Enter the inner diameter, outer diameter, and relative permittivity of a coaxial cable to calculate its impedance, inductance, capacitance, and cutoff frequency.

Coax Cable Formula

The following formula is used to calculate the impedance of a coaxial cable. 

Z = 138 * log (D/d) / Sqrt(pr)
  • Where Z is the impedance
  • D is the outer diameter of the cable
  • d is the inner diameter of the cable
  • pr is the relative permittivity of the material the cable is made from

Some additional formulas for the cable, which the calculator solves for, are as follows: 

Capacitance = 7.354*pr / log(D/d)
  • Units = pF (pico farads)
Inductance = 140.4*log(D/d)
  • Units = nH (nano henries)
Cutoff Frequency = 11.8 / [ SQRT(pr)*pi*((D+d)/2) ]
  • Units = GHz (giga hertz)

Example Problem

How to calculate a coax cable impedance?

First, determine the outer diameter of the cable. The units of this dimension must be the same as the inner diameter or the formulas will not hold. For this example, the outer diameter is 1.25 inches.

Next, determine the inner diameter of the cable. Using the same units as above, the inner diameter is found to be .75 inches.

Next, determine the relative permittivity of the medium, in this case, the material of the cable. For this problem, we will use a relative permittivity of 3.

Finally, calculate the impedance using the formula above:

Z = 138 * log (D/d) / Sqrt(pr)

= 138 * log (1.25/.75) / Sqrt(3)

= 17.675 ohms

Enter the information from above into the calculator to determine the capacitance, inductance, and cutoff frequency.

FAQ

What is the significance of the relative permittivity in a coaxial cable’s performance?

The relative permittivity of the material between the inner and outer conductors of a coaxial cable affects its capacitance and, consequently, its impedance and velocity of propagation. A higher relative permittivity results in higher capacitance, which can slow down the signal transmission speed and affect the cable’s overall performance.

How does the diameter of a coaxial cable influence its electrical properties?

The diameters of the inner and outer conductors of a coaxial cable play a crucial role in determining its impedance, inductance, and capacitance. A larger outer diameter or a smaller inner diameter increases the cable’s impedance. The ratio of these diameters also affects the cable’s ability to carry signals over long distances without significant loss.

Why is the cutoff frequency important for coaxial cables?

The cutoff frequency of a coaxial cable is the maximum frequency at which the cable can effectively transmit a signal without excessive loss. Beyond this frequency, the cable acts more as a filter than a conductor, attenuating the signal rather than transmitting it efficiently. This parameter is crucial for ensuring that the cable supports the desired signal bandwidth for applications such as broadband internet or cable television.