Microstrip Line Calculator Back
RF / Microwave

Microstrip Transmission Line Calculator

Compute Z0, effective permittivity, guided wavelength, and conductor / dielectric loss in real time. Switch between analysis (W → Z0) and synthesis (Z0 → W) modes.

Design parameters

Strip width W (mm)
mm
Substrate height H (mm)
mm
Conductor thickness t (μm)
μm
Relative permittivity εr
Loss tangent tan δ (×10⁻³)
×10⁻³
Frequency f (GHz)
GHz
εeff
Phase velocity vp/c
Wavelength λg (mm)
αc (dB/m)
αd (dB/m)
Results
Characteristic impedance Z0 (Ω)
Cross section
Z0 vs W/H
Loss vs frequency
Theory & Key Formulas

$$Z_0 = \frac{87}{\sqrt{\varepsilon_r + 1.41}}\ln\left(\frac{5.98h}{0.8w + t}\right)$$

Schneider approximation for the microstrip characteristic impedance: \(h\) substrate height, \(w\) trace width, \(t\) copper thickness [mm], \(\varepsilon_r\) relative permittivity.

$$\varepsilon_{eff} = \frac{\varepsilon_r+1}{2} + \frac{\varepsilon_r-1}{2}\left(1+\frac{12h}{w}\right)^{-1/2}$$

Effective permittivity. Phase velocity \(v_p = c/\sqrt{\varepsilon_{eff}}\).

What is a microstrip line?

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A microstrip line is just a copper trace on top of a board with a ground plane underneath, right? Why is it special at high frequencies?
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Right — it is a controlled "highway" for fast signals. The geometry sets the characteristic impedance Z0, which is the only impedance the wave sees. When source, line, and load all share the same Z0 there are no reflections. Move the strip-width slider on the left and watch Z0 change in real time.
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So the substrate matters too? What does the εr slider really do?
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A higher εr stores more energy in the capacitance to the ground plane, so the same trace looks "fatter" electrically and Z0 drops. FR-4 has εr ≈ 4.3, while RF laminates such as Rogers RO4350B sit near 3.48. Bump εr up and εeff and λg both shift — that is why high-εr substrates make antennas physically smaller.
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When would I use synthesis mode instead of analysis mode?
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In design you usually start from a target Z0 (often 50 Ω). Synthesis mode does the inverse: pick the impedance, the tool tells you the trace width. Analysis mode is for verifying a board you already have, or when you sweep W to study sensitivity.

Physical model & key equations

The Hammerstad-Jensen approximation splits the line into wide (W/h ≥ 1) and narrow (W/h ≤ 1) regions, each with its own closed-form expression.

$$Z_0 = \begin{cases}\frac{60}{\sqrt{\varepsilon_{eff}}}\ln\!\left(\frac{8h}{W} + \frac{W}{4h}\right) & W/h \leq 1\\ \frac{120\pi}{\sqrt{\varepsilon_{eff}}\left[W/h + 1.393 + 0.667\ln(W/h+1.444)\right]} & W/h \geq 1\end{cases}$$

Z0: characteristic impedance [Ω]
εeff: effective permittivity (mix of substrate and air)
W, h: trace width and substrate height [m]

Effective permittivity captures the fact that the field propagates partly in air and partly in the substrate.

$$\varepsilon_{eff} \approx \frac{\varepsilon_r + 1}{2} + \frac{\varepsilon_r - 1}{2}\frac{1}{\sqrt{1 + 12h/W}}$$

The phase constant is \(\beta = (2\pi f/c)\sqrt{\varepsilon_{eff}}\), and the guided wavelength is \(\lambda_g = c/(f\sqrt{\varepsilon_{eff}})\).

Frequently asked questions

Analysis mode computes Z0 from the geometry (W, h, εr). Synthesis mode does the reverse: from a target Z0 and the substrate (h, εr) it gives the required trace width W. Use synthesis when you are picking a width to hit 50 Ω, and analysis when you need to verify an existing layout.
Microstrip fields straddle the substrate and the air above it. The effective permittivity εeff is a weighted blend of εr and 1 that reproduces the same phase velocity, so it is the value to use when computing wavelength or transformer length.
The tool models conductor loss (skin-effect surface resistance of the copper) and dielectric loss (proportional to tan δ). Both grow with frequency. Radiation loss is omitted; it becomes important only on thick or wide lines well above 10 GHz.
Z0 only depends on the W/h ratio so any consistent unit (mm, mil, inch) gives the same impedance. Loss and wavelength do depend on absolute size, so use millimetres for those.

Real-world applications

Wireless equipment. Smartphones, Wi-Fi routers and Bluetooth modules use microstrip everywhere — between the RF SoC and the antenna, between filters, and inside power amplifier matching networks. High-εr ceramics shrink the lines.

Radar and satcom. Microwave / mm-wave links use low-loss laminates such as Rogers RO4003. The "loss vs frequency" tab shows how the conductor and dielectric losses grow with frequency in a chosen substrate.

High-speed digital. PCIe, DDR, and SerDes lanes are routed as 50 Ω single-ended or 100 Ω differential pairs. Impedance control on each layer prevents reflections and inter-symbol interference.

Automotive sensors. Car cameras and radars share signals over LVDS / FAKRA on PCBs. Thin substrates need very narrow traces, which the synthesis mode helps size against the manufacturing minimum.

Common misconceptions

"Use the εr from the datasheet directly." The catalog εr (e.g. FR-4 ≈ 4.3) is a centre value; real lots vary roughly 4.0–4.7, and above 10 GHz the resin/glass mix matters too. For tight matching, lock εr from a measured TDR coupon.

"You can pick any Z0 by changing W." Substrate height h is usually fixed by the stack-up. On a 0.4 mm core, 50 Ω needs W ≈ 0.75 mm; if your fab limit is 0.1 mm you are fine, but on tighter stacks the chosen Z0 may be unmanufacturable.

"The closed-form Z0 is exact." The Hammerstad / Schneider formulas are quasi-static — accurate at a few GHz on a 1.6 mm board, less so when the substrate is more than λ/10 thick. Always cross-check with a 2D solver above 20 GHz.

How to Use

  1. Enter substrate height (H) in millimeters—typical FR-4 values range 0.5–1.6 mm
  2. Input trace width (W) and copper thickness (t) in mm to define geometry
  3. Set target impedance Z0 in ohms (50 Ω standard for most RF systems, 75 Ω for video)
  4. Click Calculate to solve for actual characteristic impedance, effective dielectric constant, and wavelength at your design frequency
  5. Adjust W or H iteratively until Z0 matches target within ±2 % tolerance

Worked Example

Design a 50 Ω microstrip line on FR-4 (εr ≈ 4.3). Given H = 1.0 mm, t = 0.035 mm (1 oz copper), calculator yields W ≈ 2.87 mm and effective εr ≈ 3.54. At 2.4 GHz, wavelength = 49.2 mm; at 28 GHz mmWave band, wavelength reduces to 3.9 mm, requiring trace width precision ±0.1 mm to maintain impedance control and minimize radiation losses.

Practical Notes

  1. Dielectric loss increases sharply above 10 GHz in standard FR-4; consider PTFE-glass (εr 3.0–3.2) for 5+ GHz designs
  2. Copper roughness and frequency-dependent loss tangent shift Z0 by 2–5 % in production; simulate worst-case ±σ stackup tolerances
  3. Via stitching every 0.3λ prevents common-mode radiation from microstrip fields; critical near 1–6 GHz where wavelengths span 50–150 mm