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High-Speed Digital / RF

Differential Pair Impedance Calculator — USB / HDMI 100 ohm Routing

Instantly compute the differential impedance Z_diff, odd-mode Z_odd and even-mode Z_even of a surface microstrip pair from trace width, spacing, substrate height and dielectric constant. Compare with the USB 90 ohm and HDMI 100 ohm targets on the fly.

Parameters
Trace width W
mm
Trace spacing S
mm
Substrate height H
mm
Dielectric constant ε_r
—

IPC-2141A simplified formulas (copper thickness T = 0, surface microstrip) are used.

Results
—
Single-ended Z_0
—
Differential Z_diff
—
Odd-mode Z_odd
—
Even-mode Z_even
Differential Pair Cross Section and Z_diff vs S/H

Top = cross-section of the pair (W, S, H, substrate) / Bottom = Z_diff versus S/H (red dot = current point, dashed = USB 90 ohm / HDMI 100 ohm targets)

Theory & Key Formulas

For a surface microstrip differential pair, first compute the single-ended characteristic impedance Z_0, then apply a correction for the coupling between the two traces to obtain the differential impedance Z_diff.

Single-ended microstrip Z_0 (IPC-2141 simplified form, copper thickness T = 0). H is the substrate height, W the trace width, ε_r the dielectric constant:

$$Z_0 = \frac{87}{\sqrt{\varepsilon_r + 1.41}}\,\ln\!\left(\frac{5.98\,H}{0.8\,W}\right)$$

Differential impedance Z_diff. S is the spacing between the two traces:

$$Z_\text{diff} = 2\,Z_0\,\bigl(1 - 0.48\,e^{-0.96\,S/H}\bigr)$$

Odd-mode Z_odd and even-mode Z_even:

$$Z_\text{odd} = \tfrac{1}{2}\,Z_\text{diff},\qquad Z_\text{even} = Z_0\,\bigl(1 + 0.48\,e^{-0.96\,S/H}\bigr)$$

USB 2.0/3.x targets Z_diff = 90 ohm; HDMI, SATA, PCIe and 1000BASE-T target Z_diff = 100 ohm.

What is the Differential Pair Impedance Calculator

🙋
On USB and HDMI PCBs, you always see two thin traces running in parallel. What are they actually for?
🎓
Those are "differential pairs". Roughly speaking, instead of sending a signal on one wire, you send a signal and its inverse on a pair of wires. The receiver only looks at the difference, so any external noise that lands on both wires cancels out. For high-speed digital signals this is essentially the standard — USB, HDMI, PCIe, Ethernet, all use it. Drag the "trace width W" and "spacing S" sliders above and watch the Z_diff card update in real time.
🙋
I have seen "USB is 90 ohm, HDMI is 100 ohm". What do those numbers mean?
🎓
That is the "differential impedance Z_diff" — the impedance the pair shows when viewed as a single entity. Keeping this value constant across the cable, connector and PCB traces is the lifeline of high-speed signal integrity. If it drifts, you get reflections, the waveform breaks down, and at worst the link will not even come up. Try the "USB 90 ohm" and "HDMI 100 ohm" buttons in the simulator — the sliders will jump to values that aim at those targets.
🙋
When I make the spacing S narrower, Z_diff drops. Why is that?
🎓
Nice catch. As you push the two traces together, the capacitive coupling between them grows, so the equivalent capacitance one trace sees in differential excitation gets bigger. Since Z scales as 1/sqrt(C), more C means a lower Z. In the bottom curve, when S/H goes toward 0 the Z_diff drops sharply, and above S/H around 3 it settles to roughly twice the single-ended value. That "coupling effect" is the whole essence of differential routing.
🙋
There are also "odd-mode" and "even-mode" cards. What are those?
🎓
Those are the "mode decomposition" you get when you analyze the two traces separately. The odd-mode impedance Z_odd is what one trace sees to ground when you drive the pair with opposite phases — that is the body of the differential mode, with the relation Z_diff = 2 times Z_odd. The even-mode Z_even is what one trace sees when both are driven in phase, and it matters when you treat common-mode noise propagation. In practice, this Z_even shows up when you design common-mode filters and common-mode chokes.

