Design the flat antenna that is simply a rectangle of copper etched onto a printed-circuit board: the microstrip patch antenna. Adjust the resonant frequency, substrate dielectric constant and thickness to see the required patch width and length, the effective permittivity and the fringing correction update in real time.
Parameters
Resonant frequency f
GHz
Target operating frequency of the antenna
Substrate dielectric constant ε_r
About 4.4 for FR-4, 2-3 for low-loss laminates
Substrate thickness h
mm
Thickness of the dielectric between patch and ground
A three-layer stack from the top: copper patch (width W, length L), dielectric substrate (thickness h) and ground plane. The electric field pulses as it bulges out past the two radiating edges (fringing).
Patch length L vs resonant frequency f
Patch dimensions vs substrate dielectric constant ε_r
The patch width W comes from radiation efficiency, the patch length L from the half-wavelength in the dielectric. c: speed of light, f: resonant frequency.
Fringing length correction ΔL. The bulging field makes the patch behave electrically a little longer than its physical size.
What is the Microstrip Patch Antenna Simulator?
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The name "microstrip patch antenna" sounds intimidating — what kind of antenna is it really?
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It is far less fancy than the name. Put simply, it is just a "rectangle of copper" etched onto the surface of a printed-circuit board. The whole back side of the board is a ground plane. So it is a sandwich: copper plate / dielectric / copper ground. Flat, thin, light and cheap. That is why the patch antenna is inside almost everything around you — phones, WiFi and Bluetooth modules, GPS receivers, satellite terminals.
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How can a plain rectangle of copper actually transmit and receive radio waves?
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The key is "resonance". When the patch length L is exactly half a wavelength in the dielectric, a standing wave of electric field sets up on the patch and it resonates strongly. So L sets the operating frequency. Raise the "resonant frequency" on the left — in the "patch length vs frequency" chart below you will see the required L shrink sharply as the frequency goes up. At 2.4 GHz, L is just under 3 cm, about the size of your thumb.
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I see. But what is the "effective permittivity" in the results? Is it different from the substrate's ε_r?
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Good question. The electric field between the patch and the ground does not travel neatly inside the substrate only. Part of it bulges out into the air past the patch edges. So the permittivity the wave "feels" is a value between the substrate's ε_r and air's 1. That is the effective permittivity ε_eff, and it always satisfies 1 < ε_eff < ε_r. Since the wavelength is set by ε_eff, the patch-length calculation uses ε_eff, not ε_r. Make the substrate thicker and more of the field escapes into air, so ε_eff drops toward 1.
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Is the "length correction" ΔL in the formula also related to that field bulging out?
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Exactly. At the two radiating edges the field does not cut off cleanly at the patch edge — it arcs outward. That is the fringing field. As a result the antenna behaves electrically a little longer than its physical length. That "electrical extension" is ΔL at each edge. So in design you subtract 2ΔL from the electrical length that matches the target frequency to get the physical length L you actually fabricate. The neat part: the radio waves are not radiated by the centre of the patch but by these two fringing edges.
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Then what is the patch width W for? The frequency is set by L, right?
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Right — L is the lead role for frequency, W is the supporting role. The width W mainly sets the radiation efficiency, bandwidth and input impedance. A wider patch raises radiation efficiency and slightly widens the bandwidth, but too wide and odd modes appear. The weak point of a patch antenna is narrow bandwidth — often just a few percent. To widen it, the standard move is "thicker substrate, lower permittivity". In the "patch dimensions vs ε_r" chart below you can see both W and L shrink as the permittivity rises. Want a small antenna? Use a high-permittivity substrate. Want bandwidth? Use a low-permittivity one — that is the trade-off.
Frequently Asked Questions
Balanis's transmission-line model is the standard. The patch width is W = (c/2f)·√(2/(ε_r+1)), chosen for good radiation efficiency. For the patch length, you first compute the effective permittivity ε_eff and then L = c/(2f·√ε_eff) − 2ΔL. ΔL is a length correction for the fringing fields (the electric field bulging out) at the two radiating edges. This tool follows these equations to compute W, L, ε_eff and ΔL, and checks the design with a back-calculated verification resonant frequency.
The electric field between the patch and the ground plane does not travel entirely inside the dielectric substrate — part of it bulges out into the air. So the permittivity the wave "feels" is a value between the substrate's ε_r and air's 1. This is the effective permittivity ε_eff, and it always lies in the range 1 < ε_eff < ε_r. The thinner the substrate, the more the field stays inside it and the closer ε_eff is to ε_r; the thicker it is, the closer ε_eff is to 1. Since the wavelength λ is set by ε_eff, the patch length is computed with ε_eff, not ε_r.
