A transmission line is used to connect a radio antenna
with the transceiver. It allows to carry the power of the transmitter over
an appreciable distance without much loss due to conductor resistance,
insulator losses or radiation.
A transmission line can be considered as a long ladder network of series inductances (along the conductors) and shunt capacitances (between inner and outer conductors). It differs from conventional L-C circuits in the fact that the network elements are uniformly distributed along the line. If the inductance and capacitance per unit length are L and C, then the characteristic impedance of the transmission line is:
Z0 = L/CNotice, that in this model there are no dissipative elements (resistors) so no energy is lost while electromagnetic signals are send along the line.
For the geometric topology of coaxial transmission lines the inductance and capacitance per unit length can be expressed as a function of the dimensions of the conductors. Thus also the characteristic impedance can be calculated from the physical dimensions:
Z0 = 158 * log(D/d) for air-core coaxWith D and d the diameter of the outer conductor and inner connector respectively.
If the medium between the conductors of a transmission line
is air, the travelling waves will propagate along the line with the same speed
as waves in free space. If a dielectric material is used between the conductors
for insulation or support purposes, the waves will travel considerably slower.
The ratio pf the velocity on the line to the velocity in free space is known
as velocity factor. It is approximately 0.66 for solid polythene cables such as
the popular RG-xxx cables.
If a transmission line is terminated by a resistive load
equal in value to its characteristic impedance, on one end and a generator
with source impedance also equal in value to the characteristic line impedance,
there is no reflection at the line ends and the line carries a pure travelling
wave.This is the situation of optimal power transfer from generator to load.
SWR = Z0/Z or Z/Z0 (whichever is greater)If the line system is mismatched, there is a standing wave along the line. Voltage and current amplitudes along the line are not constant but vary with the distance along the line. The SWR can also me expressed in the voltage or current ratios:
SWR = Imax/Imin SWR = Vmax/VminA simple SWR meter measuring the power ratio of the forward and backward waves can be used to measure the efficiency of a transmission line system.
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