Frequently Asked Questions

This tool targets the "edge-coupled differential microstrip" configuration, with the two traces running side by side on the same layer over a continuous ground plane on the opposite side. This is by far the most common configuration. Broadside-coupled differential pairs (the two traces stacked on different layers) use different equations, and so do differential striplines (sandwiched between two ground planes). USB, HDMI and Ethernet PHY routing on typical boards is overwhelmingly edge-coupled microstrip, which is what this calculator handles.
The tool uses the IPC-2141 simplified form (T = 0) to keep early sizing fast. Typical PCB copper thickness is 18 to 70 microns (0.5 to 2 oz/ft squared), and its effect on impedance is usually only 1 to 3 percent. For higher accuracy, use the full Wadell formulas or a 2D field solver such as Polar Si9000, HyperLynx or CST, and include copper thickness, solder mask cover and surface roughness. Before production, calibrate with PCB vendor test coupons and TDR measurements.
Look up the dielectric constant in the substrate data sheet and enter it directly. Typical values are FR4 4.3, Rogers RO4003C 3.55, Rogers RO4350B 3.66, Isola I-Tera MT40 3.45, Megtron 6 (R-5775) 3.4, and PTFE 2.1. Note that ε_r depends on frequency — it tends to drop slightly at higher frequencies — so use the data-sheet value at your operating band. The value also varies with layer thickness and glass-weave ratio even within one material grade, so for production use the vendor-specified Dk.
Aim at the nominal value itself (USB 90 ohm, HDMI 100 ohm) as your design center. Considering PCB manufacturing tolerances (trace width plus or minus 10 percent, substrate thickness plus or minus 10 percent, Dk plus or minus 5 percent, and so on), a calculated value biased to one side risks falling out of spec under production variation. In practice, sum the manufacturing tolerances in quadrature and choose a center value that keeps the worst case in spec. Share the stack-up and impedance calculation with your PCB vendor up front and adjust to their recommended values.

Real-World Applications

USB 2.0/3.x host and device design: USB 2.0 (D+/D−) and USB 3.x SuperSpeed (TX/RX) are both differential pairs, with a Z_diff = 90 ohm plus or minus 15 percent target. From phones and PCs to hubs and cameras, this calculation is performed daily around USB ports of every kind. Thin devices with 0.4 to 0.8 mm substrates are common, and it is standard practice to fix W/S/H with a tool like this first and then engage the PCB vendor.

HDMI / DisplayPort video transmission: HDMI TMDS (4 pairs) and DisplayPort Main Link (4 lanes) are designed at Z_diff = 100 ohm plus or minus 10 percent. As 4K/8K push speeds higher, signal integrity matters more than ever. The usual flow is: first narrow down the W/S/H combinations with this tool, then refine with a 2D field solver, and finally calibrate against TDR measurements.

Gigabit Ethernet and 10G/25G Ethernet: 1000BASE-T through 10GBASE-T are 100 ohm differential, and 25G/40G/100G SerDes paths are also 100 ohm differential on board. Server, switch and storage backplanes and add-in cards rely on calculators like this to pin down the stack-up and pair geometry. Above 10G, low-Dk/low-Df materials (Megtron 6, Isola I-Tera and the like) are typically chosen.

PCIe, SATA and MIPI chip-to-chip links: PCIe Gen3/4/5 (8/16/32 GT/s), SATA 6G and MIPI D-PHY/M-PHY are also 85 to 100 ohm differential. With many differential pairs squeezed into a small area around SoCs, GPUs, SSDs and camera modules, exploring W/S/H combinations with a tool like this is the starting point for design.

Common Misconceptions and Cautions

The most common misconception is to think that "Z_diff is simply 2 times the single-ended Z_0". In reality, as the two traces get closer the coupling capacitance grows and Z_diff drops below the naive doubling. In this tool too, at S/H = 0.2 Z_diff is about 80 percent of 2 times the single-ended value, as you can read off the lower curve. If your USB D+/D− or HDMI TMDS pair runs with spacing on the same order as the trace width, ignoring the coupling correction can throw the calculation off by 15 to 20 percent. "I made 50 ohm single-ended, so two of those side by side will give 100 ohm differential" is a recipe for pain after assembly.

The next most common mistake is routing the pair asymmetrically — letting one trace stray closer to ground or another signal than the other. Differential routing lives or dies by symmetry. If one trace gets closer to other signals or to a ground boundary, odd and even modes no longer decouple cleanly, differential-to-common-mode conversion appears, and both EMI (radiation) and SI (signal integrity) suffer. Keep the two traces at equal distance and on equal conditions everywhere, route layer-change vias symmetrically as a pair, and keep adjacent pairs at least the 3W rule away. This tool assumes a symmetric pair; asymmetric routing needs a separate analysis.

Finally, do not commit to mass production based solely on the calculated value from this kind of simulator. It is an IPC-2141 simplified estimate accurate to about plus or minus 5 to 10 percent, and it ignores copper thickness, surface roughness, glass-weave style, solder mask, temperature and humidity. The realistic flow is: (1) pick initial W/S/H/ε_r with this tool, (2) lock the stack-up with the PCB vendor's official impedance calculation (Polar Si9000 and so on), and (3) calibrate against TDR measurements on test coupons. Treat this tool as the early-stage instrument for getting a feel for where in the design space to attack.

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