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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.

 
Flexible braided coax coaxial cable drawing - RF Cafe Most often used braided flexible (shown at left) and solid tube semi-rigid (shown at right) types are listed here.

Click here for popular coax cable properties.
Semi-rigid coax coaxial cable drawing - RF Cafe


Capacitance (C) = Coaxial cable capacitance equation - RF Cafe


Inductance (L) = Coaxial cable inductance equation - RF Cafe


Impedance (Z0) = Coaxial cable impedance equation - RF Cafe


 


Velocity = Speed of light in a vacuum equation - RF Cafe  %c (speed of light in a vacuum)


Cutoff Frequency =


(here is a calculator)

Reflection Coefficient = Coaxial cable reflection coefficient equation


VSWR = Coaxial cable VSWR equation

Peak Voltage = Coaxial cable peak voltage equation

, where
d = outside diameter of inner conductor in inches
D = inside diameter of outer conductor in inches
S = maximum voltage gradient of cable insulation in volts/mil
ε (εr) = relative dielectric constant
K = safety factor
f = frequency in MHz

Cable attenuation is the sum of the conductor losses and the dielectric losses per the following equations.
Coaxial cable attenuation equation center conductor

Coaxial cable attenuation equation dielectric

ρr = 1 for copper, 10 for steel

Coaxial cable attenuation chart graph

, where d = outside diameter of inner conductor in mm
D = inside diameter of outer conductor in mm
εr = relative dielectric constant
f = frequency in GHz
ρrd = inner conductor material resistivity relative to copper
ρrD = outer conductor material resistivity relative to copper
δ = loss tangent

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