Microstrip Impedance Calculator
Characteristic impedance (Z0) of a microstrip trace, or the width needed to hit a target impedance like 50 Ω.
Z0 = (87/√(εr+1.41)) × ln(5.98h / (0.8w+t)) (Wheeler's approximation)
10mil trace, 1.6mm FR4
20mil, 0.2mm dielectric (thin)
15mil, Rogers-like εr=3.5
Solved numerically from Wheeler's equation for w, given a target Z0
50Ω, 1.6mm FR4
90Ω, 1.6mm FR4
50Ω, thin 0.2mm dielectric
What Microstrip Impedance Is and Why It Matters
A microstrip is simply a copper trace on the outer layer of a PCB, running above a continuous ground plane, separated by the board's dielectric material. At DC or low frequency, a trace is "just a wire" — but at high frequencies (fast digital edges, RF signals), the trace and the ground plane beneath it behave as a transmission line with a characteristic impedance Z0. If the trace's Z0 doesn't match the impedance of the driver, receiver, or transmission line it connects to, part of the signal reflects back instead of continuing forward — causing ringing, overshoot, and signal integrity problems.
Wheeler's approximation (the formula this tool uses)
Z0 = (87/√(εr+1.41)) × ln(5.98h / (0.8w+t)) — a well-established closed-form approximation (from Harold Wheeler's original 1965 work) that is accurate to within a few percent for typical PCB geometries where h is small compared with the board's other dimensions. Here w is trace width, h is the height above the ground plane (essentially the dielectric thickness), t is copper thickness, and εr is the dielectric constant of the board material — all in consistent units (this calculator handles the unit conversion internally).
What each variable does to Z0, intuitively
- Wider trace (w ↑) → lower Z0. A wider trace has more capacitance to the ground plane below it, which lowers the characteristic impedance.
- Taller dielectric (h ↑) → higher Z0. Moving the trace further from the ground plane reduces that same capacitance, raising Z0.
- Higher dielectric constant (εr ↑) → lower Z0. A more "electrically dense" dielectric increases capacitance for the same physical geometry.
- Thicker copper (t) has a small secondary effect, slightly lowering Z0 as it grows, because thicker copper effectively widens the trace's fringing fields.
| Quantity / Material | Typical value |
|---|
| Standard FR4 dielectric constant | εr ≈ 4.2–4.6 |
| High-frequency laminate (e.g. Rogers) | εr ≈ 3.0–3.6 |
| Common single-ended target impedance | 50 Ω |
| Common video/differential-pair reference | 75 Ω (single-ended), 90–100 Ω (differential) |
Real-World Applications & Fully-Explained Examples
- RF & wireless PCB design: matching antenna feed lines to 50 Ω.
- High-speed digital buses: USB, HDMI, Ethernet controlled-impedance traces.
- Video signal traces: 75 Ω composite/component video.
- Test & measurement equipment: matching to 50 Ω instrumentation.
- Stackup planning: choosing dielectric thickness for a target Z0 at a fixed trace width.
- Fab house DFM checks: verifying a stackup delivers the specified impedance.
Worked examples — explained in full
1. 10 mil trace on standard 1.6 mm FR4 (εr=4.5). w=10 mil=0.254 mm, h=1.6 mm, t=0.035 mm. Z0=(87/√5.91)×ln(5.98×1.6/(0.8×0.254+0.035))=(87/2.431)×ln(9.568/0.238)=35.79×ln(40.2)=35.79×3.694≈132.2 Ω — a narrow trace on a thick board gives a high impedance.
2. Same board, but wider (30 mil) trace. w=30 mil=0.762 mm, same h=1.6 mm, εr=4.5, t=0.035 mm. Z0=(87/√5.91)×ln(5.98×1.6/(0.8×0.762+0.035))=35.79×ln(9.568/0.645)≈96.5 Ω — tripling the width dropped Z0 from 132.2 Ω to 96.5 Ω, because the wider copper adds capacitance to the ground plane.
3. Solving for 50 Ω on the same stackup. Using the "Z0 → Width" tab with h=1.6 mm, εr=4.5, t=0.035 mm and a 50 Ω target, the numerical solver returns w≈2.91 mm (114.7 mil) — over 11× wider than the 10 mil trace in example 1, showing how much copper 50 Ω needs on a "thick" 1.6 mm board.
