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# General Theory of Transmission Lines

A TRANSMISSION LINE is a device designed to guide electrical energy from one point to another. It is used, for example, to transfer the output rf energy of a transmitter to an antenna.

GENERAL THEORY OF TRANSMISSION LINES

## Introduction:

A TRANSMISSION LINE is a device designed to guide electrical energy from one point to another. It is used, for example, to transfer the output rf energy of a transmitter to an antenna. This energy will not travel through normal electrical wire without great losses. Although the antenna can be connected directly to the transmitter, the antenna is usually located some distance away from the transmitter.

On board ship, the transmitter is located inside a radio room, and its associated antenna is mounted on a mast. A transmission line is used to connect the transmitter and the antenna. The transmission line has a single purpose for both the transmitter and the antenna.

This purpose is to transfer the energy output of the transmitter to the antenna with the least possible power loss. How well this is done depends on the special physical and electrical characteristics (impedance and resistance) of the transmission line.

## Transmission Line Theory:

The electrical characteristics of a two-wire transmission line depend primarily on the construction of the line. The two-wire line acts like a long capacitor. The change of its capacitive reactance is noticeable as the frequency applied to it is changed. Since the long conductors have a magnetic field about them when electrical energy is being passed through them, they also exhibit the properties of inductance.

The values of inductance and capacitance presented depend on the various physical factors are:

For example, the type of line used, the dielectric in the line, and the length of the line must be considered. The effects of the inductive and capacitive reactance of the line depend on the frequency applied. Since no dielectric is perfect, electrons manage to move from one conductor to the other through the dielectric.

Each type of two-wire transmission line also has a conductance value. This conductance value represents the value of the current flow that may be expected through the insulation, If the line is uniform (all values equal at each unit length), then one small section of the line may represent several feet. This illustration of a two-wire transmission line will be used throughout the discussion of transmission lines; but, keep in mind that the principles presented apply to all transmission lines.

A transmission line has the properties of inductance, capacitance, and resistance just as the more conventional circuits have. Usually, however, the constants in conventional circuits are lumped into a single device or component. For example, a coil of wire has the property of inductance. When a certain amount of inductance is needed in a circuit, a coil of the proper dimensions is inserted.

The inductance of the circuit is lumped into the one component. Two metal plates separated by a small space, can be used to supply the required capacitance for a circuit. In such a case, most of the capacitance of the circuit is lumped into this one component. Similarly, a fixed resistor can be used to supply a certain value of circuit resistance as a lumped sum.

Ideally, a transmission line would also have its constants of inductance, capacitance, and resistance lumped together. Unfortunately, this is not the case. Transmission line constants are as described in the following paragraphs.

## Distributed Constants:

Transmission line constants, called distributed constants, are spread along the entire length of the transmission line and cannot be distinguished separately. The amount of inductance, capacitance, and resistance depends on the length of the line, the size of the conducting wires, the spacing between the wires, and the dielectric (air or insulating medium) between the wires.

The electrical lines which are used to transmit the electrical waves along them are represented as transmission lines. he parameters of a transmission line are: Resistance (R),Inductance (L),Capacitance (C), Conductance (G). Hence transmission line is called distributed network.

Resistance (R) is defined as the loop resistance per unit length of the wire. Unit : ohm/Km Inductance (L) is defined as the loop inductance per unit length of the wire. Unit: Henry/Km Capacitance (C) is defined as the loop capacitance per unit length of the wire.Unit :Farad/Km Conductance(G) is defined as the loop conductance per unit length of the wire.Unit: mho/Km

## Application of transmission lines.

1.They are used to transmit signal i.e. EM Waves from one point to another.

2.They can be used for impedance matching purpose.

3.They can be used as circuit elements like inductors, capacitors.

4.They can be used as stubs by properly adjusting their lengths.

Wavelength of a line is the distance the wave travels along the line while the phase angle is changing through 2π radians is a wavelength.

Characteristic impedance is the impedance measured at the sending end of the line. It is given by Z0 = Z/Y,where Z = R + jwL is the series impedance Y = G + jwC is the shunt admittance.

The secondary constants of a line are:

(i)              Characteristic Impedance

(ii)            Propagation Constant

Since the line constants R, L, C and G are distributed through the entire length of the line, they are called as distributed elements. They are also called as primary constants.

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