Coplanar Waveguide (TL)
Understanding the Coplanar Waveguide (CPW)
Invented in 1969 by C.P. Wen, the Coplanar Waveguide revolutionized the design of high-frequency printed circuits. Unlike microstrip or stripline, which rely on ground planes located on different layers of the PCB, a CPW places all critical conductors on the top layer. The electromagnetic wave propagates in a quasi-TEM mode, with the electric field lines arching from the center trace across the gaps to the adjacent ground planes.
CPW Geometry and Impedance
The characteristic impedance ($Z_0$) of a CPW is determined almost entirely by the ratio of the center trace width ($W$) to the gap width ($G$), rather than the thickness of the substrate ($h$). This provides immense design flexibility.
Where $K(k)$ represents the complete elliptic integral of the first kind, and $k = W / (W + 2G)$. Because the impedance depends on a ratio, engineers can miniaturize a $50 \Omega$ CPW line by scaling $W$ and $G$ down simultaneously, maintaining the exact same impedance while saving valuable semiconductor real estate.
Grounded CPW (CPWG) vs. Un-Grounded CPW
| Feature | Standard CPW | Grounded CPW (CPWG) |
|---|---|---|
| Substrate Bottom | Bare dielectric (no copper). | Solid copper ground plane. |
| Field Distribution | Fields split roughly 50/50 between the air above and the dielectric below. | Fields are pulled downward toward the bottom ground plane, behaving partially like a microstrip. |
| Via Requirements | No vias required. Extremely cheap and easy to fabricate. | Requires dense via stitching along the top ground planes to suppress parallel-plate waveguide modes. |
| Thermal Dissipation | Poor. Heat cannot easily escape through the bare substrate. | Excellent. The bottom ground plane acts as a massive heat sink for power amplifiers. |
Advantages Over Microstrip
The primary advantage of CPW over microstrip is the ease of mounting shunt components. If an engineer needs to ground a capacitor or a transistor source in a microstrip design, they must drill a via through the substrate to the bottom layer. At high millimeter-wave frequencies, that via acts as a massive parasitic inductor, ruining the circuit's performance. In a CPW, the ground plane is millimeters away on the same surface; components can simply be soldered across the gap, providing a near-perfect, zero-inductance ground connection.
Key Equations
Z0 = 60/√εeff × K(k′)/K(k)
k = w/(w+2s)
Mode suppression:
Via fence spacing: p < λ/4
Via to edge: < 3h (substrate thickness)
Loss:
α = αc+αd (conductor + dielectric)
Comparison
| Parameter | GCPW | Microstrip | Stripline | Notes |
|---|---|---|---|---|
| Modes | CPW+microstrip | Quasi-TEM | TEM | Via fence for GCPW |
| Ground access | Top+bottom | Bottom only | Both (inner) | GCPW best |
| Loss @30G | 0.15 dB/cm | 0.2 dB/cm | 0.12 dB/cm | Substrate dep |
| Dispersion | Low | Moderate | Lowest | GCPW good for mmW |
| Transition | Easy to WG | Needs via | Complex | GCPW versatile |
Frequently Asked Questions
What is the effective permittivity ($\epsilon_{eff}$) of a CPW?
Because the electric fields in a CPW travel half in the air ($\epsilon_r = 1$) and half in the substrate ($\epsilon_r > 1$), the wave "feels" an effective permittivity that is roughly the average of the two: $\epsilon_{eff} \approx (\epsilon_r + 1)/2$. This makes the signal velocity much faster in CPW than in stripline.
Why is gap width critical in a CPW?
The gap ($G$) defines the confinement of the electromagnetic field. A narrow gap concentrates the field tightly, increasing capacitance and lowering impedance. However, if the gap is too narrow, the risk of dielectric breakdown (arcing) between the signal trace and ground increases significantly at high power levels.
What is a "Conductor-Backed" Coplanar Waveguide?
A conductor-backed CPW is synonymous with Grounded CPW (CPWG). It features a bottom ground plane to provide mechanical rigidity, better thermal sinking, and immunity to objects placed underneath the board. However, it absolutely must feature "via stitching" to tie the top and bottom grounds together to prevent unwanted resonance modes.