Transmission Line Loss & Delay

Calculates conductor loss, dielectric loss, total insertion loss, and propagation delay for microstrip traces and coaxial cables. Conductor loss is dominated by skin effect and scales as √f; dielectric loss scales linearly with f and loss tangent.

Equations & Parameters ▸

\(R_s = \sqrt{\dfrac{\pi f \mu_0}{\sigma}}\qquad \alpha_c = 8.686\,\dfrac{R_s}{Z_0\,w_{\rm eff}}\;\text{dB/m}\qquad \alpha_d = 8.686\,\dfrac{k_0\,\varepsilon_r(\varepsilon_{\rm eff}-1)\tan\delta}{2\sqrt{\varepsilon_{\rm eff}}\,(\varepsilon_r-1)}\;\text{dB/m}\) \(t_d = \dfrac{L\sqrt{\varepsilon_{\rm eff}}}{c}\)

R_s	Surface resistance (Ω/sq) — sets skin-effect conductor loss
α_c	Conductor attenuation constant (dB/m)
α_d	Dielectric attenuation constant (dB/m); requires loss tangent tan δ > 0
t_d	Propagation delay (s); v_p = c/√ε_eff
σ	Conductivity: copper 5.8×10⁷, gold 4.1×10⁷, aluminum 3.5×10⁷ S/m

Microstrip: Hammerstad-Jensen ε_eff and Z₀. Coaxial: both conductors assumed same σ; result is lower bound (braided/stranded cables have higher loss). Set tan δ = 0 for lossless dielectric.

Line Type

Line type

Common Inputs

Frequency, f

Line length, L

Microstrip Parameters

Substrate εr

Loss tangent, tan δ

Trace width, w

Substrate height, h

Conductor thickness, t

Conductivity, σ

Results

Diagram