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Differential Pair Calculator

Design 100Ω differential pairs for USB, HDMI, Ethernet, and PCIe. Calculate odd-mode impedance, coupling factor, and optimize trace geometry for high-speed serial interfaces.

Ground Plane
P (+)
S
N (-)
W
H

Edge-Coupled Differential Microstrip

Differential Impedance Fundamentals

Understanding the relationship between single-ended, odd-mode, and differential impedance

Single-Ended (Z₀)

50Ω

Impedance of each trace when the other is grounded (no coupling)

Standard RF reference

Odd-Mode (Zodd)

~35Ω

Impedance of each trace when driven differentially (P+, N-)

Zodd ≈ Z₀ × (1 - k) ≈ 0.7 × Z₀

Differential (Zdiff)

100Ω

Total impedance between P and N traces (the spec everyone uses)

Zdiff = 2 × Zodd ≈ 100Ω

Key Formulas

Odd-Mode Impedance
Zodd = Z₀ × √[(1-k)/(1+k)]

k = coupling coefficient (0 to 1)

Differential Impedance
Zdiff = 2 × Zodd = 2 × Z₀ × √[(1-k)/(1+k)]

Zdiff ≈ 2 × Z₀ when k → 0 (loose coupling)

Common Interface Specifications

InterfaceZdiff TargetData RateNotes
USB 2.090Ω ±15%480 MbpsOften relaxed to 90Ω
USB 3.0/3.190Ω ±10%5/10 GbpsTX and RX pairs
USB4 / TB385Ω ±10%40 GbpsVery tight skew
HDMI 1.4/2.0100Ω ±15%10.2/18 Gbps4 TMDS pairs
DisplayPort100Ω ±10%32.4 GbpsHBR3
PCIe Gen385Ω ±15%8 GT/sPer lane
PCIe Gen4/585Ω ±10%16/32 GT/sTight tolerance
1G Ethernet100Ω ±10%1 GbpsCat5e compatible
10G/25G Ethernet100Ω ±10%10/25 GbpsSFP+ / SFP28
SATA III100Ω ±10%6 GbpsTX and RX
DDR4/DDR580Ω ±10%VariableDQ, DQS pairs
LVDS100Ω ±10%655 MbpsDisplay panels

Differential Pair Design Rules

Length Matching

Match P and N trace lengths within each pair:

  • • USB 3.0: < 5 mil mismatch
  • • PCIe Gen4: < 5 mil mismatch
  • • HDMI: < 10 mil mismatch
  • • Use serpentines on shorter trace

Consistent Spacing

Maintain constant S (gap) along entire length:

  • • Avoid widening at vias
  • • Use differential via pairs
  • • Keep S/W ratio constant
  • • Avoid routing between pair

Reference Plane

Continuous ground plane is critical:

  • • No slots or splits under pair
  • • Return vias near signal vias
  • • Avoid crossing plane splits
  • • Use same reference for both traces

Coupling Guidelines

Optimize coupling for best performance:

  • • S = W (1:1) for 100Ω typical
  • • Tighter S = lower Zdiff
  • • Min S: 3-4 mil (manufacturing)
  • • Max S: 3W (coupling benefit)

Via Transitions

Minimize impedance discontinuity at vias:

  • • Use via pairs with ground vias
  • • Back-drill stubs for >5 Gbps
  • • Match via length on P and N
  • • Consider anti-pad size

Test Points

Design for TDR verification:

  • • Include differential test coupons
  • • Place at panel edge
  • • Match actual trace geometry
  • • Request Zdiff measurement

Edge-Coupled vs. Broadside-Coupled

Edge-Coupled (Side-by-Side)

S
Same layer, horizontal coupling
  • Easy to route and manufacture
  • Coupling visible on same layer
  • Works on 2-layer boards
  • Requires more horizontal space

Most common for USB, HDMI, Ethernet, PCIe

Broadside-Coupled (Stacked)

H
Adjacent layers, vertical coupling
  • Saves horizontal routing space
  • Stronger coupling possible
  • Requires precise layer registration
  • Hard to visually verify alignment

Used in dense BGA breakout, flex circuits

Frequently Asked Questions

What is the relationship between Z₀, Zodd, and Zdiff?

Z₀ is the single-ended characteristic impedance. Zodd (odd-mode impedance) is the impedance seen by each trace when driven differentially. Zdiff (differential impedance) = 2 × Zodd. Due to mutual coupling, Zodd < Z₀, typically Zodd ≈ 0.7 × Z₀ for tightly coupled pairs, making Zdiff ≈ 1.4 × Z₀.

Why is 100Ω differential impedance so common?

100Ω differential became the standard because it's easily achievable with common PCB geometries and works well with differential driver ICs. Most high-speed interfaces (USB, HDMI, DisplayPort, Ethernet, PCIe) specify 100Ω ±10%. Some legacy interfaces use 90Ω (LVDS) or 85Ω.

What is the difference between edge-coupled and broadside-coupled?

Edge-coupled pairs run side-by-side on the same layer, coupled through the gap between them. Broadside-coupled pairs are stacked vertically on adjacent layers. Edge-coupled is more common and easier to route; broadside is used when horizontal space is limited but requires more precise layer registration.

How tight should differential pair spacing be?

Tighter spacing (smaller S/W ratio) increases coupling and reduces Zdiff. For 100Ω targets, S ≈ W is common (1:1 ratio). Too tight (S < W) may cause manufacturing issues and excessive coupling. Too loose (S > 3W) provides minimal differential benefit. The 3W rule for isolation doesn't apply to intentional differential pairs.

Does differential routing cancel EMI?

Differential signaling significantly reduces EMI because the fields from P and N traces partially cancel. However, this only works if the pair is symmetric (equal length, spacing, and timing). Skew between P and N converts differential signal to common-mode, which radiates. Keep skew < 5% of rise time.