30-06-2012, 02:11 PM
Study of transmission lines.
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THEORY:
Transmission lines or feeders are almost always used for connecting a transmitter and its antenna(or antenna and receiver) and it is usually regarded as a part of the antenna system.
Transmission lines are a means to convey electrical signals or power between two points separated appreciably in distance the simplest type of transmission lines is a pair of parallel wires insulated from each other as shown below. It is also know as two wire balanced transmission line.
BASIC PRINCIPLE OF TRANSMISSION LINES:
Transmission lines basic principles are applicable in understanding some aspects of antenna theory fopr example definition, current and voltage distribution etc. The basic principles are studied in terms of the two wire balanced transmission lines.
A transmission line electrical problem differs from the simple four terminal network of circuit theory in one aspect i.e. as the input voltage Vs is applied at the input terminals, it takes a finite time in reaching to end terminals. therefore ,a finite time is needed for the voltage and current to travel the length of the transmission line just as the electromagnetic wave has a finite velocity in space.
PRIMARY CONSTANTS OF A TRANSMISSION LINES:
i. RESISTANE ®:is defined as loop inductance per unit length of line .it is sum of resistance of both the wires for unit line length and its unit is ohm/km.
ii. INDUCTANCE(L):is defined as loop inductance per unit length of the line it is the sum of inductance of both wires for unit line length and its unit is henries/km.
iii. CONDUCTANCE(G):is defined as shunt conductance between the two conductors per unit length of line and its unit is mhos/km.
iv. CAPACITANCE© :is defined as shunt capacitance between two conductors per unit length of line and its unit is farad/km.
BASIC TRANSMISSION LINE EQUATIONS:
V = A e-αx. e-jβx + B eαx. ejβx
I =Ce-αx. e-jβx + Deαx. ejβx
The first term in the equation of voltage and current shows that there exist a voltage and current components traveling towards the load impedance. these are called incident waves which decay exponentially in the positive direction of x i.e. away from source and suffer a phase shift of β radians per unit length of transmission line similarly the second terms represents a wave similar to incident wave but traveling from the load end of the line towards source end .these are know as reflected waves.
CHARACTERISTIC IMPEDANCE(Z0)TRANMISSION LINE:
The characteristic impedance(Z0)of a transmission line is defined as the steady satiate vector ratio of the voltage to the current at the input of an infinite line.
Z0=√{R+jwL)/(G+jwC)}=√(Z/Y)
This is the equation of characteristic impedance in which Z is series impedance per section and Y is shunt admittance per section is the resistance ,L is inductance, G is conductance is the capacitance.