Transmission Lines

CPW Ground Width

Q: How wide do the CPW ground planes need to be before impedance stops changing?

For a conventional coplanar waveguide, the characteristic impedance becomes effectively independent of ground width once each ground plane extends roughly 3 to 5 times the slot gap g beyond the gap edge, or about one substrate thickness h, whichever is larger. Below that, the finite-ground CPW (FGCPW) behaves differently: as the ground width Wg shrinks toward g, the impedance rises by 5 to 15 ohms because the return current is squeezed into a narrower conductor, raising series inductance and reducing the line capacitance. A common 50 ohm design on 254 micron alumina with a 40 micron center conductor and 20 micron gaps reaches its asymptotic impedance once each ground is wider than about 100 to 150 microns. Designers who must conserve die area deliberately use FGCPW with Wg of 2g to 3g and then re-extract impedance in a 2.5D solver rather than assuming the semi-infinite-ground closed-form result.

Q: Why do unequal CPW ground widths excite the parasitic slotline mode?

Ideal CPW propagates an even (coplanar) mode in which the two ground planes sit at the same potential and the electric field is symmetric about the center conductor. If the left and right ground widths differ, or if the grounds are not periodically tied together, an odd (slotline) mode can be excited at discontinuities such as bends, tees, and bond-wire transitions. The slotline mode has a different phase velocity, radiates more strongly, and couples energy out of the intended even mode, producing ripple and resonant dips in S-parameters. The standard fix is to keep the two grounds geometrically symmetric and to bridge them with air bridges or bond-wire straps at intervals shorter than one tenth of a guided wavelength, which short-circuits the odd mode while leaving the even mode undisturbed.

Q: How does ground width interact with conductor-backed CPW and the substrate mode?

When a backside ground is added to make conductor-backed CPW (CBCPW), wide top grounds plus the backside plane form parallel-plate and microstrip-like return paths that can support a parasitic parallel-plate substrate mode. If the top ground width approaches a half guided wavelength at the operating frequency, that region can resonate, creating sharp suppression notches in transmission. The mitigation is to limit each ground width, stitch the top grounds to the backside ground with a dense via fence (via pitch under one twentieth of a wavelength), and keep the substrate thin. On a 100 micron GaAs CBCPW line running at 40 GHz, ground widths beyond roughly 600 to 800 microns without via stitching can produce measurable resonances inside the band of interest.

/see-pee-dubuh-yoo ground width/

Flanking either side of the signal trace in a coplanar waveguide, the ground planes have a finite lateral extent W_g that, together with the center-conductor width and slot gap, fixes the line's behavior. When each ground reaches roughly 3 to 5 gap-widths or one substrate thickness, the line approaches the semi-infinite-ground result and the characteristic impedance stops shifting. Narrow finite-ground designs (FGCPW) raise Z₀ by 5 to 15 ohms and risk exciting the parasitic slotline mode if the two grounds are asymmetric or left untied. In conductor-backed CPW the same width drives substrate resonances unless the grounds are via-stitched.

Category: Transmission Lines

Asymptotic ground: ≥ 3g to 5g or 1h

FGCPW range: W_g ≈ 2g to 5g

Why Ground Width Governs CPW Behavior

A coplanar waveguide carries its signal on a center strip with return current splitting onto the two coplanar grounds beside it. Because the field is confined mainly to the slot gaps between the strip and the grounds, classical analysis treats the grounds as semi-infinite half planes. Real circuits cannot afford that area, so the grounds are truncated to a finite width W_g. As long as each ground extends far enough that the return-current density has decayed to a negligible value at its outer edge, truncation has no measurable effect; the conformal-mapping closed-form impedance still applies. The current density falls off roughly exponentially with distance from the slot, so the practical cutoff is about three to five slot-gap widths, or one substrate thickness h on thicker boards.

Below that threshold the line becomes finite-ground CPW (FGCPW). Squeezing the return current into a narrower conductor increases the series inductance per unit length and slightly reduces the shunt capacitance, so Z₀ climbs. A 50 ohm line designed for semi-infinite grounds can drift to 55 to 65 ohms once W_g drops to one or two gap widths, which is why FGCPW geometries must be re-extracted in a full-wave or 2.5D solver rather than trusted to the textbook formula. FGCPW is nonetheless popular on GaAs MMICs because it conserves expensive die area and localizes the return path next to the signal.

