How this calculator works
Ideal cable geometry sets characteristic impedance. Coax uses the shield inner diameter and centre conductor outer diameter. Parallel-pair mode uses equal wire diameters and centre-to-centre spacing in a homogeneous dielectric; it neglects twisting and jacket boundaries. Delay and distributed capacitance and inductance follow the TEM wave relations. The optional coax cutoff is a rough TE11 estimate, not a rated operating limit.
Formula
Coax Z0 = 60 ln(D/d)/sqrt(er). Pair Z0 = 120 acosh(S/d)/sqrt(er). Delay/m = sqrt(er)/c; C/m = delay/Z0; L/m = delay x Z0; coax TE11 cutoff approximately 2c/[pi(D+d)sqrt(er)].
Worked example
An air-filled coax with D/d = e has approximately 60 ohms impedance. With er = 4, the same geometry has 30 ohms and twice the propagation delay.
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Frequently asked questions
Is characteristic impedance the DC resistance?
No. It is the wave voltage-to-current ratio of the line. Conductor DC resistance is a separate property.
Why is pair spacing measured between centres?
The parallel-wire expression uses centre-to-centre distance. Add one wire diameter to an edge-to-edge gap.
Does this describe every twisted pair cable?
No. Twist pitch, insulation and surrounding materials change its fields. Use a manufacturer specification for an actual cable.