Velocity Factor

            Electrical signals travel very fast but their speed is not infinite. Just how fast depends on the characteristics of the conductor. Transmission lines can be considered to be very uniform conductors; the capacitance and inductance per unit of length is constant over the whole length of the line. Each infinitesimally small series inductance must have its related magnetic field developed and each small parallel capacitor must be charged. All of this takes time and so a signal in a transmission line is delayed compared to the time a radio signal in free space would take to travel the same distance. This delay, the ratio of the speed of transmission of the signal to the speed of light, is called the velocity factor.

           The velocity factor is a physical characteristic of the line and depends primarily on the dielectric used to construct the line. For parallel conductor lines using air dielectric the velocity factor is about 0.98; for polyethylene coaxial cable it is about 0.66. Foam dielectric coaxial cables have air bubbles in the polyethylene and have velocity factors from about 0.70 to 0.85.

Velocity factors are always provided in cable catalogues and also can be determined from most standard reference manuals such as Bill Orr's The Radio Handbook. If you know the dielectric constant for the material separating the two conductors in a transmission line the velocity factor can be calculated using the following relationship:

                                                      1

            Velocity Factor = ----------------------------

                                         √ (Dielectric Constant)

This says that the Velocity Factor for a particular transmission line is equal to the reciprocal of the square root of the dielectric constant of the material between the two conductors.

Voltage Standing Wave Ratio (VSWR)

When a transmission line is not terminated in a load equal to its characteristic impedance, standing waves of voltage and current will exist along the line as a result of reflection from the load end. The magnitude of these reflected waves depends upon the amount of mismatch between Z₀ of the transmission line and the impedance of the load.

The Voltage Standing Wave Ratio, VSWR or SWRfor short, is a measure of the degree of mismatch between the load and the transmission line. It is defined as the ratio of the maximum RMS voltage or current forward to the minimum RMS voltage or current of the resultant standing waves.

These waves do, in fact, stand still on the line. A line terminated in its characteristic impedance, Z₀, will have an VSWR of 1:1 ; with no reflected wave maximum and minimum have the same amplitude. If the line is shorted or open the VSWR is infinite.

                               E_max

                VSWR = -------

                               E_min

                             E_f + E_r

                         = ---------

                             E_f - E_r

where:

E_max is the maximum standing wave voltage
E_min is the minimum standing wave voltage
E_f is the forward RMS voltage (or current)
E_r is the reflected RMS voltage or current

VSWR may also be defined in the context of power:

                             1 + √ p

                VSWR = ----------

                             1 - √ p

where:

p is the ratio p_reflected/p_forward.

In terms of Refection coefficient “Г”

                                          1 + │Г│                  

                       VSWR   = -------------

                                          1 - │Г│                  

Refection coefficient “Г” defined as

                                 V_r

                   Г        = ----

                                 V_f

Where,

                  V_r = reflected wave voltage

                  V_f = forward wave voltage

VSWR is used as an efficiency measure for transmission lines, electrical cables that conduct radio frequency signals, used for purposes such as connecting radio transmitters and receivers with their antennas, and distributing cable television signals. A problem with transmission lines is that impedance mismatches in the cable tend to reflect the radio waves back toward the source end of the cable, preventing all the power from reaching the destination end. SWR measures the relative size of these reflections. An ideal transmission line would have an SWR of 1:1, with all the power reaching the destination and none of the power reflected back. An infinite SWR represents complete reflection, with all the power reflected back down the cable. The SWR of a transmission line can be measured with an instrument called an SWR meter, and checking the SWR is a standard part of installing and maintaining transmission lines.