Inverted Microstrip Line Calculator

Inverted microstrip prints the strip on the underside of the substrate, facing a ground plane across an air gap. The wave travels mainly in air and the substrate is just a carrier, so loss is low and ε_eff is close to 1.

Analyze W → Z_oSynthesize Z_o → WStrip faces groundε_eff close to 1Pramanick–Bhartia model

① Inputs

Relative permittivity ε_rSubstrate thickness ammAir gap bmmCopper t (reference)µmFrequency fMHz

A. Analyze: known size → impedance

Strip width Wmm

B. Synthesize: known impedance → size

Target impedance Z_oΩ

② Results

Item	Value
Characteristic impedance Z_o	Ω
Synthesized width W	mm
Effective permittivity ε_eff
Velocity factor k = 1/√ε_eff
Quarter wavelength λ/4 (guided)	mm

Cross-section

Signal conductorGroundDielectricAir

Symbols vs inputs: Relative permittivity εr　Substrate thickness a　Air gap b　Copper t (reference)　Strip width W

Impedance vs dimension (other inputs fixed)

Common laminates ε_r (click to apply)

Material	ε_r
FR-4 Low-cost general PCB laminate; higher loss above 1 GHz, εr varies with frequency and lot	4.3–4.6
Rogers RO4003C Hydrocarbon ceramic laminate, FR-4-compatible processing	3.38 (design 3.55)
Rogers RO4350B Common for power amplifiers, antennas and 5–6 GHz circuits	3.48 (design 3.66)
Rogers RO3003 PTFE ceramic, low loss and stable εr for mmWave	3.00
RT/duroid 5880 PTFE glass, very low loss, wider lines	2.20
RO3010 / RT6010 High permittivity for compact circuits	10.2
Alumina Al₂O₃ Thin/thick-film microwave substrate	≈ 9.8

How to use

Enter the substrate ε_r and substrate thickness a.
Enter the air gap b from the strip (substrate underside) to the ground plane, and the frequency f.
Known width: enter W and press Analyze for Z_o. Known target: enter Z_o and press Synthesize for W.
The copper thickness field t is kept for reference; this model does not include thickness.

Theory and formulas

The tool uses the Pramanick–Bhartia closed-form model for inverted microstrip (a = substrate thickness, b = air gap from strip to ground):

u = W / b
f(u) = 6 + (2π − 6) · exp( −(30.666/u)^0.7528 )
a₁ = (0.5173 − 0.1515 · ln(a/b))²　　b₁ = (0.3092 − 0.1047 · ln(a/b))²
√ε_eff = 1 + (a/b) · (a₁ − b₁ · ln(W/b)) · (√ε_r − 1)
Z_o = 60/√ε_eff · ln( f(u)/u + √(1 + 4/u²) )
k = 1/√ε_eff　　λ/4 = k · c / (4f)

Design tips

Impedance is set mainly by W/b (close to an air microstrip); the substrate ε_r is a small correction. This tool gives W ≈ 2.1 mm for 50 Ω with RO4003C 0.508 mm and a 0.5 mm gap.
With a small air gap, flatness and support tolerances strongly affect impedance; use precision spacers or a machined housing.
A metal lid close above the substrate lowers the impedance; confirm with simulation.
This is a quasi-static model without dispersion or copper thickness.

FAQ

What are the advantages of inverted microstrip?: The field is concentrated in the air between strip and ground, giving low dielectric loss and low ε_eff with relaxed dimensional tolerances — useful at mmWave and in low-loss circuits.
How is it different from suspended microstrip?: In suspended microstrip the strip is on top and the field passes through the substrate to ground. In inverted microstrip the strip is on the underside facing ground directly, so more of the field is in air.
Where is b measured?: From the substrate underside (where the strip is) to the top of the ground plane, as shown in the cross-section.

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