Coaxial Cable Assembly
Tharaka Dissanayake, PhD (Elec)

What are the things that we have to consider in ordering a cable assembly? First and foremost we have to decide the type of cable, whether it is RG, Semi-Rigid etc. Then we have to decide the connector series, SMA, BNC etc. We can specify the plug type, whether it is straight, bent or some other special type. The connectors come with various body plating; mainly Gold, Nickel and Silver. For the cables used under extreme environmental conditions we may wish to have the connector body passivated to prevent rust formation. In addition, the outer cover and shielding of the coax can vary between products. Let us look at some technical terms and definitions related to coaxial cables.

Characteristic Impedance

By definition, the characteristic impedance is the impedance measured at one end of a transmission line with infinite length. Of course, infinite length transmission lines do not exist, then why should we characterize coaxial cables as 50 Ω, 75 Ω or 300 Ω? The values are important in impedance matching. If the device you connect to the cable has input impedance equal to the characteristic impedance of the cable, then the device is matched to the transmission line. A maximum power transfer can be guaranteed from cable to the device and vice versa, when they are impedance matched. The characteristic impedance of a coaxial cable is given by

(1) where - relative permittivity of the inner dielectric of the coax, D - outer diameter of the dielectric cylinder, d - diameter of the inner conductor. Obviously, the characteristic impedance depends on the ratio between the diameters and the permittivity of the dielectric. For many dielectrics the relative permeability () is equal to 1. If not it must be included in (1).

Cutoff Frequency

It is important to know the largest frequency the coax can handle without signal distortion for proper operation of our cable assembly. This frequency is known as the cutoff frequency. Beyond this frequency it is possible that the signals transmitted through coax are contaminated by higher order modes. The cutoff frequency of a coax is given by

(2)

Note that the units of D and d are in millimeters. (Remember, if you find real numbers in equations, always inquire the units of the parameters). According to (2) it is possible to increase the cutoff frequency by decreasing the conductor diameter. For high frequency applications thin coaxial wires are required. However, it is not possible to make conductor diameter as small as you like. Let us look at the losses in coaxial cables to understand the reason.

Losses in Cables

The losses in cables are basically twofold. One is the conductor loss and the other is the dielectric loss. The conductor loss is obviously a result of the resistance of conductors. The dielectric loss is caused by the complex permittivity of the dielectric material used in the coax.

The resistive loss is given by

(3)

 is the resistivity of the outer conductor and  is the resistivity of the inner conductor.  is the frequency.  and  are relative permeability of the outer and inner conductors, respectively. The loss given by (3) is caused by the phenomena called the skin effect and it is proportional to the square root of the frequency. Moreover, the larger the diameters the lower the loss. As we have seen earlier the cutoff frequency is reduced when the diameters are increased. That is the reason why we have to compromise between the cutoff and the losses.

The dielectric loss is given by

(4)

The  is the tangent of the angle of the complex permittivity of the dielectric material, known as the loss tangent. Do not worry if you are not comfortable with complex numbers. Usually the dielectric material data provide the loss tangent straightaway. Note that the dielectric loss is proportional to the frequency as opposed to the conductor loss, which is proportional to the square root of the frequency. Therefore, at higher frequencies dielectric loss tends to dominate over the conductor loss.

Combining Cables and Connectors

Just like the cable properties, the connectors have their own losses and cutoff frequencies. Therefore, when you are building cable assemblies it is important to know the limits. For example, an SMA connector may have the cutoff frequency of 18 GHz. If you use this connector with a RG-58A cable, which has the cutoff of 35 GHz, the cutoff frequency of the assembly is only going to be 18 GHz. The same applies to losses. From manufacturer data it is possible to calculate the loss of a piece of cable you are using. However, if the interface between the cable and the connector is not properly made, using an expensive low-loss cable and connectors in your cable assembly is pointless. Therefore, it is important to get your cable assembly made by a reliable supplier and get each and every piece tested for quality.