4. Thinner dielectric. Keeping w=10 mil but moving to a much thinner h=0.2 mm dielectric (common on inner layers of a multi-layer stackup): Z0=35.79×ln(5.98×0.2/0.238)≈57.7 Ω — down from 132.2 Ω at h=1.6 mm, since Z0 depends on h through a logarithm and thin dielectrics need much narrower traces to hit the same target impedance as thick ones.
5. Lower-εr material. Same w=10 mil, h=1.6 mm geometry, but switching from FR4 (εr=4.5) to a Rogers-style RF laminate (εr=3.5): Z0=(87/√4.91)×ln(40.2)≈145.0 Ω — higher than example 1's 132.2 Ω, because the lower dielectric constant reduces the trace-to-plane capacitance.
6. Why controlled impedance matters practically. A 50 Ω driver feeding a trace that is accidentally 75 Ω sees a mismatch that reflects roughly (75−50)/(75+50)≈20% of the signal back toward the source — enough to cause visible ringing and timing errors on a fast digital edge.
Frequently Asked Questions
What is microstrip characteristic impedance?
It is the impedance a high-frequency signal "sees" as it travels along a PCB trace running above a continuous ground plane. It depends on the trace's width, its height above the plane, the dielectric constant of the board material, and (slightly) the copper thickness.
What is Wheeler's formula?
Z0 = (87/√(εr+1.41))×ln(5.98h/(0.8w+t)), a well-known closed-form approximation for microstrip impedance, accurate to within a few percent for typical PCB geometries and widely used for quick design estimates.
Why do I need to control trace impedance?
If a trace's impedance does not match the source, load, or transmission line it connects to, part of a fast signal reflects back at the mismatch, causing ringing, overshoot, and potential timing or signal-integrity failures — especially critical for high-speed digital and RF signals.
What is a typical target impedance?
50 Ω single-ended is the most common target for RF and many digital interfaces; 75 Ω is standard for video; differential pairs (like USB or Ethernet) often target 90–100 Ω differential.
How does trace width affect impedance?
Wider traces have lower impedance, because a wider trace has more capacitive coupling to the ground plane beneath it. To lower Z0, widen the trace; to raise it, narrow the trace.
How does dielectric height (h) affect impedance?
A taller dielectric (trace further from the ground plane) raises impedance, because it reduces the capacitive coupling to the plane. Thin, inner-layer dielectrics generally need much narrower traces to hit the same target impedance as a thick outer-layer stackup.
What dielectric constant should I use for FR4?
Standard FR4 is typically around εr≈4.2–4.6 at the frequencies relevant to most digital design, though it does vary somewhat with frequency and between manufacturers — check your fabricator's stackup documentation for the precise value they specify.
How accurate is Wheeler's formula compared with field-solver software?
It typically agrees with full 2D field-solver results to within a few percent for common PCB geometries, making it excellent for quick hand estimates and early design decisions. For a final, fabrication-critical impedance specification, most PCB houses run (or provide) a proper field solver against your exact stackup.
Why does my fab house ask for "controlled impedance" traces?
They need to know your target Z0 and the relevant trace/stackup parameters so they can tune the actual dielectric thickness and trace width during manufacturing to hit your specification, since normal manufacturing tolerances alone would not guarantee a precise impedance.
Does copper thickness matter much?
It has a smaller effect than width or height — thicker copper slightly lowers impedance because it effectively widens the trace's fringing electric field, but it is a secondary factor compared with trace width and dielectric height.
Is this formula valid for inner-layer (stripline) traces?
No — this formula is specifically for microstrip, a trace on an outer layer with a single reference plane below it. A trace between two reference planes (stripline) uses a different formula because the fields are enclosed on both sides.
How do I hit exactly 50 ohms on my board?
Use the "Z0 → Width" tab with your actual stackup's dielectric height and dielectric constant (from your fab house's documentation) to find the exact trace width needed, then confirm with your fabricator before finalising, since manufacturing tolerances can shift the result slightly.