Cable Impedance Calculator
Calculate characteristic impedance, inductance, capacitance, propagation velocity, wavelength, delay, and electrical phase from coaxial cable geometry, dielectric properties, length, and operating frequency. Cable Impedance Calculator helps engineers, technicians, and installers design, test, and troubleshoot transmission lines.
Highlights
- Calculate characteristic impedance from coaxial cable geometry and dielectric properties.
- Determine inductance and capacitance per unit length for transmission line modeling.
- Estimate propagation velocity and velocity factor through the cable.
- Calculate signal wavelength and propagation delay at a selected frequency.
- Measure electrical length and phase for transmission line and antenna applications.
Table of Contents
How Cable Impedance Calculator Works?
The calculator models the cable as an ideal coaxial transmission line with a central conductor, a cylindrical outer shield, and a uniform dielectric. Let a be the inner-conductor radius, b be the inside radius of the shield, and εr be the relative permittivity. Because both radii are obtained from the supplied diameters, the impedance depends on the diameter ratio.
Z0 is the characteristic impedance. Increasing the shield-to-conductor diameter ratio increases impedance, while increasing the dielectric permittivity decreases it.
The distributed inductance and capacitance are calculated from the coaxial geometry:
Here, L′ is inductance per unit length and C′ is capacitance per unit length. The constants μ0 and ε0 are the permeability and permittivity of free space. These quantities also satisfy Z0 = √(L′/C′).
For a lossless, homogeneous dielectric, the signal velocity is:
The velocity factor expresses this speed relative to the speed of light:
For operating frequency f and cable length l, the wavelength, one-way propagation delay, and electrical phase are:
The electrical length can also be expressed in radians as θ = 2πl/λ. The calculation requires a shield inner diameter greater than the inner-conductor diameter so that the coaxial geometry is physically meaningful.
| Output | Determining relationship | Meaning |
|---|---|---|
| Characteristic impedance | Z0 = √(L′/C′) | Impedance presented by an infinitely long, uniform line |
| Inductance per length | L′ | Magnetic energy storage along the cable |
| Capacitance per length | C′ | Electric energy storage between conductors |
| Propagation velocity | v = c/√εr | Signal travel speed in the dielectric |
| Wavelength | λ = v/f | Distance represented by one signal cycle inside the cable |
| Propagation delay | t = l/v | One-way travel time through the specified length |
| Electrical length | 360l/λ | Phase accumulation through the cable |
Practical Use Cases
RF and microwave engineers can estimate whether a coaxial geometry will approach a target impedance and determine the wavelength and phase shift at a selected operating frequency when designing matching networks, test fixtures, and RF interconnects.
Antenna installers can calculate the velocity factor, one-way delay, and electrical length of a feed line to understand phase changes between an antenna and radio equipment.
Signal-integrity engineers can use the distributed inductance and capacitance values to create a first-order transmission-line model for high-speed digital or analog links.
Cable manufacturers and designers can compare conductor geometry and dielectric choices to evaluate their effects on characteristic impedance, propagation speed, and wavelength before prototyping.
Field technicians can estimate expected impedance and signal delay from measured cable dimensions and dielectric data when troubleshooting reflections, timing errors, or suspected cable mismatches.
Students and electronics hobbyists can explore how changing the conductor ratio, dielectric permittivity, cable length, or frequency changes the electrical behavior of a coaxial line.
Accuracy and Limitations
The calculator uses closed-form, lossless coaxial-line equations and is accurate for a uniform cable with circular concentric conductors, a homogeneous and frequency-independent dielectric, and propagation dominated by the TEM mode. It does not include conductor resistance, dielectric loss, braid porosity, surface roughness, connector discontinuities, manufacturing tolerances, frequency-dependent permittivity, dispersion, or reflections caused by load mismatch. The reported delay and electrical length are one-way ideal values, and the geometry must have a shield inner diameter greater than the inner-conductor diameter; real cable measurements can therefore differ, especially at high frequencies or with braided, irregular, foam, or multilayer constructions.
Quick Examples
Example #1: Standard RF Coaxial Cable
Estimate transmission-line characteristics for a typical 50-ohm-style coaxial cable used in radio-frequency systems.
Example #2: High-Frequency Test Cable
Analyze a short, low-loss cable operating in the gigahertz range for laboratory and test-equipment connections.
Example #3: Long-Legacy Coaxial Run
Evaluate signal delay, wavelength, and impedance for a long cable installation using a higher-permittivity dielectric.
