error is counted.
The ground plane that the Microstrip Patch Antenna Calculator shows under the result is the patch plus six substrate thicknesses in each direction, 39.02 by 47.61 mm here. That leaves 3h of ground past every edge. Treat it as a floor, since the gain figure assumes a ground plane much larger than the patch.
Input Impedance and Inset Feed Depth
A patch fed at its radiating edge has a high input impedance. On the 2.4 GHz example the edge resistance is 129 Ω, far from a 50 Ω line. Moving the feed toward the center lowers it, and it falls to zero at the middle of the patch.
How fast it falls depends on the feed. A coax probe follows a cosine-squared curve. A notched microstrip feed drops faster, and measurements on low-permittivity boards reported by Microwaves & RF put it close to the fourth power.
Here x0 is the inset depth from the radiating edge. Solving for 50 Ω gives 6.20 mm on the example patch. Many tools apply the cosine-squared curve to every feed, which gives 8.42 mm and cuts the notch 2.2 mm too deep.
The Microstrip Patch Antenna Calculator uses the fourth-power curve for the inset feed and the squared curve for a probe. Notch width also shifts the match, so plan to tune the depth on the first board.
Set Feed Type to Coax Probe Feed and the card shows the probe position instead. It is 8.42 mm from the edge, or 6.29 mm from the patch center. A probe at the exact center sees no resistance, so the patch cannot be matched there.
The second row gives a way to skip the notch. A quarter-wave line of 80.4 Ω between the patch edge and the 50 Ω feed does the same job. Find its trace width with the Microstrip Impedance Calculator and its length with the Microstrip Wavelength Calculator.
Bandwidth, Efficiency and Gain
The bandwidth card in the Microstrip Patch Antenna Calculator uses the closed-form expression by Jackson and Alexopoulos, published in IEEE Transactions on Antennas and Propagation in 1991. It returns the fractional bandwidth at 2:1 VSWR.
The three terms in the bracket are dielectric loss, copper loss and radiation. Rs is the surface resistance of copper, λ0 is the free-space wavelength and η0 is 376.73 Ω. The factors p, c1 and ehed come from the patch shape and the permittivity.
On the 2.4 GHz FR-4 patch those terms are 0.0200, 0.0008 and 0.0160. Dielectric loss is the largest of the three. It is bigger than the radiation term that does the useful work.
That explains a result of 62.5 MHz bandwidth with only 39% radiation efficiency. Set the loss tangent to zero and the same patch drops to 28.5 MHz. More than half of the FR-4 bandwidth is loss, not radiation.
Gain is directivity times efficiency. The example has 6.3 dBi of directivity, and the 39% efficiency pulls the gain down to 2.2 dBi. Carry that gain into the Link Budget Calculator when you check range.
Below the cards, the Microstrip Patch Antenna Calculator repeats the same design on five substrates, so the size and loss trade can be read in one place. At 2.4 GHz and 1.6 mm the comparison looks like this.
| Substrate (Dk) | Patch L × W | Bandwidth | Efficiency |
|---|---|---|---|
| FR-4 (4.4) | 29.42 × 38.01 mm | 62.5 MHz | 39% |
| RO4350B (3.66) | 32.22 × 40.92 mm | 37.3 MHz | 72% |
| RO4003C (3.55) | 32.71 × 41.41 mm | 36.0 MHz | 76% |
| RT/duroid 5880 (2.2) | 41.32 × 49.38 mm | 37.5 MHz | 88% |
| Air (1.0) | 60.18 × 62.46 mm | 35.6 MHz | 96% |
FR-4 gives the smallest patch and the widest band, yet it radiates little more than a third of the input power. RT/duroid 5880 needs 40% more length and returns 88%.
The Rogers rows use the 10 GHz loss tangent, including 0.0009 for RT/duroid 5880. The RO4000 data sheet also gives 0.0031 for RO4350B at 2.5 GHz. Entered as a Custom loss tangent, it moves the 2.4 GHz efficiency from 72% to 74%.
Why a Built Patch Misses Its Frequency
The dielectric constant is the usual cause. FR-4 is not controlled for RF work, and its Dk runs from about 4.2 to 4.6 between suppliers and lots. Frequency from Size in the Microstrip Patch Antenna Calculator shows what that does to the example copper.
At 4.2 the 29.42 by 38.01 mm patch resonates at 2.454 GHz. At 4.6 it resonates at 2.349 GHz. That is a 105 MHz spread on an antenna with only 62.5 MHz of bandwidth, enough to push the band off target.
Microwave Journal documented an FR-4 patch that measured 232 MHz away from its simulated resonance. The datasheet Dk had been quoted at 10 MHz, well below the operating frequency.
The fix is to build one board, measure it, and correct the length. Change the length only, since width has little effect on the resonance. For repeatable results, move to a laminate with a controlled Dk.
How Thick the Substrate Can Be
Thickness is judged against the free-space wavelength. Bandwidth grows with thickness, but above about 5% of a wavelength the feed gets hard to match and the Microstrip Patch Antenna Calculator shows a warning. Past 10% it stops, because the thin-substrate model no longer holds.
At 2.4 GHz those limits are 6.25 mm and 12.5 mm, so ordinary boards pass. At 28 GHz they fall to 0.54 mm and 1.07 mm, and at 77 GHz to 0.19 mm and 0.39 mm. A 1.6 mm board is rejected at both, so pick a thin laminate or type a Custom thickness.
Thin boards have the opposite problem. Halving the FR-4 example to 0.8 mm cuts efficiency from 39% to 24%, because loss takes a larger share. Doubling it to 3.2 mm raises efficiency to 52% and bandwidth to 95.8 MHz.
Microstrip Patch Antenna Calculator FAQ
Can it size a square patch?
Yes. Switch to Frequency from Size and enter the same value for length and width. On 1.6 mm FR-4 a 29.66 mm square resonates at 2.4 GHz, slightly longer than the rectangular patch.
The narrower width raises the edge resistance from 129 Ω to 184 Ω and trims the bandwidth from 62.5 MHz to 56.8 MHz. The inset depth for 50 Ω grows to 7.21 mm as a result.
Does it cover a circular microstrip patch antenna?
No. A rectangular microstrip patch antenna calculator cannot size a disc, because a circular patch resonates in the TM11 mode. Its frequency depends on the radius through the Bessel root 1.841.
Here ae is the patch radius plus a fringing correction, and εr is the dielectric constant. Use that relation for a disc, then build and trim it the same way as a rectangular patch.
What input impedance does it report?
The Microstrip Patch Antenna Calculator input impedance figure is the resonant resistance at the radiating edge. It is a real value at resonance, and it does not include the series inductance of a coax probe.
Loss lowers that resistance sharply. The FR-4 example reads 129 Ω, but the same patch with no loss would read 283 Ω. A low-loss laminate therefore needs a deeper inset, such as 8.29 mm on RO4350B.