Transmission Lines

CPW Gap Design

Q: Should I make the CPW gap larger or smaller to raise the characteristic impedance?

Raise the impedance by widening the gap g relative to the center-strip width s. Characteristic impedance in CPW depends only on the aspect ratio k = s/(s+2g), not on the absolute size, so a thin strip with wide gaps gives high impedance and a wide strip with narrow gaps gives low impedance. For example, on a 254 micron alumina substrate with a 40 micron strip and 60 micron gaps the line is near 50 ohms; doubling the gaps to 120 microns while keeping the strip at 40 microns pushes the impedance toward 70 ohms. Because impedance is set by the ratio, you can scale s and g together to keep 50 ohms while shrinking the line for tight layouts or to widen it for higher current handling and lower conductor loss.

Q: How does the CPW gap affect conductor loss and unloaded Q?

Narrow gaps crowd the electric field and concentrate current at the strip and ground edges, raising conductor loss and lowering unloaded Q. Widening the gap spreads the field and reduces edge current density, which improves Q until the gap becomes large enough that radiation and surface-wave loss begin to dominate. On a typical 50 ohm CPW with gaps in the 20 to 80 micron range, attenuation often falls by 20 to 40 percent as gaps widen from 20 to 50 microns, then flattens. Practical resonator and filter designs choose gaps in the 30 to 100 micron window on alumina or quartz to balance conductor loss against radiation and to keep the gap above the substrate-thickness fraction where conductor-backed parasitic modes appear.

Q: What is the maximum CPW gap before radiation and parasitic modes become a problem?

Keep the total ground-to-ground span, s plus 2g, below roughly one tenth of the guided wavelength, and keep the gap smaller than about half the substrate thickness on conductor-backed CPW. When the ground separation grows beyond about 0.1 lambda the slot can launch radiation and the structure starts behaving like a slot antenna; at 30 GHz on alumina (effective permittivity near 5.5) a guided wavelength is about 4.3 mm, so the total span should stay under roughly 400 microns. On conductor-backed CPW, gaps larger than half the substrate thickness let the parallel-plate mode between the top metal and the backside ground couple in, degrading isolation. Adding metallized via fences along the grounds raises the cutoff of those parasitic modes and lets you use slightly wider gaps.

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The choice of slot width, g, separating the center signal conductor from the two adjacent ground planes in a coplanar waveguide. Because the characteristic impedance of CPW depends on the dimensionless aspect ratio k = s/(s+2g) rather than on absolute geometry, the gap and the center-strip width, s, must be designed as a pair. Widening the gap raises impedance and spreads the electric field for higher unloaded Q, while narrowing it lowers impedance and concentrates current at the conductor edges. The gap also governs dispersion, radiation onset, and how cleanly discontinuities and series elements behave, making it one of the most consequential dimensions in any planar millimeter-wave layout. On alumina and quartz substrates, gaps typically range from 15 to 100 μm for 50 Ω lines operating to 110 GHz.

Category: Transmission Lines

Typical Gap: 15 to 100 μm

Sets: Z₀ via s/(s+2g)

How the Slot Width Sets CPW Impedance

In a coplanar waveguide the signal travels on a center strip of width s, flanked on the same surface by two ground planes separated from the strip by equal gaps of width g. The fields concentrate in those two slots, so the gap is not a secondary detail but a primary impedance-setting dimension. The closed-form analysis of CPW, developed by Wen in 1969 using conformal mapping, shows that the line impedance is a function only of the aspect ratio k = s/(s+2g). This is a powerful property: a designer can scale s and g up or down together to keep a constant 50 Ω while trading line size against current handling and conductor loss.

The independence from absolute size holds as long as the substrate is electrically thick relative to the slots and the conductors are thin. Once the ground-to-ground span s+2g approaches a tenth of the guided wavelength, or once the gap becomes comparable to the substrate thickness on a conductor-backed CPW, the simple ratio model breaks down and parasitic parallel-plate modes, dispersion, and radiation must be accounted for. This is why millimeter-wave layouts keep gaps small and add via fences along the grounds rather than simply widening the slots.

Designers usually fix the impedance target first, then pick a strip width compatible with the photolithography and current budget, and finally solve for the gap that yields the required k. Narrow gaps below about 10 μm become sensitive to etch tolerance, where a 1 μm error shifts impedance by several ohms, while very wide gaps invite radiation. The sweet spot for most 50 Ω alumina or quartz circuits lands between 20 and 80 μm.

Governing Equations

Aspect ratio (the design variable):
k = s / (s + 2g) k′ = √(1 − k²)

Characteristic impedance (conformal mapping):
Z₀ = (30π / √ε_eff) × [K(k′) / K(k)] Ω

Effective permittivity (thick substrate):
ε_eff ≈ (ε_r + 1) / 2

Where s = center-strip width, g = slot (gap) width, K(k) = complete elliptic integral of the first kind, ε_r = substrate relative permittivity. Example: alumina (ε_r = 9.8), s = 40 μm, g = 26 μm → k ≈ 0.435, ε_eff ≈ 5.4, Z₀ ≈ 50 Ω.

Gap Width vs. Performance Trade-offs

Gap regime (50 Ω alumina)	Typical g	Strip s	Conductor loss	Radiation risk	Best use
Tight (compact)	10 to 20 μm	15 to 30 μm	High	Very low	Dense MMIC routing
Moderate	20 to 50 μm	30 to 80 μm	Medium	Low	General 50 Ω interconnect
Wide (low loss)	50 to 100 μm	80 to 160 μm	Low	Moderate	Resonators, low-loss lines
Very wide	> 100 μm	> 160 μm	Lowest	High	Avoid above 0.1 λ_g span

Common Questions

Frequently Asked Questions

Should I make the CPW gap larger or smaller to raise the characteristic impedance?

Widen the gap g relative to the strip width s. Impedance depends on k = s/(s+2g), so a thin strip with wide gaps gives high Z₀. On 254 μm alumina with a 40 μm strip, 60 μm gaps sit near 50 Ω; doubling the gaps to 120 μm pushes toward 70 Ω. Because impedance follows the ratio, you can scale s and g together to hold 50 Ω while shrinking or widening the line.

How does the CPW gap affect conductor loss and unloaded Q?

Narrow gaps crowd the field and concentrate edge current, raising conductor loss and lowering Q. Widening the gap spreads the field and improves Q until radiation and surface-wave loss take over. On a 50 Ω line, attenuation often drops 20 to 40 percent as gaps widen from 20 to 50 μm, then flattens. Resonators typically use 30 to 100 μm gaps to balance conductor loss against radiation.

What is the maximum CPW gap before radiation and parasitic modes become a problem?

Keep the ground-to-ground span s+2g below about 0.1λ_g, and on conductor-backed CPW keep g under roughly half the substrate thickness. At 30 GHz on alumina (ε_eff ≈ 5.5, λ_g ≈ 4.3 mm) the span should stay under about 400 μm. Gaps larger than half the substrate thickness let the parallel-plate mode couple in; via fences along the grounds raise the cutoff and allow slightly wider gaps.

Related Terms

← CPW Design Equations CPW Ground Width →