Slot Line Impedance Calculator

A slot line is a narrow slot cut in the metal on one side of a substrate, with the electric field across the slot. It is a balanced, non-TEM line whose impedance and ε_eff vary with frequency — used in slot and Vivaldi antennas and microstrip-to-slot baluns.

Analyze W → Z_oSynthesize Z_o → Wε_r 2.2–20Frequency dependentClosed-form fit

① Inputs

Relative permittivity ε_r2.2–20Substrate height hmmFrequency fMHz

A. Analyze: known size → impedance

Slot width Wmm

B. Synthesize: known impedance → size

Target impedance Z_oΩ

② Results

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

Cross-section

Signal conductorSecond conductorDielectric

Symbols vs inputs: Relative permittivity εr　Substrate height h　Slot 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 substrate ε_r (valid 2.2–20; values outside are clamped) and substrate height h.
Enter the frequency f in MHz. Slot-line impedance depends on frequency, so use the real operating frequency.
Known slot: enter W and press Analyze for Z_o.
Known target: enter Z_o and press Synthesize for the slot width W.

Theory and formulas

The tool uses the Garg–Gupta and Janaswamy–Schaubert closed-form expressions fitted to spectral-domain results. λ₀ = c/f is the free-space wavelength; separate coefficient sets cover ranges of ε_r, W/h and W/λ₀. For example, for 9.7 ≤ ε_r ≤ 20 and W/h ≤ 0.2:

λ_s/λ₀ = 0.923 − 0.195 ln ε_r + 0.2 W/h − (0.126 W/h + 0.02) · ln(100h/λ₀)
Z_o = 72.62 − 15.283 ln ε_r + 50 (W/h − 0.02)(W/h − 0.1)/(W/h) + ln(100W/h) · (19.23 − 3.693 ln ε_r)
　　 − [ 0.139 ln ε_r − 0.11 + W/h · (0.465 ln ε_r + 1.44) ] · (11.4 − 2.636 ln ε_r − 100h/λ₀)²
ε_eff = (λ₀/λ_s)²　　k = λ_s/λ₀ = 1/√ε_eff　　λ/4 = k · λ₀ / 4

The other ε_r ranges (2.22–3.8, 3.8–9.8) and W/λ₀ ranges use their own fitted coefficients, selected automatically.

Design tips

Recommended range: for ε_r 2.2–9.7, 0.0015 ≤ W/λ₀ ≤ 1.0; for ε_r 9.7–20, 0.02 ≤ W/h ≤ 1.0. Accuracy drops outside.
Slot-line impedance is typically 60–200 Ω; 50 Ω is hard on thin low-ε_r boards. This tool gives about 100 Ω at W ≈ 0.71 mm for ε_r 10.2, h = 0.635 mm, 5 GHz.
High-ε_r substrates (e.g. RO3010, alumina) confine the field near the slot and reduce radiation, so they are common for slot-line circuits.
A slot line is often crossed by a microstrip on the back to form a balun, with roughly λ/4 open microstrip and shorted slot stubs beyond the crossing.

FAQ

How are slot line and coplanar strips related?: They are complementary: a slot line is a gap in metal, coplanar strips are two metal strips. Both are balanced lines.
Why does frequency change the impedance?: Slot line is not TEM; its field distribution changes with frequency, so impedance and ε_eff depend on h/λ₀.
Synthesis reports no convergence — what now?: The fitted model cannot reach that impedance for the given ε_r, h and f. Adjust the target or the substrate height and stay inside the recommended range.

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