5.10.4Discontinuities

A transmission line’s characteristic impedance will be constant throughout its length so long as its conductor geometry and dielectric properties are consistent throughout its length. Abrupt changes in either of these parameters, however, will create a discontinuity in the cable capable of producing signal reflections. This is why transmission lines must never be sharply bent, crimped, pinched, twisted, or otherwise deformed.

The probe for a guided-wave radar (GWR) liquid level transmitter is another example of a transmission line, one where the vapor/liquid interface creates a discontinuity: there will be an abrupt change in characteristic impedance between the transmission line in vapor space versus the transmission line submerged in a liquid due to the di ering dielectric permittivities of the two substances. This sudden change in characteristic impedance sends a reflected signal back to the transmitter. The time delay measured between the signal’s transmission and the signal’s reception by the transmitter represents the vapor space distance, or ullage.

For more detail on the theory and function of radar level measurement, see section 20.5.2 beginning on page 1477.

5.10.5Velocity factor

The speed at which an electrical signal propagates down a transmission line is never as fast as the speed of light in a vacuum, owing to the permittivity of the line’s electrical insulation being greater than that of a vacuum. A value called the velocity factor expresses the propagation velocity as a ratio to light, and its value is always less than one:

Velocity factor = vc

Where,

v = Propagation velocity of signal traveling along the transmission line c = Speed of light in a vacuum (≈ 3.0 × 108 meters per second)

Velocity factor is a function of dielectric constant, but not conductor geometry. A greater permittivity value results in a slower velocity (lesser velocity factor).

5.10.6Cable losses

Ideally, a transmission line is a perfectly loss-less conduit for electrical energy. That is, every watt of signal power entering the transmission line is available at the end where the load is connected. In reality, though, this is never the case. Conductor resistance, as well as losses within the dielectric (insulating) materials of the cable, rob the signal of energy.

For transmission lines, power loss is typically expressed in units of decibels per 100 feet or per 100 meters. A “decibel,” as you may recall, is ten times the logarithm of a power ratio:

Gain or Loss in dB = 10 log

P

Pref

Thus, if a transmission line receives 25 milliwatts of signal power at one end, but only conveys

18 milliwatts to the far end, it has su ered a 1.427 dB loss (10 log 00..018025 = −1.427 dB) from end to end. Power loss in cables is strongly dependent on frequency: the greater the signal frequency, the

more severe the power loss per unit cable length.