At the two radiating edges of the patch the electric field does not stop abruptly at the patch edge — it arcs outward beyond it. These are the fringing fields. As a result the antenna behaves electrically a little longer than its physical length L. This 'electrical extension' is expressed as ΔL at each edge, so the effective length is Leff = L + 2ΔL. In design you work the other way: subtract 2ΔL from the Leff that corresponds to the target frequency to get the physical length L. Ignoring ΔL makes the finished patch resonate a few percent higher than the design value.
The patch length L sets the resonant frequency. The patch resonates at about a half-wavelength in the dielectric, so a shorter L raises the frequency and a longer L lowers it. The patch width W mainly affects the radiation efficiency, bandwidth and input impedance. A wider patch improves radiation efficiency and slightly widens the bandwidth, but if it is too wide higher-order modes are easily excited. In practice W is chosen a little less than a half-wavelength, and L is used to tune the frequency precisely. To widen the bandwidth, choose a thicker, lower-permittivity substrate.
Real-World Applications
Smartphones and wireless modules: WiFi (2.4 / 5 GHz), Bluetooth, GPS (1.575 GHz), cellular (Sub-6 5G) — most antennas in modern communications gear are patch antennas or variants of them. Flat, thin and printable directly onto a PCB, they fit into the tiny space inside a housing. To cover several bands, designers cut slots into a single patch or stack multiple patches.
Satellite communication and GPS receivers: For the GPS antennas in car navigation and drones, and for satellite-broadcast and satellite-internet flat terminals, circularly polarised patch antennas are the standard choice. Truncating corners or using two feed points produces right-hand or left-hand circular polarisation. A phased array of many patches on a flat face pointing skyward can steer its beam electronically without moving mechanically.
Radar and automotive sensors: The 77 GHz millimetre-wave radar that watches the road ahead of a car is an array of many tiny patches arranged in a grid. By controlling the feed phase to each patch the beam is scanned to measure the distance and relative speed of the vehicle ahead. The choice of substrate thickness and permittivity strongly affects radiation efficiency, bandwidth and manufacturing precision.
Pre-study for electromagnetic CAE analysis: Before a detailed 3-D field solver such as HFSS, CST or OpenEMS, the initial dimensions are set with a transmission-line estimate like this tool. Starting from good initial values greatly shortens the optimisation loop in the 3-D analysis. Conversely, if the 3-D resonant frequency differs greatly from this estimate, it is a sanity check pointing to a mistake in the feed structure or substrate parameters.
Common Misconceptions and Pitfalls
The biggest pitfall is designing the patch with L = exactly half a wavelength, ignoring the fringing. Because the field bulges out past the radiating edges, the antenna behaves electrically longer than its physical size. Build it without subtracting ΔL and the finished patch resonates a few percent above the design value. Aiming for 2.4 GHz and ending up resonating near 2.5 GHz is the classic symptom of this mistake. The ΔL this tool computes (about 0.74 mm in the default case, just under 1.5 mm for both edges) is by no means negligible — always subtract it from L.
Next, treating the dielectric constant ε_r as a single datasheet number. FR-4 is often quoted as "about 4.4", but the real value scatters roughly between 4.1 and 4.7 depending on the manufacturer, glass-to-resin ratio, frequency and temperature. Moreover, substrates with a high loss tangent tanδ (around 0.02 for FR-4) reduce radiation efficiency and limit the gain you can achieve. With a narrow-band patch antenna, an ε_r shift of a few percent can push the resonant frequency outside the band. In production, allow for substrate lot variation and leave tuning margin in the feed-point position and patch dimensions.
Finally, giving up with "a patch antenna is bound to be narrow-band". It is true that a simple patch on a thin, high-permittivity substrate has only a few percent of bandwidth. But this can be greatly improved by the choice of substrate and the antenna structure. A thicker substrate with lower permittivity widens the bandwidth, and techniques such as a stacked patch (two patches stacked vertically), E-shaped or U-shaped slots, and parasitic elements can reach more than 10% bandwidth. If you feel "the bandwidth is not enough", the first step is to review the substrate thickness and permittivity. Use this tool to vary h and ε_r and grasp how the dimensions and ε_eff change before moving on to structural tricks.
How to Use
Enter operating frequency (2–6 GHz typical for Wi-Fi, cellular, or satellite bands) in the freqNum field.
Input substrate thickness hNum in millimeters (common values: 0.8 mm, 1.6 mm, 3.2 mm for PCB).
Click simulate to compute patch dimensions W and L, effective permittivity ε_eff, fringing-field correction ΔL, and resonance verification.
Worked Example
Design a patch antenna for 2.4 GHz Wi-Fi on FR-4 substrate: freqNum = 2.4 GHz, epsNum = 4.7, hNum = 1.6 mm. Simulator outputs W ≈ 38.2 mm, L ≈ 29.8 mm, ε_eff ≈ 3.91, ΔL ≈ 0.62 mm (accounting for fringing capacitance), verification frequency = 2.395 GHz. Physical patch area = 38.2 × 29.8 = 1139 mm². Actual PCB layout includes 50 Ω microstrip feed line and ground plane.