What is the telegrapher's equation and how does it relate to transmission line behavior?
Telegrapher's Equations
The telegrapher's equations model a transmission line as an infinite cascade of infinitesimal lumped elements: series resistance R and inductance L (representing conductor properties) and shunt conductance G and capacitance C (representing dielectric properties). This model is valid when the cross-sectional dimensions are much smaller than the wavelength, which is satisfied for all TEM transmission lines below their first higher-order mode.
| 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 |
Frequently Asked Questions
What are typical RLGC values?
For 50 Ω PTFE coax: L ≈ 250 nH/m, C ≈ 100 pF/m, R ≈ 0.5-5 Ω/m (frequency-dependent), G ≈ 0.001-0.1 S/m (frequency-dependent). R increases as √f (skin effect). G increases proportionally to f (dielectric loss).
Can I extract RLGC from S-parameters?
Yes. Measure S-parameters of a known length of transmission line. Convert to ABCD parameters. Extract γ and Z0. Then: R+jωL = γ·Z0 and G+jωC = γ/Z0. This gives RLGC at each measured frequency point.
When do the telegrapher's equations fail?
When the cross-section is not electrically small (dimensions approaching λ/10), when higher-order modes propagate, or when the structure is not uniform along its length (tapers, bends, junctions). In these cases, full-wave electromagnetic simulation is needed.