Every real transmission line attenuates signals as they travel. Two independent mechanisms cause this loss: conductor loss (resistive heating in the metal) and dielectric loss (power absorbed in the substrate or insulator). Total attenuation α = αc + αd in Np/m; multiply by 8.686 to convert to dB/m.

Conductor Loss & Skin Effect

At RF frequencies current crowds into a thin surface layer of thickness δs = √(1/πfµ₀σ) — the skin depth. AC resistance rises as √f. The surface resistance (resistance per square) is:

For a coaxial line with inner conductor radius a and outer radius b:

For microstrip the conductor loss depends on the effective strip width w and involves a correction for current crowding at the edges; simplified for w/h > 1:

Dielectric Loss

The loss tangent tan δ of the substrate causes power absorption proportional to frequency. For microstrip (Pozar, Microwave Engineering eq. 3.30):

where k₀ = 2πf/c and εeff is the effective permittivity. For coaxial line:

Dielectric loss is proportional to frequency and often dominates conductor loss at GHz frequencies in lossy substrates such as FR4 (tan δ ≈ 0.02).

Total Loss & Unit Conversion

Insertion loss over a physical length L is simply α_dB × L dB. Both frequency and length increase loss linearly (for dB/m at fixed f, or for fixed length scaling with f).

Propagation Delay

Signals travel at the phase velocity vph = c/√εeff, giving a time delay:

On FR4 microstrip (εeff ≈ 3.5), vph ≈ 0.53c — roughly 6 ps/mm of delay. Delay is independent of frequency for a non-dispersive TEM line.

Practical Values

• FR4 microstrip 50 Ω, 1.6 mm substrate: ≈ 0.5 dB/cm at 10 GHz
• Rogers RO4003C microstrip 50 Ω: ≈ 0.09 dB/cm at 10 GHz (tan δ = 0.0027)
• RG-58 coax: ≈ 0.22 dB/m at 100 MHz; ≈ 1.1 dB/m at 2.4 GHz
• LMR-400 coax: ≈ 0.068 dB/m at 1 GHz; ≈ 0.12 dB/m at 2.4 GHz