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Coaxial Cable Equations

Most professional engineers and technicians will never have the need to calculate the capacitance, inductance, or impedance of a coaxial cable since they are usually designing systems using well-defined components that are manufactured to exacting specifications. Students, hobbyists (Ham radio operators), and research types are probably the ones most likely to actually plug numbers into a calculator. For those people, I present these equations.

 

Braided Flexible Coax
Flexible braided coax coaxial cable drawing - RF Cafe
Semi-Rigid Coax
Semi-rigid coax coaxial cable drawing - RF Cafe

 

Capacitance (C)

 

  Coaxial Cable Capacitance - RF Cafe

, where

a = outside radius of inner
      conductor (inches)

b = inside radius of outer
      conductor (inches)

c = speed of light in a vacuum
   = 299,792 km/s = 186,282 mi/s

ε = dielectric constant = ε0 * εr

ε0 = permittivity of free space
    = 8.85419x10-12 F/m

εr = relative dielectric constant

μr = relative permeability

Coaxial cable capacitance per unit length equation - RF Cafe

Coaxial cable pF/ft equation - RF Cafe

Coaxial cable pF/meter equation - RF Cafe

Note: a and b can be in any units of length as long as they are both the same.

Inductance (L)

Note: a and b can be in any units of length as long as they are both the same. However, l must be in the units shown.

Impedance (Z0)

Coaxial cable impedance equation - RF Cafe

Note: a and b can be in any units of length as long as they are both the same. L has units of Farads and C has units of Henries.

Speed of Light (%c)

Speed of light in coaxial cable equation - RF Cafe

Note: V has the same length units as c.

Cutoff Frequency

Coaxial cable cutoff frequency (inches, GHz) - RF Cafe

Coaxial cable cutoff frequency (mm, GHz) - RF Cafe

Note: a and b must be in units of length shown.

Reflection Coefficient & VSWR

Coaxial cable reflection coefficient equation - RF Cafe     Coaxial cable VSWR equation - RF Cafe

Note: Γ is unitless. VSWR is written as a VSWR:1 ratio.

Coaxial Cable Attenuation

Cable attenuation is the sum of the conductor losses and the dielectric losses per the following equations.

Coaxial cable attenuation equation conductor - RF Cafe

Coaxial cable attenuation equation dielectric - RF Cafe


Coaxial cable attenuation chart graph - RF Cafe

Note: While re-working this page I was able to confirm all equations with original sources except these two, so use them with caution. I cannot recall where I got them.

, where

a = outside diameter of inner
      conductor (m)

b = inside diameter of outer
      conductor (m)

 f = frequency (GHz)

Z = impedance (Ω)

tan(δ) = loss tangent

εr = relative dielectric constant

ρra = inner conductor material
        resistivity relative to copper

ρrb = outer conductor material
        resistivity relative to copper

Note: ρr = 1 for copper,
             = 10 for steel

Related Pages on RF Cafe
- Coaxial Cable Specifications
- Capacitor Dielectrics & Descriptions
- Dielectric Constant, Strength, & Loss Tangent
- Conductor Bulk Resistivity & Skin Depths
- Coaxial Cable Equations
- Coaxial Cable Specifications
- Coaxial Cable Vendors
- Coaxial Resonator
- Skin Depth Calculator
- Coaxial Connector Usage Chart