Differential Pair Impedance

Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h))

Quick answer

This calculator solves Zdiff ≈ 2 × Z0 × (1 − 0.48 × exp(−0.96 × s/h)) for Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)). With Single-Ended Z0 0.47 kΩ, Trace Spacing (mm) 10 mm, Dielectric Height (mm) 22 mm, the result is 648.4.

Calculator

Result
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Formula

Zdiff ≈ 2 × Z0 × (1 − 0.48 × exp(−0.96 × s/h))

Description

Differential impedance of a coupled pair is less than twice the single-ended impedance due to electromagnetic coupling between the traces. When the traces are far apart (s >> h), coupling is negligible and Zdiff approaches 2×Z0. As traces are brought closer, mutual capacitance and inductance increase, reducing Zdiff. Typical differential impedance targets are 90Ω (USB 2.0), 85Ω (PCIe), or 100Ω (USB 3.0, Ethernet). Maintaining consistent spacing throughout the route is essential for impedance control.

Variables

  • Zdiff — Differential impedance (Ω)
  • Z0 — Single-ended impedance of each trace (Ω)
  • s — Edge-to-edge spacing between traces (mm)
  • h — Height above ground plane (mm)

Practical Notes

This empirical formula is for microstrip differential pairs. Stripline differential pairs use a different coupling correction factor. Tight coupling (small s/h) improves common-mode noise rejection but makes Zdiff more sensitive to spacing variations. USB 2.0 requires 90Ω ±10%, USB 3.x requires 85Ω ±15%. Always length-match differential pairs to within the specified skew tolerance.

Symbols and units

Symbol Meaning Default unit Accepted units
Z0 Single-Ended Z0 Ω mΩ, Ω, kΩ, MΩ
s Trace Spacing (mm) mm mm
h Dielectric Height (mm) mm mm

Step by step

  1. 1. What you know: Single-Ended Z0 0.47 kΩ, Trace Spacing (mm) 10 mm, Dielectric Height (mm) 22 mm
  2. 2. The relation: Zdiff ≈ 2 × Z0 × (1 − 0.48 × exp(−0.96 × s/h))
  3. 3. Substitute: Z0 = 0.47 kΩ, s = 10 mm, h = 22 mm
  4. 4. Result: Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) = 648.4

Worked examples

Minimum range

Given: Single-Ended Z0 1 Ω, Trace Spacing (mm) 0.1 mm, Dielectric Height (mm) 0.22 mm

Result: Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) = 1.379

Low range

Given: Single-Ended Z0 10 Ω, Trace Spacing (mm) 1 mm, Dielectric Height (mm) 2.2 mm

Result: Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) = 13.79

Typical

Given: Single-Ended Z0 0.47 kΩ, Trace Spacing (mm) 10 mm, Dielectric Height (mm) 22 mm

Result: Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) = 648.4

High range

Given: Single-Ended Z0 4.7 kΩ, Trace Spacing (mm) 100 mm, Dielectric Height (mm) 220 mm

Result: Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) = 6484

Maximum range

Given: Single-Ended Z0 47 kΩ, Trace Spacing (mm) 1000 mm, Dielectric Height (mm) 2200 mm

Result: Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) = 64840

How Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) changes with Single-Ended Z0

Single-Ended Z0 (input) Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) (result)
47 Ω 64.84
117.5 Ω 162.1
0.235 kΩ 324.2
0.3525 kΩ 486.3
0.47 kΩ 648.4
0.705 kΩ 972.5
0.94 kΩ 1297
1.88 kΩ 2593
3.29 kΩ 4538
4.7 kΩ 6484

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Frequently asked questions

How do you calculate Differential Pair Impedance?

Use Zdiff ≈ 2 × Z0 × (1 − 0.48 × exp(−0.96 × s/h)). With Single-Ended Z0 0.47 kΩ, Trace Spacing (mm) 10 mm, Dielectric Height (mm) 22 mm, Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) works out to 648.4.

What is the formula for Differential Pair Impedance?

The formula is Zdiff ≈ 2 × Z0 × (1 − 0.48 × exp(−0.96 × s/h)). Differential impedance of a coupled pair is less than twice the single-ended impedance due to electromagnetic coupling between the traces.

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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