What is a transmission line?

From RF Design Wiki · By the RF Design Wiki editorial team · Published October 21, 2026 · Last reviewed October 21, 2026 · How we research

A transmission line is a pair of conductors whose length is a significant fraction of a wavelength, so voltage and current vary along it as traveling waves. It is modeled by per-unit-length resistance R, inductance L, conductance G and capacitance C. The characteristic impedance is Z₀ = √((R + jωL)/(G + jωC)), which is √(L/C) for a lossless line, and the propagation constant is γ = α + jβ = √((R + jωL)(G + jωC)).^[1]

What are the telegrapher's equations?

dV/dz = −(R + jωL)I and dI/dz = −(G + jωC)V. Their solution is a forward wave V⁺e^−γz plus a reflected wave V⁻e^+γz. The ratio V⁻/V⁺ at the load is the reflection coefficient Γ_L = (Z_L − Z₀)/(Z_L + Z₀).^[1]

How does loss behave?

For low loss, α ≈ R/(2Z₀) + GZ₀/2 Np/m (multiply by 8.686 for dB). R rises as √f because of skin effect; G = ωC·tan δ rises as f, so dielectric loss dominates at high frequencies on lossy laminates.^[1]

What types of transmission line are used?

Type	Mode	Typical use
Coaxial	TEM	Cables, connectors
Microstrip	Quasi-TEM	PCB outer layers
Stripline	TEM	Inner PCB layers
Coplanar waveguide	Quasi-TEM	mmWave PCB, MMICs, probing
Rectangular waveguide	TE₁₀	High power, low loss, mmWave
Twisted pair, twin-lead	TEM	Balanced lines

What is phase velocity?

v_p = ω/β = 1/√(LC) for a lossless line, equal to c/√ε_eff. Group velocity equals phase velocity on a dispersionless TEM line; microstrip and waveguide are dispersive.^[1]

Frequently asked questions

When is a trace a transmission line?

When its length exceeds roughly a tenth of the wavelength, or for digital signals when delay exceeds a fraction of the rise time.

Does Z0 depend on length?

No, characteristic impedance depends on geometry and materials, not length.

What is a matched line?

One terminated in its characteristic impedance, so there is no reflection.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

“Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.

Categories: Transmission lines

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