TRANSMISSION LINES AND WAVEGUIDES UNIT-I TRANSMISSION LINE THEORY INTRODUCTION TO TRANSMISSION LINE THEORY Transmission Lines and Waveguides A TRANSMISSION LINE is a device designed to guide electrical energy from one point to another. It is used, for exam ple, to transf er the output rf energy of a transm itter to an antenna. This energy will not travel through norm al electric al wire without great losses. Although the antenna can be connected directly to the transm itter, the antenna is usually located some distance away from the transmitter. On board ship, the transm itter is located inside a radio room, and its associated antenna is m ounted on a mas t. A transm ission line is used to connect the transm itter and the antenna. The transm ission line has a single purpose f or both the transmitter and the antenna. This purpose is to transfer the energy output of the transm itter to the antenna with the least possible power loss. How well this is done depends on the s pecial physical and electrical characteristics (impedance and resistance) of the transmission line. TRANSMISSION LINE THEORY The electrical characteristics of a two-wire transm ission line depend prim arily 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 m agnetic field about them when elec trical 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 that we discussed earlier. For exam ple, 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 m anage to m ove from one conductor to the other through the dielectric. Each type of two-wire transm ission line also has a conductance value. This conductance value represents the value of the current f low that m ay be expec ted through the insulation, If the line is uniform (all values equal at each unit length), then one small section of
the line m ay 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 transm ission lines.W e will explain the theories using LUMPED CONSTANTS and DISTRIBUTED CONSTANTS to further simplify these principle. LUMPED CONSTANTS A transmission line has the properties of inductance, capacitance, and resistance just as the m ore conventional circuits have. Usually, however, the constants in conventional c irc uits are lum ped into a single device or com ponent. For exam ple, a coil of wire has the property of inductance. W hen a certain am ount of inductance is needed in a circuit, a coil of the proper dimensions is inserted. The inductance of the circuit is lum ped into the one com ponent. Two m etal plates separated by a small s pace, can be used to supply the required capacitance for a circuit. In such a case, most of the capacitance of the circuit is lum ped into this one component. Similarly, a fixed resistor can be used to supply a certain value of circuit resistance as a lum ped sum. Ideally, a transm ission line would also have its constants of inductance, capacitance, and resistance lumped together, as shown in figure 3-1. 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 following paragraphs will be useful to you as you study distributed constants on a transmission line.
Two-wire transmission Iine. Inductance of a Transmission Line W hen current flows through a wire, m agnetic lines of force are set up around the wire. As the current increases and dec reases in am plitude, the f ield around the wire expands and collapses accordingly. The energy produced by the magnetic lines of force collapsing back into the wire tends to k eep the current flowing in the same direction. This represents a certain amount of inductance, which is expressed in m icrohenrys per unitlength. Figure illustrates the inductance and magnetic fields of a transm ission line. Capacitance of a Transmission Line Capacitance also exists between the transmission line wires, as illustrated in figure 3-3. Notice that the two parallel wires act as plates of a capacitor and that the air between them acts as a dielectric. The capacitance between the wires is usually expressed in picofarads per unit length. This electric field between the wires is similar to the field that exists between the two plates of a c a p a c it o r . Resistance of a Transmission Line The transm ission line shown in figure 3-4 has electrical resistance along its length. This
resistance is usually expressed in ohms per unit length and is shown as existing continuously from one end of the line to the other.. Leakage Current Since any dielectric, even air, is not a perfect insulator, a small current known as LEAKAGE CURRENT f lows between the two wires. In effect, the insulator acts as a resis tor, perm itting current to pass between the two wires. Figure 3-5 shows this leakage path as resistors in parallel connected between the two lines. This property is called CONDUCTANCE (G) and is the opposite of resistance. Conductance in transmission lines is expressed as the reciprocal of resistance and is usually given in micro mhos per unit length. ELECTROMAGNETIC FIELDS CHARACTERISTIC IMPEDANCE The distributed constants of resistance, inductance, and capacitance are basic properties common to all transmission lines and exist whether or not any current flow exists. As soon as current f low and voltage exist in a transm ission line, another property becomes quite evident. This is the presence of an electromagnetic field, or lines of force, about the wires of the transmission line. The lines of force themselves are not visible; however, understanding the force that an electron experiences while in the field of these lines is very im portant to your understanding of energy transmission. There are two kinds of fields; one is associated with voltage and the other with current. The field assoc iated with voltage is c alled the ELECTRIC (E) FIELD. It exerts a force on any electric charge placed in it. The field associated with current is called a MAGNETIC (H) FIELD, because it tends to extra force on any m agnetic pole placed in it. Figure 3-6 illustrates the way in which the E fields and H f ields tend to orient them selves between conductors of a typical two-wire transmission line. The illustration shows a cross section of the transmission lines. The E field is represented by solid lines and the H field by dotted lines. The arrows indicate the direc tion of the lines of force. Both f ields norm ally exist together and are