Coplanar Strips
How Coplanar Strips Carry a Balanced Mode
Coplanar strips belong to the family of uniplanar transmission lines, meaning every conductor sits on one face of the substrate. The two strips of equal width carry equal and opposite currents, so the structure supports a balanced mode with a plane of odd symmetry running down the center of the slot. That symmetry plane behaves as a virtual ground, which is why CPS feeds dipoles, bowties, and other balanced radiators directly without a separate ground return. Removing the ground plane and the via holes that microstrip demands is a major fabrication advantage on GaAs and InP wafers, where backside processing and through-substrate vias add cost, parasitic inductance, and yield risk.
Because roughly half of the electromagnetic field travels through air above the substrate and half through the dielectric, the effective permittivity of CPS is approximately the average of the substrate and air values. This air loading raises the characteristic impedance relative to microstrip and keeps the phase velocity higher, so CPS lines are inherently high-impedance structures. Reaching 50 Ω requires wide strips and a very narrow slot, which is one reason designers more often exploit CPS where 80 to 150 Ω is useful, such as antenna feeds, series stubs, and balanced interconnects. CPS is the geometric dual of coplanar waveguide and a close relative of slotline, so transitions between these lines are routinely built into the same circuit.
Impedance From Conformal Mapping
The closed-form impedance of CPS comes from conformal mapping of the two-strip cross section onto a parallel-plate region, which reduces the calculation to a ratio of complete elliptic integrals of the first kind. The mapping is exact for a zero-thickness, infinitely wide substrate and remains accurate to a few percent for practical thicknesses. The strip width w and slot spacing s set the elliptic modulus, and the substrate fixes the effective permittivity, giving a compact design equation suitable for first-pass layout before full-wave verification.
Z0 = (120π / √εeff) × K(k) / K(k′) Ω
Elliptic modulus from geometry:
k = s / (s + 2w) k′ = √(1 − k2)
Effective permittivity (thick substrate):
εeff ≈ (εr + 1) / 2
Where w = strip width, s = slot width, εr = substrate relative permittivity, and K() is the complete elliptic integral of the first kind. Example: on GaAs (εr ≈ 12.9) with w = s, k = 1/3, εeff ≈ 6.95 and Z0 ≈ 91 Ω.
Geometry Versus Impedance and Loss
| w/s ratio | Modulus k | Z0 (εr = 12.9) | Loss @ 30 GHz | Typical use |
|---|---|---|---|---|
| 2.0 | 0.20 | ~75 Ω | 0.18 dB/mm | Lowest-Z feed / match |
| 1.0 | 0.33 | ~91 Ω | 0.22 dB/mm | Balanced interconnect |
| 0.5 | 0.50 | ~112 Ω | 0.28 dB/mm | Dipole / antenna feed |
| 0.25 | 0.67 | ~136 Ω | 0.34 dB/mm | High-Z series stub |
| 0.1 | 0.83 | ~172 Ω | 0.42 dB/mm | Wide-slot radiator feed |
Frequently Asked Questions
How do coplanar strips differ from coplanar waveguide?
Both lines keep all conductors on one substrate face, but the modes are opposite. CPW has a center signal strip between two grounds and carries a single-ended, ground-referenced mode; CPS has two equal conductors with no dedicated ground and carries a balanced, differential mode about a virtual ground in the slot. The two are duals (conductor and aperture regions interchanged), so a CPW-to-CPS transition or a balun links them. CPS suits balanced antennas and mixers; CPW suits single-ended circuits needing easy shunt grounding.
How is the characteristic impedance of coplanar strips calculated?
Conformal mapping reduces the two-strip cross section to a ratio of complete elliptic integrals: Z0 = (120π/√εeff) × K(k)/K(k′), with k = s/(s + 2w) and k′ = √(1 − k2). With about half the field in air, εeff ≈ (εr + 1)/2. CPS lands naturally at 80 to 150 Ω on alumina or GaAs; reaching 50 Ω needs wide strips and a narrow slot.
Why is coplanar strips preferred for differential and balanced circuits?
The two strips carry equal and opposite currents, giving a true differential mode with a virtual ground along the slot. That feeds balanced antennas, push-pull amplifiers, and balanced mixers with no ground plane or via holes, which is valuable on GaAs and InP where backside vias are costly. It also rejects common-mode noise. The trade-offs are higher impedance, more radiation loss than shielded lines, and sensitivity to unbalanced drive, usually fixed with a balun.