Microstrip Impedance

Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t))

Quick answer

This calculator solves Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) for Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)). With Dielectric Constant εr 0.5, Dielectric Height (mm) 10 mm, Trace Width (mm) 22 mm, Copper Thickness (mm) 47 mm, the result is -4.86.

Calculator

Result
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Formula

Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t))

Description

A microstrip is a transmission line formed by a trace on the top or bottom layer of a PCB with a ground plane beneath it, separated by the dielectric substrate. The characteristic impedance depends on the trace geometry and the substrate's dielectric constant. This empirical approximation works well for w/h ratios between 0.1 and 2.0 and is accurate to within 2% for typical PCB geometries. Controlled impedance traces are essential for high-speed digital signals (USB, PCIe, DDR, Ethernet) and RF circuits to prevent signal reflections.

Variables

  • Z₀ — Characteristic impedance (Ω)
  • εr — Relative dielectric constant of substrate (FR-4 ≈ 4.2-4.8)
  • h — Height of dielectric between trace and ground plane (mm)
  • w — Trace width (mm)
  • t — Copper thickness (mm)

Practical Notes

Common impedance targets: USB 90Ω differential, PCIe 85Ω differential, DDR4 40Ω single-ended, 100BASE-TX 100Ω differential, RF 50Ω single-ended. PCB fabricators can hold impedance tolerances of ±10% for standard stackups. Always use the fab house's stackup data for accurate calculations, as εr varies with frequency and manufacturing process.

Symbols and units

Symbol Meaning Default unit Accepted units
er Dielectric Constant εr — —
h Dielectric Height (mm) mm mm
w Trace Width (mm) mm mm
t Copper Thickness (mm) mm mm

Step by step

  1. 1. What you know: Dielectric Constant εr 0.5, Dielectric Height (mm) 10 mm, Trace Width (mm) 22 mm, Copper Thickness (mm) 47 mm
  2. 2. The relation: Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t))
  3. 3. Substitute: er = 0.5, h = 10 mm, w = 22 mm, t = 47 mm
  4. 4. Result: Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) = -4.86

Worked examples

Minimum range

Given: Dielectric Constant εr 0.025, Dielectric Height (mm) 0.1 mm, Trace Width (mm) 0.22 mm, Copper Thickness (mm) 0.47 mm

Result: Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) = -5.607

Low range

Given: Dielectric Constant εr 0.25, Dielectric Height (mm) 1 mm, Trace Width (mm) 2.2 mm, Copper Thickness (mm) 4.7 mm

Result: Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) = -5.214

Typical

Given: Dielectric Constant εr 0.5, Dielectric Height (mm) 10 mm, Trace Width (mm) 22 mm, Copper Thickness (mm) 47 mm

Result: Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) = -4.86

High range

Given: Dielectric Constant εr 0.8, Dielectric Height (mm) 100 mm, Trace Width (mm) 220 mm, Copper Thickness (mm) 470 mm

Result: Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) = -4.518

Maximum range

Given: Dielectric Constant εr 8, Dielectric Height (mm) 1000 mm, Trace Width (mm) 2200 mm, Copper Thickness (mm) 4700 mm

Result: Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) = -2.19

How Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) changes with Dielectric Constant εr

Dielectric Constant εr (input) Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) (result)
0.05 -5.559
0.125 -5.422
0.25 -5.214
0.375 -5.028
0.5 -4.86
0.75 -4.57
1 -4.327
2 -3.638
3.5 -3.031
5 -2.653

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Frequently asked questions

How do you calculate Microstrip Impedance?

Use Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)). With Dielectric Constant εr 0.5, Dielectric Height (mm) 10 mm, Trace Width (mm) 22 mm, Copper Thickness (mm) 47 mm, Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) works out to -4.86.

What is the formula for Microstrip Impedance?

The formula is Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)). A microstrip is a transmission line formed by a trace on the top or bottom layer of a PCB with a ground plane beneath it, separated by the dielectric substrate.

Related Concepts

All PCB & Traces formulas →
Trace Current Capacity (IPC-2221) Trace Resistance Trace Voltage Drop Via Current Capacity (IPC-2221) Microstrip Impedance Stripline Impedance Differential Pair Impedance Near-End Crosstalk

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