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Microstrip Impedance From Zo Calculator

This calculator determines the required microstrip trace width or substrate height based on a desired characteristic impedance (Zo), dielectric constant, and board thickness. It’s essential for impedance-controlled PCB layout in RF and high-speed digital design.

Microstrip Geometry Estimator from Target Zo

Input Fields
Z_0
Ω
Target characteristic impedance
εr
Relative permittivity of the substrate
h
mm
Height of the substrate (dielectric layer)
If enabled, the result will update automatically when you change any value.

Microstrip Width from Zo Formula

Formula
$$\text{If } Z_0 \leq \frac{44 – \varepsilon_r}{\varepsilon_r + 1}: \\ \frac{w}{h} = \frac{8 \cdot e^{A}}{e^{2A} – 2} \\[1em] \text{where } A = \frac{Z_0 \cdot \sqrt{\varepsilon_r + 1.41}}{87} \\[1em] \text{If } Z_0 > \frac{44 – \varepsilon_r}{\varepsilon_r + 1}: \\[1em] \frac{w}{h} = \frac{2}{\pi} \cdot \left( B – 1 – \ln(2B – 1) + \frac{\varepsilon_r – 1}{2\varepsilon_r} \cdot \left( \ln(B – 1) + 0.39 – \frac{0.61}{\varepsilon_r} \right) \right) \\ \text{where } B = \frac{377\pi}{2Z_0\sqrt{\varepsilon_r}}$$

Where:

  • $$Z_0$$ = characteristic impedance (Ω)
  • $$w$$ = trace width (mm)
  • $$h$$ = dielectric height (mm)
  • $$varepsilon_r$$ = dielectric constant (unitless)

These inverse formulas are derived from microstrip impedance equations to back-calculate the geometry required for a specific impedance.


Microstrip Impedance From Zo – Calculation Example

Given:

  • $$Z_0$$ = 50 Ω
  • $$h$$ = 0.8 mm
  • $$\varepsilon_r$$ = 4.4

Calculation:

  1. $$A = \frac{50 \cdot \sqrt{4.4 + 1.41}}{87} = \frac{50 \cdot \sqrt{5.81}}{87} ≈ \frac{50 \cdot 2.41}{87} ≈ 1.384$$
  2. $$\frac{w}{h} = \frac{8 \cdot e^{1.384}}{e^{2.768} – 2} ≈ \frac{8 \cdot 3.99}{15.91 – 2} = \frac{31.92}{13.91} ≈ 2.29$$
  3. $$w = 2.29 \cdot 0.8 = 1.83~\text{mm}$$


This tool is essential for PCB designers working with impedance-controlled signals. Instead of calculating the impedance from geometry, it solves the inverse problem—finding the correct geometry (trace width or height) for a given target Zo. This is critical when working with differential pairs, RF filters, and high-speed buses like HDMI, USB, or DDR memory layouts.

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