How do I calculate the loss per unit length of a microstrip line at a given frequency?
Microstrip Loss Components
Understanding the individual loss mechanisms enables optimization. Conductor loss is minimized by using wider traces (lower current density), smooth copper foil (reduces roughness correction), and thicker copper (lower sheet resistance). Dielectric loss is minimized by choosing low-tan δ substrates. Radiation loss is minimized by using thinner substrates (h/λ << 1) and avoiding discontinuities (bends, steps, junctions).
| Parameter | Semi-Rigid | Conformable | Flexible |
|---|---|---|---|
| Loss (dB/m at 10 GHz) | 0.8-2.5 | 1.0-3.0 | 1.5-5.0 |
| Phase Stability | Excellent | Good | Fair |
| Bend Radius | Fixed after forming | Hand-formable | Continuous flex OK |
| Shielding (dB) | >120 | >90 | >60-90 |
| Cost (relative) | 2-5x | 1.5-3x | 1x |
Cable Selection Criteria
Conductor loss for microstrip: αc ≈ (Rs/(Z0·W)) × K_roughness, where Rs = √(πfμ/σ) is the surface resistance and K_roughness is the Hammerstad roughness correction factor. At 10 GHz on copper: Rs = 0.026 Ω/sq. For a 50 Ω, 59 mil wide trace: αc ≈ 0.026/(50×0.059×25.4) × Np/mm, converted to dB/inch.
- Performance verification: confirm specifications against the application requirements before finalizing the design
- Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
- Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades
- Interface compatibility: verify impedance, connector type, and mechanical form factor match the system architecture
Loss and Phase Stability
Dielectric loss for microstrip: αd = (πf√εeff × tan δ)/(c) × (εr/εeff) × ((εeff-1)/(εr-1)), in Np/m. This simplifies to approximately: αd (dB/inch) ≈ 2.3 × f(GHz) × tan δ × √εeff, for a rough estimate. The dielectric loss is independent of trace width, so it cannot be reduced by changing the geometry.
Frequently Asked Questions
Which loss dominates?
Below 1-3 GHz: conductor loss dominates on all substrates. Above 3-10 GHz: dielectric loss dominates on FR4. On low-loss laminates (Rogers, PTFE), conductor loss may dominate up to 20-30 GHz. Above 30-40 GHz, surface roughness becomes the dominant conductor loss mechanism.
How do I reduce conductor loss?
Use wider traces (lower Z0 if acceptable), thicker copper (2 oz instead of 1 oz), smooth copper foil (HLP or VLP), and gold plating only where necessary (gold increases loss). For minimum-loss designs, consider Z0 of 35-40 Ω instead of 50 Ω if the system can accommodate the lower impedance.
Is radiation loss significant?
For straight traces on thin substrates (h < λ/20), radiation loss is negligible. But at discontinuities (bends, T-junctions, open stubs), radiation can be significant above 10 GHz. Each 90° microstrip bend radiates approximately 0.1-0.3 dB at 30 GHz on 10 mil substrates. Use chamfered or curved bends to minimize radiation.