Coax Impedance / Coaxial Cable Impedance

- details of the calculation, application and determination of coax impedance - coax cable impedance, inductance and capacitance.

All forms of feeder including coax cable have a characteristic impedance.

The coax impedance is one of the main parameters in its specification, one that governs which type of coax cable is obtained.

Coax impedance / characteristic impedance

All feeders possess a characteristic impedance. For RF coax cable there are two main standards that have been adopted over the years, namely 75 and 50 ohms.

75 ohm coax cable is used almost exclusively for domestic TV and VHF FM applications. However for most commercial RF applications 50 ohms coax cable has been taken as the standard for many years.

The reason for the choice of these two impedance standards is largely historical but arises from the properties provided by the two impedance levels:

  • 75 ohm coax cable gives the minimum weight for a given loss
  • 50 ohm coax cable gives the minimum loss for a given weight.

These two standards are used for the vast majority of coax cable which is produced but it is still possible to obtain other impedances for specialist applications. Higher values are often used for computer installations, but other values including 25, 95 and 125 ohms are available. 25 ohm miniature RF cable is extensively used in magnetic core broadband transformers. These values and more are available through specialist coax cable suppliers.

Coax impedance background

When analysed a coaxial cable can be considered as a distributed series inductance with a distributed capacitance between the inner and outer conductors. The levels of inductance can be calculated as seen below.

Coax capacitance

The capacitance of a coaxial line varies with the spacing of the conductors, the dielectric constant, and as a result the impedance of the line. The lower the impedance, the higher the coax capacitance for a given length because the conductor spacing is decreased. The coax capacitance also increases with increasing dielectric constant, as in the case of an ordinary capacitor.

The equation relating the coax cable capacitance to the diameters of the inner and outer conductors and the dielectric constant of the medium between them

Where:
    C = Capacitance in pF / metre
    εr = Relative permeability of the dielectric
    D = Inner diameter of the outer conductor
    d = Diameter of the inner conductor

Coax inductance

The inductance of the line can also be calculated. Again this is proportional to the length of the line.

However the inductance is independent of the dielectric constant for the material between the conductors.

The equation relating the coax cable inductance to the diameters of the inner and outer conductors

Where:
    L = Inductance in µH / metre
    D = Inner diameter of the outer conductor
    d = Diameter of the inner conductor

Coax impedance determination

The impedance of the RF coax cable is chiefly governed by the diameters of the inner and outer conductors. On top of this the dielectric constant of the material between the conductors of the RF coax cable has a bearing. The relationship needed to calculate the impedance is given simply by the formula:

The equation relating the coax cable impedance to the diameters of the inner and outer conductors and the dielectric constant of the medium between them

Where:
    Zo = Characteristic impedance in Ω
    εr = Relative permeability of the dielectric
    D = Inner diameter of the outer conductor
    d = Diameter of the inner conductor

Note: The units of the inner and outer diameters can be anything provided they are the same, because the equation uses a ratio.


Coax Impedance Calculator

     

Enter Values:

Outer diameter:  
Inner diameter:   same units as above.
εr:  
 
 
 
 

Results:

Impedance:   Ω


Importance of coax impedance

The coax impedance is one of the major specifications associated with any piece of coax cable. As it will determine the matching within the system and hence the level of standing waves and power transfer, it is a crucial element. It is therefore necessary to ensure that the correct coax impedance is chosen for any system.

By Ian Poole


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