Coplanar Waveguide (CPWG) Impedance Calculator
Using quasi-static conformal mapping equations, accurately calculate the characteristic impedance $Z_0$, effective dielectric constant $\epsilon_{eff}$, propagation delay, and guided wavelength for Grounded Coplanar Waveguide (CPWG) traces. Ideal for Wi-Fi 2.4G/5.8G, Bluetooth, Sub-1GHz, GPS, and 5G RF antenna design.
Standard 2-Layer FR-4 (1.6mm thickness, $\epsilon_r \approx 4.4$): 50Ω impedance is achieved with Trace Width W = 1.2 mm (47 mil) and Ground Gap S = 0.25 mm (10 mil).
4-Layer JLC / Standard Stackup (L1-L2 core/prepreg 0.2mm): 50Ω is achieved with W = 0.45 mm (18 mil), S = 0.25 mm.
Ground Via Stitching: Ground fence vias must be placed every 1.5mm ~ 2.0mm along the coplanar ground to prevent slot-line radiation modes.
CPWG Simulation Results
| Effective Permittivity εeff | — |
| Propagation Delay Tpd | — ps/mm (— ps/inch) |
| Guided Wavelength λ | — mm |
| Recommended Max Via Pitch (λ/10) | — mm |
| Estimated Solder Mask Drop | — Ω |
Conformal Mapping Model
k1 = W / (W + 2S)
k2 = tanh(πW/4H) / tanh(π(W+2S)/4H)
Z0 = (60π / √εeff) / [K(k1)/K'(k1) + K(k2)/K'(k2)]
Standard 50Ω CPWG Design Reference Table (FR-4, 1 oz Copper)
| PCB Layer Stackup | Dielectric Height H | Trace Width W | Ground Gap S | Impedance Z0 | Typical Application |
|---|---|---|---|---|---|
| 2-Layer 1.6mm | 1.60 mm | 1.20 mm | 0.25 mm (10 mil) | 50.2 Ω | ESP32 / IoT 2.4GHz Wi-Fi Antenna |
| 2-Layer 1.0mm | 1.00 mm | 1.00 mm | 0.25 mm (10 mil) | 50.6 Ω | Compact BLE wearables & modules |
| 4-Layer (JLC 7628) | 0.21 mm | 0.45 mm | 0.25 mm (10 mil) | 49.8 Ω | 4-layer compact Wi-Fi / 5G sub-6 |
| 4-Layer (High Density) | 0.21 mm | 0.40 mm | 0.20 mm (8 mil) | 50.8 Ω | BGA fanout and tight routing |
| Rogers 4350B 20mil | 0.508 mm | 0.80 mm | 0.30 mm (12 mil) | 50.1 Ω | Precision RF amplifiers & microwave |
Frequently Asked Questions on RF CPWG Design (FAQ)
1. Broken ground reference: CPWG requires a continuous, unbroken ground plane directly beneath the trace on the layer below.
2. Insufficient ground stitching vias: If coplanar ground copper lacks dense vias connected to main ground, it behaves as a parasitic resonator.
3. Pad parasitic capacitance: Matching component pads (0402 R/L/C) add capacitance; removing copper ground directly underneath the pad restores 50Ω.
For consumer 2.4 GHz Wi-Fi/BLE, solder mask is acceptable if you design for ~52Ω bare copper (the mask drops it to ~50Ω). For frequencies above 5 GHz or precision RF, opening the solder mask (ENIG gold finish) is recommended to prevent batch-to-batch variation.
While smaller S allows narrower traces, PCB etching tolerances below 0.15mm (6 mil) cause impedance variations exceeding ±10%. Standard fabrication capability recommends S ≥ 0.2 mm (8 mil) for consistent yields.
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