Cable Impedance Calculator

Transmission line parameters depend heavily on physical dimensions and material properties. For coaxial cables, the characteristic impedance (Z₀) is derived from the inner conductor diameter, the inner surface shield diameter, and the relative permittivity (substrate dielectric constant) of the insulating material. The primary formula for coaxial impedance is Z₀ = (60 / √εᵣ) * ln(D / d), where εᵣ is the substrate dielectric, D is the inner shield diameter, and d is the inner conductor diameter. Additional equations determine distributed capacitance, inductance per unit length, signal propagation delay, and upper cutoff frequency based on these physical geometries.

Consider a coaxial cable configuration with a solid inner conductor diameter (d) of 1 mm, an inner shield diameter (D) of 3.5 mm, and a polyethylene substrate dielectric (εᵣ) of 2.25. First, calculate the natural logarithm of the diameter ratio: ln(3.5 / 1) = ln(3.5) ≈ 1.2528. Next, divide 60 by the square root of the dielectric constant (√2.25 = 1.5), yielding 40. Multiplying 40 by 1.2528 gives a characteristic impedance of approximately 50.1 ohms, which aligns perfectly with standard 50-ohm RF system requirements.

Always verify the manufacturer specifications for your dielectric constant, as moisture absorption and frequency variations can alter effective permittivity. Ensure precise measurements of conductor diameters, as microscopic deviations heavily impact high-frequency impedance matching. Finally, account for cutoff frequency limits when designing wideband applications to prevent unwanted higher-order mode propagation.