Microstrip Wavelength Calculator converts a trace’s frequency, dielectric constant, width, and height into its guided wavelength, effective dielectric constant, and propagation delay.
Find the Guided Wavelength of a Microstrip Trace for RF PCB Design
This calculator converts a microstrip trace’s frequency, substrate dielectric constant, width, and height into its guided wavelength, effective dielectric constant, and related RF quantities like phase velocity and propagation delay. RF and PCB design engineers use it to size microstrip patch antennas, matching stubs, and filter elements, where trace lengths are specified as fractions of a wavelength rather than fixed dimensions.
Entering Frequency, Dielectric Constant, Trace Width, and Substrate Height
Enter the operating frequency in GHz, the substrate’s relative dielectric constant (εR), the trace width (W) in mm, and the substrate height (H) in mm. The calculator returns the guided wavelength (λg) in mm, plus the effective dielectric constant, quarter- and half-wave lengths, phase velocity, and propagation delay.
How Guided Wavelength Is Calculated
The calculation first finds the width-to-height ratio, W/H, then applies one of two closed-form equations for the effective dielectric constant, depending on whether W/H is above or below 1. These are Hammerstad’s microstrip equations, as reproduced in Pozar’s Microwave Engineering, the standard textbook reference for planar transmission lines.
For $W/H \geq 1$:
$$\varepsilon_{eff} = \frac{\varepsilon_R+1}{2} + \frac{\varepsilon_R-1}{2}\left(1+12\frac{H}{W}\right)^{-1/2}$$
For $W/H < 1$:
$$\varepsilon_{eff} = \frac{\varepsilon_R+1}{2} + \frac{\varepsilon_R-1}{2}\left[\left(1+12\frac{H}{W}\right)^{-1/2}+0.04\left(1-\frac{W}{H}\right)^2\right]$$
The free-space wavelength is $\lambda_0 = c/f$, and the guided wavelength inside the microstrip is:
$$\lambda_g = \frac{\lambda_0}{\sqrt{\varepsilon_{eff}}}$$
Quarter-wave ($\lambda_g/4$) and half-wave ($\lambda_g/2$) lengths, phase velocity ($v_p = c/\sqrt{\varepsilon_{eff}}$), and propagation delay ($1/v_p$) all follow directly from εeff. A common input mistake is plugging the substrate’s bulk εR straight into the λg formula instead of computing εeff first — since part of the trace’s field travels through air above the substrate, εeff is always lower than εR, and skipping that step returns a guided wavelength that’s too short.
Microstrip Cross-Section
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Where the Static Formula Breaks Down
Hammerstad’s equations are quasi-static — they assume the field pattern doesn’t change shape with frequency. In reality, εeff rises with frequency (dispersion), most noticeably on thick, high-εR substrates above a few GHz.
A calculator using only the static formula will slightly overstate λg at higher frequencies; the error is typically under 2–3% below about 5 GHz on thin substrates but grows on thicker boards, which is why patch antenna dimensions from a static calculator are usually cross-checked against a field solver before fabrication.
Common Mistakes When Calculating Microstrip Wavelength
- Using εR instead of εeff when computing λg, which understates the guided wavelength since εeff always sits between 1 and εR.
- Mixing units for W and H — for example, entering trace width in mils and substrate height in mm — which throws off the W/H ratio and every downstream result.
- Applying the wrong εeff branch equation when W/H is close to 1, or dropping the extra $0.04(1-W/H)^2$ correction term that only applies when W/H < 1.
Typical Substrate Dielectric Constants
Manufacturer datasheets usually list both a process (manufacturing-tolerance) Dk and a design Dk; use the design value for wavelength and impedance calculations.
| Substrate | εR (Design Value) | Source |
|---|---|---|
| FR-4 (general purpose) | 4.3–4.4 typical design value | Common manufacturer datasheets (~4.2–4.6 at 1 MHz) |
| Rogers RO4003C | 3.55 design (3.38 ± 0.05 process) | Rogers Corporation datasheet |
| Rogers RO4350B | 3.66 design (3.48 ± 0.05 process) | Rogers Corporation datasheet |
Common Questions About Microstrip Guided Wavelength
What’s the difference between εR and the effective dielectric constant?
εR is a fixed property of the substrate material. εeff is what the guided wave actually experiences, since part of its field exists in air above the trace — it always falls between 1 and εR.
What happens to guided wavelength if I increase substrate height?
Raising H at a fixed W lowers the W/H ratio, which reduces εeff and increases λg — the wave is guided less by the dielectric and slowed down less.
Why does W/H determine which formula to use?
Narrow traces (W/H < 1) have proportionally more field in air, so Hammerstad’s equations add a correction term to account for that extra fringing at the edges.
Does this formula work at any frequency?
It’s quasi-static and most accurate at low-to-moderate GHz frequencies. On thick or high-εR substrates at higher frequencies, dispersion raises εeff beyond what the static formula predicts.
Why use guided wavelength instead of free-space wavelength to size a patch antenna?
A patch antenna’s physical length must match how the wave actually propagates in the dielectric-loaded trace, which is shorter than the free-space wavelength by a factor of √εeff.