Microstrip Structure
Microstrip consists of a conducting strip of width W on the top of a dielectric substrate of height H and relative permittivity εr, backed by a solid ground plane on the bottom. The electromagnetic field is partially in the dielectric and partially in the air above the strip, making microstrip a quasi-TEM transmission line with an effective permittivity εe < εr.
Closed-Form Impedance Formulas (Hammerstad-Jensen)
Let u = W/H
For u ≤ 1:
εe = (εr+1)/2 + (εr−1)/2 · (1 + 12/u)^−0.5
Z₀ = (60/√εe) · ln(8/u + u/4)
For u > 1:
εe = (εr+1)/2 + (εr−1)/2 · (1 + 12/u)^−0.5
Z₀ = (120π/√εe) / [u + 1.393 + 0.667·ln(u + 1.444)]
Accuracy: better than 1% for 0.05 ≤ u ≤ 20
50 Ω Trace Width for Common Substrates (H = 1.6 mm)
| Substrate | εr | W (50 Ω, H=1.6 mm) | εe | vp (× c) |
|---|---|---|---|---|
| FR4 | 4.5 | 2.94 mm | 3.43 | 0.54 |
| Rogers RO4003C | 3.55 | 3.50 mm | 2.81 | 0.60 |
| Rogers RO4350B | 3.66 | 3.43 mm | 2.88 | 0.59 |
| RT/Duroid 5880 | 2.20 | 4.73 mm | 1.88 | 0.73 |
| Taconic TLX-8 | 2.55 | 4.32 mm | 2.11 | 0.69 |
Guided Wavelength and Quarter-Wave Lengths at Key Frequencies
| Frequency | FR4 λg | FR4 λ/4 | RO4003C λg | RO4003C λ/4 |
|---|---|---|---|---|
| 900 MHz | 178 mm | 44.5 mm | 198 mm | 49.5 mm |
| 1800 MHz | 89 mm | 22.3 mm | 99 mm | 24.8 mm |
| 2.4 GHz | 67 mm | 16.7 mm | 74 mm | 18.5 mm |
| 5 GHz | 32 mm | 8.0 mm | 36 mm | 9.0 mm |
| 28 GHz | 5.7 mm | 1.4 mm | 6.4 mm | 1.6 mm |
Attenuation
Conductor loss: αc ≈ Rs/(Z₀·W) [dB/m, Rs = skin-effect resistance] Dielectric loss: αd ≈ 27.3·εr·(εe−1)·tan(δ) / [λ₀·√εe·(εr−1)] [dB/m] Typical total loss at 2.4 GHz: FR4 (1 oz copper): ~1.5–2.5 dB/100 mm RO4003C: ~0.5–0.8 dB/100 mm RT/Duroid 5880: ~0.2–0.4 dB/100 mm
RF View Microstrip Calculator: In the Utilities tab, enter substrate εr, height H, and strip width W to get Z₀, εe, λg, and quarter-wave length at any frequency. Results feed directly into the Auto Matching synthesizer for one-click microstrip matching.