Controlled Impedance Tolerance
ΔZ/Z = √((Δh/h)² + (Δw/w)² + (Δεr/εr)²)
Quick answer
This calculator solves ΔZ/Z = √((Δh/h)² + (Δw/w)² + (Δεr/εr)²) for ΔZ/Z. With Δh/h (dielectric thickness) 50 %, Δw/w (trace width) 1.1, Δεr/εr (dielectric const.) 2.35, the result is 2.642.
Calculator
Formula
Description
The impedance of a controlled-impedance trace depends on the dielectric thickness (h), trace width (w), and dielectric constant (εr). Manufacturing variations in each parameter contribute to the total impedance tolerance. Assuming the errors are independent and normally distributed, the RSS (root sum of squares) combination gives the expected total impedance variation. Typical PCB fabrication tolerances: dielectric thickness ±10%, trace width ±10-20% (depending on process), εr ±5%. The resulting impedance tolerance is typically ±10% for standard processes and ±5% for controlled-impedance specified boards.
Variables
- Δh/h — Relative tolerance of dielectric thickness (ratio)
- Δw/w — Relative tolerance of trace width (ratio)
- Δεr/εr — Relative tolerance of dielectric constant (ratio)
Practical Notes
The result is the relative impedance tolerance (ratio). Multiply by 100 for percentage. For a 50 Ω trace with Δh/h = 0.10, Δw/w = 0.15, Δεr/εr = 0.05: ΔZ/Z = √(0.01 + 0.0225 + 0.0025) ≈ 0.187 = 18.7%. This means the impedance could range from about 40.7 to 59.3 Ω. Impedance coupons (test structures) on the panel edge allow direct measurement and verification of the achieved impedance.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| dh_h | Δh/h (dielectric thickness) | — | —, % |
| dw_w | Δw/w (trace width) | — | —, % |
| der_er | Δεr/εr (dielectric const.) | — | —, % |
Step by step
- 1. What you know: Δh/h (dielectric thickness) 50 %, Δw/w (trace width) 1.1, Δεr/εr (dielectric const.) 2.35
- 2. The relation: ΔZ/Z = √((Δh/h)² + (Δw/w)² + (Δεr/εr)²)
- 3. Substitute: dh_h = 50 %, dw_w = 1.1, der_er = 2.35
- 4. Result: ΔZ/Z = 2.642
Worked examples
Minimum range
Given: Δh/h (dielectric thickness) 2.5 %, Δw/w (trace width) 5.5 %, Δεr/εr (dielectric const.) 11.8 %
Result: ΔZ/Z = 0.1326
Low range
Given: Δh/h (dielectric thickness) 25 %, Δw/w (trace width) 0.55, Δεr/εr (dielectric const.) 1.18
Result: ΔZ/Z = 1.326
Typical
Given: Δh/h (dielectric thickness) 50 %, Δw/w (trace width) 1.1, Δεr/εr (dielectric const.) 2.35
Result: ΔZ/Z = 2.642
High range
Given: Δh/h (dielectric thickness) 0.8, Δw/w (trace width) 1.76, Δεr/εr (dielectric const.) 3.76
Result: ΔZ/Z = 4.228
Maximum range
Given: Δh/h (dielectric thickness) 8, Δw/w (trace width) 17.6, Δεr/εr (dielectric const.) 37.6
Result: ΔZ/Z = 42.28
How ΔZ/Z changes with Δh/h (dielectric thickness)
| Δh/h (dielectric thickness) (input) | ΔZ/Z (result) |
|---|---|
| 5 % | 2.595 |
| 12.5 % | 2.598 |
| 25 % | 2.607 |
| 37.5 % | 2.622 |
| 50 % | 2.642 |
| 0.75 | 2.701 |
| 1 | 2.781 |
| 2 | 3.276 |
| 3.5 | 4.357 |
| 5 | 5.633 |
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<p><a href="https://vbatpower.com/formulas/controlled-impedance-tol/">Controlled Impedance Tolerance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Controlled Impedance Tolerance?
Use ΔZ/Z = √((Δh/h)² + (Δw/w)² + (Δεr/εr)²). With Δh/h (dielectric thickness) 50 %, Δw/w (trace width) 1.1, Δεr/εr (dielectric const.) 2.35, ΔZ/Z works out to 2.642.
What is the formula for Controlled Impedance Tolerance?
The formula is ΔZ/Z = √((Δh/h)² + (Δw/w)² + (Δεr/εr)²). The impedance of a controlled-impedance trace depends on the dielectric thickness (h), trace width (w), and dielectric constant (εr).
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