# Ohmforge Microstrip & Stripline Impedance Calculator

> PCB trace impedance Z0, εeff and delay (Hammerstad–Jensen, Wheeler), or the width for 50 Ω. Characteristic impedance of a PCB trace: surface microstrip with the Hammerstad–Jensen equations (thickness correction included) or a centred stripline with Wheeler's formula, plus effective permittivity, propagation delay and guided wavelength. Synthesis mode solves the trace width for a target impedance such as 50 Ω with Brent's root finder; every result is cross-checked against an independent formula and the IPC-2141 rule of thumb.

Part of usefulweb.app (https://usefulweb.app/). Part of [Ohmforge](https://ohmforge.usefulweb.app/) (ownerApp: ohmforge). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://ohmforgemicrostripimpedance.usefulweb.app/ (interactive tool at https://ohmforgemicrostripimpedance.usefulweb.app/tool)
- JSON API: POST https://ohmforgemicrostripimpedance.usefulweb.app/api/v1/calculate with a JSON object of inputs (schema: https://ohmforgemicrostripimpedance.usefulweb.app/api/v1/tool)
- OpenAPI: https://ohmforgemicrostripimpedance.usefulweb.app/openapi.json
- MCP (Streamable HTTP): https://ohmforgemicrostripimpedance.usefulweb.app/mcp - tool `ohmforge_microstrip_impedance`

## Inputs
- structure (select): Line
- task (select): Task
- widthMm (number): Trace width W - Analysis only.
- heightMm (number): Dielectric height h (microstrip) or plane spacing b (stripline) - Microstrip: from the trace to its reference plane. Stripline: total distance between the two planes.
- thicknessUm (number): Copper thickness t - 35 µm = 1 oz/ft², 18 µm = ½ oz; 0 = ideal thin strip.
- er (number): Relative permittivity εr - FR-4 about 4.2–4.6 (falls with frequency), Rogers RO4350B 3.66, PTFE 2.2. Use the laminate maker's value at your frequency.
- targetZ0 (number): Target impedance - Synthesis only.
- frequencyMHz (number): Frequency (optional) - For the guided wavelength; 0 = skip.

## Method
- Microstrip: Hammerstad–Jensen (1980) closed-form equations — Z0 of the air line Z01(u) with u = W/h, effective permittivity εe(u, εr) with their a(u) and b(εr) fits (accuracy better than 0.2 % for 0.01 ≤ u ≤ 100), and the strip-thickness correction Δu (Wheeler's) applied separately to the air line and the dielectric. Z0 = Z01(ur)/√εe(ur).
- Stripline (strip centred between two planes, spacing b): Wheeler's 1978 formula with the thickness correction (about 0.5 % accuracy for W/(b − t) < 10); for t = 0 it is compared with Cohn's exact conformal-mapping result η0/(4√εr)·K(k)/K(k′), k = sech(πW/2b), evaluated with the arithmetic–geometric mean.
- Synthesis solves Z0(W) = target with Brent's method (Proofline numerical engine) over W/h from 0.01 to 100 (stripline: up to 20) on a logarithmic width axis.
- Delay = √εeff / c, guided wavelength = c / (f·√εeff). The IPC-2141 rule-of-thumb formulas are shown for comparison only; they are less accurate, especially outside their range.

## Limits
- Quasi-static, lossless model: no dispersion (microstrip Z0 and εeff rise at high frequency), no solder mask, no roughness, no etch trapezoid and no nearby copper pour. Ask your PCB maker for their stack-up and impedance-controlled width; manufacturing tolerances are typically ±10 %.