Basic Electrical Engineering Series
Transmission Lines
Transmission line theory uses 2 port network theory, and is concerned with a line of any length which may be considered to consist of a distributed network of series impedances and shunt admittances. The series impedance consists of a series inductive element and a series 'copper loss' resitive element. The shunt admittance consists of a shunt capacitve element and shunt 'leakage' conductance.
These constitute what are known as the secondary line parameters, as follows:
R – series resitance per unit length (copper loss)
L – series inductance per unit length
C – shunt capacitance per unit length
G – shunt conductance per unit length (leakage)
In a transmission line we are concerned with the transmission of power along the line, which is subject to attenuation and phase distortion. These effects are combined in what is known as the complex propagation coefficient.
The rel;ationship between these quantaties are as follows:
where g is the propagation coefficient, a is the attenuation coefficient and b is the phase chnge coefficient.
These quantaties are known as the primary line parameters.
The primary line parameters are related to the secondary line parameters as follows.
the characteristic impedance, Zo is
Hyperbolic Line Equations
For a line of length l, the sending end voltage and current are related to the receiveing end voltage and current as follows:
and from the dividend of these two expressions
Transmission Matrix of a line
Consider the two port network circuit below.
General two port network
The equations representing this circuit are as follows:
V1 = AV2 + B I2
I1 = CV2 + D I2
For a transmission line of length l, the transfer matrix is as follows
Transmission Line Parrameter Determination
The secondary line parrameters may be determined from the geometry of the cable, line etc, and from these the primary parrameters found.
However two simple practical tests may be carried out and from these measurements, all parrameters determined.
The two tests required are the open and short circuit line impedances. That is the input impedance of the line with the output shorted, and the input impedance of the line with the output open circuit.
From these the following may be determined
to be continued