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Edge-coupled microstrip

PCB Differential Impedance Calculator

Estimate edge-coupled microstrip differential impedance Zdiff from W, H, S, and εr. Hammerstad/Wadell Z0 plus IPC-2141A-style coupling. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (zdiff-wide, zdiff-wh-eq-1, zdiff-narrow, invalid-domain, metamorphic) · Matrix
Known limitations
  • Edge-coupled microstrip; S is edge-to-edge gap; H is dielectric height from trace to reference plane; zero copper thickness; homogeneous dielectric; no soldermask; no dispersion/roughness/weave.
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Edge-coupled microstrip Zdiff (and single-ended Z0 / εeff).
Scope
Zero copper thickness (T=0)
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-13.cvp-self-consistency
Verification revision
2026-09-13.cvp-self-consistency · 4/4 property · digest 182774947424
Legacy regression
12/12 tests · Production surface contract 4/4
Trust layers
Verification VERIFIED · Production CURRENT · overall VERIFIED
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Internal · Pass · electrical-engineer
Named expert review
Not performed
CVP suite
4/4 golden · 5/5 CVP boundary · 9/9 invalid · 4/4 property · 2/2 metamorphic · 2/2 cross-interface · 2/2 cross-calculator · 4/4 CVP contract · Manifest
Sources
  • IPC-2141A / Wadell — Coupled microstrip approximations
  • Pozar Microwave Engineering — Microstrip / coupled lines
Sources
Evidence
4 legacy golden · 4 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 9/9 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Effective permittivityεeff = (εr+1)/2 + ((εr−1)/2)·(1/√(1+12/(W/H)))Domain: zero-thickness microstrip; same wide-branch εeff as the Microstrip calculator
Single-ended Z0W/H ≥ 1: Z0 = η0 / (√εeff · (u + 1.393 + 0.667·ln(u+1.444))); W/H < 1: Z0 = (60/√εeff)·ln(8/u + u/4)Domain: u = W/H; η0 = 120π Ω
DifferentialZdiff ≈ 2·Z0·(1 − 0.48·e^(−0.96·S/H))Domain: edge-coupled; S = edge-to-edge gap
iModel = Hammerstad/Wadell zero-thickness microstrip Z0 + IPC-2141A-style edge-coupling correction. Hybrid closed form — not a 2D field solver. IPC-2141 single-ended approximations with T=0 can differ by ~3% on Z0. Copper thickness T=0; homogeneous dielectric; no soldermask, dispersion, copper roughness, or weave. Extends the Microstrip Impedance calculator (Z0/εeff parity for W/H ≥ 1).

How to use

1

Enter trace width W and dielectric height H

W is trace width. H is dielectric height from the trace to the reference plane. Both must be > 0. UI accepts mm or mil; the API uses metres.

2

Enter pair spacing S and εr

S is the edge-to-edge gap between the two traces (not center-to-center). S > 0 and εr ≥ 1.

3

Read Z0, εeff, and Zdiff

Z0 and εeff come from the zero-thickness microstrip model; Zdiff applies the coupling correction. Verify critical links in a field solver.

Example calculations

Common configurations with formula and result.

ϟ

FR4 example

W=0.2 mm · H=0.1 mm · S=0.2 mm · εr=4.2

εeff → Z0 → Zdiff
Z0 ≈ 49.93 Ω → Zdiff ≈ 92.83 Ω

PCB Differential Impedance calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-09-13

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
Differential pairs (USB, HDMI, Ethernet) target a differential impedance Zdiff. This tool uses Hammerstad/Wadell zero-thickness microstrip Z0, then an IPC-2141A-style edge-coupling correction Zdiff ≈ 2·Z0·(1 − 0.48·e^(−0.96·S/H)). S is the edge-to-edge gap.
What it calculates
Edge-coupled microstrip Zdiff (and single-ended Z0 / εeff).
Inputs
  • W_m>0 (trace width)
  • H_m>0 (dielectric height to reference plane)
  • S_m>0 (edge-to-edge gap)
  • er≥1
Outputs
  • Zdiff_ohm
  • Z0_ohm
  • er_eff
Formula
εeff(W/H,εr); Z0(u,εeff); Zdiff≈2·Z0·(1−0.48·e^(−0.96·S/H))
Assumptions
  • Zero copper thickness (T=0)
  • Homogeneous dielectric; no soldermask
  • Edge-coupled pair; S is edge-to-edge gap
  • H is dielectric height from trace to reference plane
  • No dielectric dispersion, copper roughness, or weave
Units
  • m, — → Ω
Boundary conditions
  • W,H,S≤0 → VALUE_MUST_BE_POSITIVE
  • er<1 → VALUE_MUST_BE_POSITIVE
Example
W=0.2 mm, H=0.1 mm, S=0.2 mm, er=4.2 → Z0≈49.93 Ω, Zdiff≈92.83 Ω
Validation cases

1 published on this page · 12/12 tests · Production surface contract 4/4 · View evidence

  • W=2e-4 H=1e-4 S=2e-4 er=4.2 → Z0≈49.928 Ω, Zdiff≈92.829 Ω
Sources
  • IPC-2141A / Wadell — Coupled microstrip approximations
    Supports: Zdiff from Z0 and S/H coupling
  • Pozar Microwave Engineering — Microstrip / coupled lines
    Supports: Effective εr and Z0 approximations
Last reviewed
2026-09-13
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Estimate edge-coupled microstrip differential impedance.

Default: W=0.2 mm · H=0.1 mm · S=0.2 mm · εr=4.2 → Z0 ≈ 49.93 Ω → Zdiff ≈ 92.83 Ω.

Supported and not supported

Supported — Edge-coupled microstrip Zdiff · shared Z0/εeff with the Microstrip calculator when W/H ≥ 1 · API electrical.pcb.diff_impedance

Not supported — Stripline · broadside coupled · soldermask correction · copper thickness · dielectric dispersion / roughness / weave

Agent / API notes

Capability id: electrical.pcb.diff_impedance · tool id: pcb-diff-impedance · pin 1.0.0.

W_m, H_m, S_m are metres. S_m is the edge-to-edge gap, not center-to-center.

Other calculators in this family: Microstrip Impedance Calculator, PCB Trace Thermal Calculator, PCB Trace Width Calculator (IPC-2221), Stripline Impedance Calculator, Via Current Capacity Calculator . Explore all PCB & Signal Integrity.

→ Microstrip Impedance Calculator Compute microstrip characteristic impedance Z0 from W/H/εr, or synthesize width for a target Z0 (zero-thickness IPC-2141 / Wadell–Hammerstad). Runs locally in your browser. › → PCB Trace Thermal Calculator Estimate copper trace I²R power and temperature rise with a board thermal resistance. Runs locally in your browser. › → PCB Trace Width Calculator (IPC-2221) Size PCB copper traces from current and temperature rise using the classic IPC-2221 I = k·ΔT^0.44·A^0.725 relation for external and internal layers. Runs locally in your browser. › → Stripline Impedance Calculator Estimate symmetric stripline characteristic impedance from W, b, and εr. Extends microstrip / Zdiff. Runs locally in your browser. › → Via Current Capacity Calculator Estimate PCB via ampacity from drill diameter, plating thickness, and temperature rise using the IPC-2221 I = k·ΔT^0.44·A^0.725 relation on the plating cross-section. ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this exact?

No — it is an engineering approximation for first-pass design. Validate with a solver for fabrication.

Is S center-to-center or edge-to-edge?

Edge-to-edge gap. Center-to-center would be S + W.

Is copper thickness included?

No. The Z0 model is zero-thickness (T=0), same family as the Microstrip Impedance calculator.