Ground symmetry matters as much as ground width. The intended even (coplanar) mode keeps both grounds at equal potential. If the left and right widths differ, or if the grounds are not periodically tied together with air bridges or bond-wire straps, discontinuities can launch the odd slotline mode, which radiates, has a different phase velocity, and shows up as ripple in measured S-parameters. Keeping the grounds geometrically equal and bridging them at intervals shorter than one tenth of a guided wavelength preserves mode purity.

Impedance and Mode Onset Equations

Aspect ratio (semi-infinite ground):
k = a / b = (W/2) / (W/2 + g)  where W = center width, g = slot gap

Characteristic impedance (no backing):
Z₀ = (30π / √ε_eff) × K(k′) / K(k)  ε_eff ≈ (ε_r + 1) / 2

Practical ground-width cutoff:
W_g ≥ max(3g to 5g, h) → Z₀ within ≈ 2% of semi-infinite value

Air-bridge / strap spacing for slotline-mode suppression:
s_strap < λ_g / 10  λ_g = c / (f × √ε_eff)

K() is the complete elliptic integral of the first kind, k′ = √(1 − k²), ε_r = substrate dielectric constant, h = substrate thickness, λ_g = guided wavelength. Example: alumina ε_r = 9.8, ε_eff ≈ 5.4, so λ_g at 40 GHz ≈ 3.2 mm and straps should sit closer than 320 μm.

Ground-Width Regimes Compared

Ground regime	W_g (in slot gaps g)	Z₀ shift vs. ideal	Dominant risk	Required mitigation	Typical use
Semi-infinite (ideal)	≥ 5g or ≥ h	Reference (0)	Wasted die area	None	Discrete / large boards
Wide finite ground	3g to 5g	+0 to +3 ohms	Edge radiation at bends	Symmetric layout	General MMIC routing
Narrow FGCPW	1g to 3g	+5 to +15 ohms	Slotline-mode coupling	Re-extract; add straps	Compact GaAs/InP MMIC
Conductor-backed CPW	Wide top + backside	Lowered by backing	Substrate / parallel-plate resonance	Dense via fence	Multilayer modules
Asymmetric grounds	Unequal left/right	Mode-dependent	Odd-mode excitation	Equalize widths + bridges	Avoid in production

Common Questions

Frequently Asked Questions

How wide do the CPW ground planes need to be before impedance stops changing?

Once each ground extends about 3 to 5 slot gaps (g) beyond the gap edge, or roughly one substrate thickness h, Z₀ sits within about 2% of the semi-infinite-ground value. A 50 ohm line on 254 μm alumina with a 40 μm center conductor and 20 μm gaps reaches that asymptote near W_g ≈ 100 to 150 μm. Narrower FGCPW geometries raise Z₀ by 5 to 15 ohms and should be re-extracted in a 2.5D solver instead of trusting the closed-form result.

Why do unequal CPW ground widths excite the parasitic slotline mode?

Ideal CPW runs an even mode with both grounds at the same potential. Asymmetric ground widths, or grounds left untied, let discontinuities such as bends, tees, and bond-wire transitions launch the odd slotline mode, which radiates and shifts phase velocity, producing S-parameter ripple. Keep the two grounds geometrically equal and bridge them with air bridges or bond-wire straps spaced under λ_g/10 to short the odd mode while leaving the even mode untouched.

How does ground width interact with conductor-backed CPW and the substrate mode?

Adding a backside ground turns the line into CBCPW, where wide top grounds plus the backside plane form parallel-plate return paths that can resonate. If a top ground approaches a half guided wavelength, sharp transmission notches appear. Stitch the top grounds to the backside with a via fence pitched under λ_g/20 and keep the substrate thin. On 100 μm GaAs CBCPW at 40 GHz, unstitched grounds wider than roughly 600 to 800 μm can resonate in-band.

Related Terms

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