- Technical Blog From My Notebook

Sunday, June 19, 2016

Power measurement in a transmission line

In a transmission line, power is measured by means of a voltmeter between the conductors,and an ammeter in series with one of the conductors (Fig.). Then the power, P (in watts) is equal to the product of the voltage E (in volts) and the current I(in amperes). This technique can be used in any transmission line, be it for 60-Hz utility service, or in a radio transmitting station. But is this indication of power the same as the power actually dissipated by the load at the end of the line? Not necessarily.

Recall, from the discussion of impedance, that any transmission line has a characteristic impedance. This value, Zo, depends on the size of the line conductors, the spacing between the conductors, and the type of dielectric material that separates the conductors. For a coaxial cable, Zo can be anywhere from about 50 to 150 Ω. For a parallel-wire line, it can range from about 75 Ω to 600 Ω.If the load is a pure resistance R containing no reactance, and if R _ Zo, then thepower indicated by the voltmeter/ammeter scheme will be the same as the true power
dissipated by the load. The voltmeter and ammeter must be placed at the load end of the transmission line.
If the load is a pure resistance R, and R < Zo or R > Zo, then the voltmeter and ammeter will not give an indication of the true power. Also, if there is any reactance in the load, the voltmeter/ammeter method will not be accurate.
The physics of this is rather sophisticated, and a thorough treatment of it is beyond
the scope of this course. But you should remember that it is always desirable to have the load impedance be a pure resistance, a complex value of R _ j0, where R _ Zo. Small discrepancies, in the form of a slightly larger or smaller resistance, or a small reactance, can sometimes be tolerated. But in very-high-frequency (VHF), ultra-high-frequency (UHF) and microwave radio transmitting systems, even a small impedance mismatch between the load and the line can cause excessive power losses in the line.

An impedance mismatch can usually be corrected by means of matching transformersand/or reactances that cancel out any load reactance.

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