Transmission Line Impedance Calculator (Coaxial)
Find the characteristic impedance, capacitance per unit length, and velocity factor of a coaxial transmission line from its conductor diameters and dielectric constant.
📡 What is Coaxial Transmission Line Impedance?
A coaxial cable's characteristic impedance (Z0) is the ratio of voltage to current for a signal traveling down the cable, set entirely by its geometry, the outer conductor's inner diameter (D), the inner conductor's outer diameter (d), and the dielectric constant of the insulator between them. It has nothing to do with the cable's length or the load connected at its end; Z0 is a property of the cable itself, the same way resistivity is a property of a material rather than a specific wire.
Matching characteristic impedance correctly is one of the most fundamental tasks in RF and high-speed digital design. A transmitter feeding an antenna through mismatched coax reflects some of its power back toward the source instead of radiating it, wasting output and potentially damaging the transmitter. A cable-TV or satellite installer relies on every connector and cable segment being 75 ohms end to end, since even small impedance discontinuities cause visible signal degradation. High-speed digital interfaces (USB, HDMI, Ethernet) use controlled-impedance cabling for exactly the same reason, at high enough frequencies, any cable behaves as a transmission line, not just a simple wire.
A common misconception is that a cable's impedance depends on what is plugged into it. It does not, Z0 is fixed by the cable's own geometry and dielectric. What does depend on the load is the reflection coefficient and standing wave ratio (VSWR), which describe how much of a signal reflects when the cable's fixed Z0 does not match the load impedance, an entirely separate (though related) calculation.
This calculator takes your coaxial cable's outer and inner conductor diameters and its dielectric constant, and returns the characteristic impedance, the capacitance per unit length, the velocity factor, and a chart showing how Z0 changes as the D/d diameter ratio changes, so you can see at a glance how close a given geometry lands to a standard 50 ohm or 75 ohm target.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — PTFE-Dielectric Cable
D = 8 mm, d = 2 mm, εr = 2.1 (PTFE)
Example 2 — RG-58-Like Cable, Near 50 Ω
D = 7.24 mm, d = 2.05 mm, εr = 2.3 (polyethylene)
Example 3 — Air-Dielectric Line
D = 10 mm, d = 4 mm, εr = 1.0 (air)
❓ Frequently Asked Questions
🔗 Related Calculators
What is the characteristic impedance of a coaxial cable?
Characteristic impedance Z0 is the ratio of voltage to current for a wave traveling down the cable, determined entirely by the cable's geometry (outer diameter D, inner diameter d) and its dielectric constant, not by cable length. It is given by Z0 = (60/sqrt(er)) x ln(D/d).
How do you calculate coaxial cable impedance from its dimensions?
Z0 = (60/sqrt(er)) x ln(D/d), where D is the outer conductor's inner diameter, d is the inner conductor's outer diameter, and er is the relative permittivity (dielectric constant) of the insulating material between them. For D=8mm, d=2mm, er=2.1 (PTFE), Z0 is approximately 57.40 ohms.
Why are 50 ohm and 75 ohm the standard coax impedances?
50 ohms is close to the geometry that maximizes power-handling capacity for a given outer diameter, making it the standard for transmitters and RF test equipment. 75 ohms is close to the geometry that minimizes attenuation (signal loss) for a given outer diameter, making it the standard for long-distance video and cable-TV runs.
What is capacitance per unit length in a coaxial cable?
Capacitance per unit length C' = 2*pi*e0*er / ln(D/d) describes how much charge the cable stores per meter for a given voltage between the conductors. It directly affects the cable's characteristic impedance and its cutoff behavior at high frequencies.
What is velocity factor and why does it matter?
Velocity factor vf = 1/sqrt(er) is the fraction of the speed of light at which a signal actually propagates down the cable. A typical PTFE-dielectric coax has vf around 0.66 to 0.70, meaning the signal travels at about two-thirds the speed of light, important for calculating electrical delay and matching cable length to signal wavelength.
What happens if the outer diameter is not larger than the inner diameter?
The formula requires D/d greater than 1, since ln(D/d) must be positive for a physically valid coaxial geometry (the outer conductor must actually surround the inner conductor with a gap between them). This calculator rejects any input where D is not strictly greater than d.
How does dielectric constant affect impedance?
Z0 is inversely proportional to the square root of the dielectric constant er, so a higher-permittivity insulator (like PVC at er around 3 to 4) produces a lower impedance than a lower-permittivity insulator (like PTFE at er around 2.1) for the exact same conductor diameters.
What is a typical dielectric constant for common coax cable materials?
Air has er = 1.0 (the theoretical minimum), solid PTFE (Teflon) has er around 2.1, polyethylene has er around 2.25 to 2.3, and foam-dielectric cables fall in between air and their base solid material, typically er around 1.4 to 1.6, depending on foam density.
Does frequency affect the characteristic impedance calculated here?
No, not in this idealized lossless-line model. The geometric characteristic impedance Z0 = (60/sqrt(er)) x ln(D/d) is frequency-independent by definition. Real cables show a small impedance variation at very low or very high frequencies due to skin effect and dielectric loss, which this simplified calculator does not model.
Can this calculator be used for cable design, not just analysis?
Yes. Enter your target Z0 as a design goal, then adjust the D/d ratio or dielectric constant inputs and recalculate until the computed Z0 matches your target, the chart makes it easy to see how much D/d needs to change for a given dielectric to hit a specific impedance.