Cpw Impedance Calculator: Formula & How to Use

A CPW (Coplanar Waveguide) impedance calculator works out the characteristic impedance (in ohms) of a transmission line where the signal trace and its ground planes are all on the same layer of a PCB. You enter the trace width, gap to ground, substrate thickness, and dielectric constant, and the calculator returns the impedance in ohms, which is typically what you need to match a 50 Ω system.

Formula

The calculator uses two common approximations. The first is the standard microstrip formula, which is a good starting point but does not account for the coplanar ground. The second is a simplified coplanar waveguide approximation that includes the gap width. For a more precise result, a field solver is recommended, but these formulas are accurate to about 5–10% for typical PCB geometries.

Microstrip approximation:
Z₀ = (87 / √(Er + 1.41)) × ln(5.98 × H / (0.8 × W + T))

Coplanar waveguide approximation:
Z_{0_CPW} = (60 / √((Er + 1) / 2)) × (4 × (W + G) / (0.67 × (0.8 × W + T)))

Where:

• W = trace width (mm)
• G = gap between trace and ground (mm)
• H = substrate thickness (mm)
• Er = relative dielectric constant of the substrate
• T = copper thickness (mm)

Both formulas assume a 50 Ω target and are valid for W/H ratios between 0.1 and 3.0. The microstrip formula is for a trace over a ground plane, while the CPW formula adds the gap term. For a true CPW, the ground is on the same side, so the gap is critical.

Worked Example

Using the default values: W = 0.5 mm, G = 0.25 mm, H = 1.6 mm, Er = 4.3, T = 0.035 mm.

Microstrip:

1. 0.8 × 0.5 + 0.035 = 0.435
2. 5.98 × 1.6 / 0.435 = 21.99
3. ln(21.99) = 3.09
4. 87 / √(4.3 + 1.41) = 87 / 2.39 = 36.4
5. 36.4 × 3.09 = 112.5 Ω

CPW approximation:

1. 0.8 × 0.5 + 0.035 = 0.435
2. 4 × (0.5 + 0.25) / (0.67 × 0.435) = 3.0 / 0.291 = 10.31
3. 60 / √((4.3 + 1) / 2) = 60 / 1.63 = 36.8
4. 36.8 × 10.31 = 379.4 Ω

The CPW approximation gives ~379 Ω, which is far from 50 Ω. This shows that the simplified formula is not valid for all geometries—it works only when the gap is much smaller than the substrate height. In practice, a real CPW with a 0.5 mm trace and 0.25 mm gap on 1.6 mm FR4 would have an impedance around 50–60 Ω, but you need a field solver to get an accurate number.

When to Use a CPW Impedance Calculator

Use a CPW calculator when you are designing RF circuits, antennas, or high-speed digital lines on a PCB where controlled impedance is required. Common applications include:

• Wi-Fi and Bluetooth modules (50 Ω)
• GPS antenna feeds (50 Ω)
• RFID circuits
• High-speed USB, HDMI, or Ethernet traces
• Test fixtures and probes

If your trace is on an outer layer with ground planes on the same layer, CPW is the right model. If the trace is on an inner layer with ground above and below, use a stripline calculator instead.

How to Choose the Right Geometry

To hit a target impedance (usually 50 Ω), you adjust three main variables:

• Trace width (W): wider trace = lower impedance
• Gap (G): larger gap = higher impedance
• Substrate thickness (H): thicker substrate = higher impedance (for microstrip)
• Dielectric constant (Er): higher Er = lower impedance

For a 50 Ω CPW on 1.6 mm FR4 (Er ≈ 4.3), a typical starting point is W = 0.5 mm, G = 0.2 mm, but you must verify with a field solver. Many PCB manufacturers provide impedance calculators or design rules for their specific stackup.

Common Mistakes and Misconceptions

One common mistake is using a microstrip formula for a CPW trace. The microstrip formula ignores the gap, which can lead to large errors. Another mistake is forgetting to include copper thickness (T) in the formula—it affects the effective width, especially for thick copper.

A frequent misconception is that a CPW and a microstrip are interchangeable. They are not: a CPW has ground on the same layer, which changes the field distribution. Also, some people assume that a 50 Ω trace is always the same width, but it depends on the stackup and the dielectric.

Another error is using the wrong dielectric constant. FR4 has an Er that varies with frequency (typically 4.2–4.8), and the calculator uses a static value. For high frequencies (>1 GHz), consider the frequency-dependent value.

Limitations of the Calculator

These formulas are approximations. For precise impedance control, you should use a 2D field solver (e.g., from your PCB manufacturer or software like OpenEMS, KiCad’s PCB calculator, or commercial tools). The simplified CPW formula here is only valid when the gap is much smaller than the substrate height and when the trace is not too wide. For most real designs, the error can be 10–20%.

Also, the calculator does not account for solder mask, which lowers impedance slightly. If you have a solder mask over the trace, the effective Er increases, so the actual impedance will be a few ohms lower.

Frequently Asked Questions

What is the difference between CPW and microstrip?
Microstrip has a ground plane on the opposite side of the substrate, while CPW has ground traces on the same side as the signal. CPW is useful when you cannot have a solid ground plane underneath, or when you need easy access to ground on the same layer.

Why does my CPW impedance calculator give a different value than my PCB manufacturer?
Most manufacturers use a field solver that accounts for the exact stackup, solder mask, and copper roughness. The simplified formula here is a rough estimate. Always ask your manufacturer for their recommended stackup and impedance values.

Can I use this calculator for a grounded CPW (GCPW)?
No. A grounded CPW has an additional ground plane below the substrate, which changes the impedance. This calculator is for a standard CPW without a bottom ground plane. For GCPW, use a dedicated GCPW calculator.

What is the best way to get a 50 Ω CPW on FR4?
A typical starting point is a 0.5 mm trace with a 0.2 mm gap on 1.6 mm FR4, but you must verify with a field solver. The exact values depend on the copper thickness and the solder mask.

Does the copper thickness matter for impedance?
Yes, especially for thick copper (e.g., 2 oz or more). The formula includes T, and a thicker trace lowers impedance slightly. For 1 oz copper (0.035 mm), the effect is small but measurable.

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in w | Trace width (W) | mm | 0.5 | 0.01 | 100
in g | Gap to ground (G) | mm | 0.25 | 0.01 | 100
in h | Substrate thickness (H) | mm | 1.6 | 0.01 | 100
in er | Dielectric constant (Er) | - | 4.3 | 1 | 100
in t | Copper thickness (T) | mm | 0.035 | 0 | 10
out z0 | Characteristic impedance | ohm | (87 / sqrt(er + 1.41)) * ln(5.98 * h / (0.8 * w + t)) | 2
out z0_cpw | CPW impedance (approx) | ohm | (60 / sqrt((er + 1) / 2)) * (4 * (w + g) / (0.67 * (0.8 * w + t))) | 2