impedance calculator coaxial cable - Aaron Graves, PhDude Replica

Coaxial Cable Impedance Calculator

Calculate characteristic impedance (Z₀) and related transmission-line values for an ideal coaxial cable.

Inner conductor diameter, d

Inner diameter of outer conductor, D

Use the same units for both d and D (mm, inches, etc.). Only the ratio D/d matters for Z₀.

Relative permittivity (ε_r)

Relative permeability (μ_r)

Cable length (meters, optional)

Frequency (MHz, optional, for wavelength)

What this coaxial impedance calculator does

This tool estimates the characteristic impedance of a coaxial transmission line using conductor geometry and dielectric properties. In practical RF design, this is one of the first checks you do when building or selecting a cable for radios, test equipment, antennas, and high-speed systems.

In addition to impedance, the calculator also returns useful derived values:

Velocity factor
Propagation velocity
Delay per meter
Approximate capacitance and inductance per meter
Total capacitance and one-way delay for a chosen cable length
Wavelength in cable (if frequency is entered)

Core formula used

Characteristic impedance of ideal coax

The calculator uses the standard lossless coax approximation:

Z₀ = 60 × √(μ_r/ε_r) × ln(D/d)

D = inner diameter of the outer conductor
d = outer diameter of the inner conductor
ε_r = relative permittivity of dielectric
μ_r = relative permeability (usually ~1 for non-magnetic materials)

If you assume μ_r = 1 (common for PE, PTFE, and foam dielectrics), this simplifies to: Z₀ ≈ (60 / √ε_r) ln(D/d).

How to use the calculator

Enter the center conductor diameter d.
Enter the shield inner diameter D.
Enter dielectric constant ε_r.
Leave μ_r at 1 unless you have a special magnetic dielectric.
Optionally add length and frequency for extra outputs.
Click Calculate.

Important: D must be greater than d. If not, the logarithm term fails and the line geometry is physically invalid.

Typical coax target impedances

Most real-world cables target one of these values:

50 Ω — RF transmit systems, instrumentation, lab cables
75 Ω — video, CATV, SDR receive chains, lower attenuation applications
93 Ω — some specialized instrumentation and legacy systems

Example D/d ratios (μ_r = 1)

Dielectric	ε_r (approx.)	D/d for 50 Ω	D/d for 75 Ω
Air	1.00	2.30	3.49
Foam PE	1.43	2.71	4.46
Solid PE / PTFE-ish example	2.25	3.49	6.52

Design notes for better accuracy

1) Real cables are not perfectly lossless

This calculator gives ideal transmission-line values. Actual cable behavior depends on conductor loss, dielectric loss tangent, braid coverage, temperature, and frequency.

2) Keep dimensions consistent

Because impedance depends on ratio D/d, you can input mm or inches. Just ensure both diameters use the same unit.

3) Dielectric constant matters a lot

Small changes in ε_r shift impedance and velocity factor. Manufacturer datasheets may list effective ε_r values that better match real cable construction.

Quick interpretation of results

Z₀ high? Increase ε_r or reduce D/d ratio.
Z₀ low? Decrease ε_r or increase D/d ratio.
Velocity factor tells how fast signals propagate relative to the speed of light.
Delay helps when matching cable lengths in phased or timing-critical systems.

Final takeaway

A coaxial cable impedance calculator is a fast way to validate geometry before prototyping. If you need precision for production-grade RF hardware, use this as a first-pass design tool, then verify with manufacturer data, simulation, and VNA measurements.