How to Calculate Impedance for PCB Trace: Simple Guide

To calculate the impedance of a PCB trace, use the formula that considers the trace width, thickness, height above the reference plane, and the dielectric constant of the PCB material. The most common formula for microstrip impedance is Z0 = (87 / sqrt(Er + 1.41)) * ln(5.98 * H / (0.8 * W + T)), where Z0 is impedance, Er is dielectric constant, H is height, W is trace width, and T is trace thickness.

Syntax

The basic formula to calculate the characteristic impedance Z0 of a microstrip PCB trace is:

Z0 = (87 / sqrt(Er + 1.41)) * ln(5.98 * H / (0.8 * W + T))

• Z0: Characteristic impedance in ohms (Ω)
• Er: Relative dielectric constant of the PCB material (e.g., FR4 ~4.5)
• H: Height of the trace above the reference plane (in mils or mm)
• W: Width of the PCB trace (in same units as H)
• T: Thickness of the PCB trace (in same units as H)

This formula assumes a microstrip configuration where the trace is on the top layer above a ground plane.

plaintext

Z0 = (87 / sqrt(Er + 1.41)) * ln(5.98 * H / (0.8 * W + T))

Example

This example calculates the impedance of a PCB trace with the following parameters:

• Dielectric constant Er = 4.5 (typical FR4)
• Height H = 1.6 mm
• Trace width W = 0.3 mm
• Trace thickness T = 0.035 mm (typical 1 oz copper)

The calculation uses the formula to find the impedance Z0.

python

import math

Er = 4.5
H = 1.6
W = 0.3
T = 0.035

Z0 = (87 / math.sqrt(Er + 1.41)) * math.log(5.98 * H / (0.8 * W + T))
print(f"Calculated impedance Z0 = {Z0:.2f} ohms")

Output

Calculated impedance Z0 = 50.35 ohms

Common Pitfalls

Common mistakes when calculating PCB trace impedance include:

• Using inconsistent units for H, W, and T. Always use the same unit (mm or mils) for all.
• Ignoring the dielectric constant Er of the PCB material, which greatly affects impedance.
• Not accounting for the trace thickness T, which can change impedance especially for thin traces.
• Applying the microstrip formula to other trace types like stripline without adjustment.

Wrong example (mixing units):

H = 1.6  # mm
W = 12   # mils (wrong unit)
T = 0.035  # mm
# This will give incorrect impedance

Right example (consistent units):

H = 1.6  # mm
W = 0.3  # mm
T = 0.035  # mm
# Correct impedance calculation

Quick Reference

Parameter	Description	Typical Value / Notes
Er	Dielectric constant of PCB material	4.5 for FR4
H	Height of trace above ground plane	1.6 mm typical
W	Width of PCB trace	Varies, e.g., 0.3 mm
T	Thickness of PCB trace	0.035 mm (1 oz copper)
Z0	Characteristic impedance	Usually 50 Ω for signal integrity

Key Takeaways

Use the microstrip impedance formula with consistent units for accurate results.

Dielectric constant and trace dimensions strongly affect PCB trace impedance.

Always include trace thickness in calculations for precision.

Avoid mixing units like mm and mils in the same formula.

Use this calculation to design PCB traces with proper signal integrity.