Module 10—Introduction to Wave Propagation, Transmission Lines, and Antennas Pages
i  ix, 11 to 110,
111 to 120, 121 to 130,
131 to 140, 141 to 147,
21 to 210, 211 to 220,
221 to 230, 231 to 240,
240 to 247, 31 to 310,
311 to 320, 321 to 330,
331 to 340, 341 to 350,
351 to 358, 41 to 410,
411 to 420, 421 to 430,
431 to 440, 441 to 450,
451 to 460, Index
Figure 332.—Voltage, current, and impedance on open line. At all odd quarterwave points (1/4λ, 3/4λ, etc.), the voltage is minimum, the current is maximum, and the impedance is minimum. Thus, at all odd quarterwave points, the openended transmission line acts as a seriesresonant circuit. The impedance is equivalent to a very low resistance, prevented from being zero only by small circuit losses. At all even quarterwave points (1/2λ, 1λ, 3/2λ, etc.), the voltages is maximum, the current is minimum, and the impedance is maximum. Comparison of the line with an LC resonant circuit shows that at an even number of quarterwavelengths, an open line acts as a parallelresonant circuit. The impedance is therefore an extremely high resistance. In addition, resonant open lines may also act as nearly pure capacitances or inductances. The illustration shows that an open line less than a quarterwavelength long acts as a capacitance. Also, it acts 341
as an inductance from 1/4 to 1/2 wavelength, as a capacitance from 1/2 to 3/4 wavelength, and as an inductance from 3/4 to 1 wavelength, etc. A number of open transmission lines, with their equivalent circuits, are shown in the illustration. Impedance of Various Lengths of Shorted Lines Follow figure 333 as we study the shorted line. At the odd quarterwavelength points, the voltage is high, the current is low, and the impedance is high. Since these conditions are similar to those found in a parallelresonant circuit, the shorted transmission line acts as a parallelresonant circuit at these lengths. Figure 333.—Voltage, current, and impedance on shorted line.
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At the even quarterwave points voltage is minimum, current is maximum, and impedance is minimum. Since these characteristics are similar to those of a seriesresonant LC circuit, a shorted transmission line whose length is an even number of quarterwavelengths acts as a seriesresonant circuit. Resonant shorted lines, like openend lines, also may act as pure capacitances or inductances. The illustration shows that a shorted line less than 1/4 wavelength long acts as an inductance. A shorted line with a length of from 1/4 to 1/2 wavelength acts as a capacitance. From 1/2 to 3/4 wavelength, the line acts as an inductance; and from 3/4 to 1 wavelength, it acts as a capacitance, and so on. The equivalent circuits of shorted lines of various lengths are shown in the illustration. Thus, properly chosen line segments may be used as parallelresonant, seriesresonant, inductive, or capacitive circuits. STANDING WAVES ON A TRANSMISSION LINE There is a large variety of terminations for rf lines. Each type of termination has a characteristic effect on the standing waves on the line. From the nature of the standing waves, you can determine the type of termination that produces the waves. TERMINATION IN Z_{0} Termination in Z_{0} (characteristic impedance) will cause a constant reading on an ac meter when it is moved along the length of the line. As illustrated in figure 334, view A, the curve, provided there are no losses in the line, will be a straight line. If there are losses in the line, the amplitude of the voltage and current will diminish as they move down the line (view B). The losses are due to dc resistance in the line itself. 343
Figure 334.—Effects of various terminations on standing waves. TERMINATION IN AN OPEN CIRCUIT In an opencircuited rf line (figure 334, view C), the voltage is maximum at the end, but the current is minimum. The distance between two adjacent zero current points is 1/2λ, and the distance between alternate zero current points is 1. The voltage is zero at a distance of 1/4λ from the end of the line. This is true at any frequency. A voltage peak occurs at the end of the line, at 1/2λ from the end, and at each 1/2λ thereafter. 344
TERMINATION IN A SHORT CIRCUIT On the line terminated in a short circuit, shown in figure 334, view D, the voltage is zero at the end and maximum at 1/4λ from the end. The current is maximum at the end, zero at 1/4λ from the end, and alternately maximum and zero every 1/4λ thereafter. TERMINATION IN CAPACITANCE When a line is terminated in capacitance, the capacitor does not absorb energy, but returns all of the energy to the circuit. This means there is 100 percent reflection. The current and voltage relationships are somewhat more involved than in previous types of termination. For this explanation, assume that the capacitive reactance is equal to the Z_{0} of the line. Current and voltage are in phase when they arrive at the end of the line, but in flowing through the capacitor and the characteristic impedance (Z_{0}) connected in series, they shift in phase relationship. Current and voltage arrive in phase and leave out of phase. This results in the standingwave configuration shown in figure 334, view E. The standing wave of voltage is minimum at a distance of exactly 1/8 from the end. If the capacitive reactance is greater than Z_{0} (smaller capacitance), the termination looks more like an open circuit; the voltage minimum moves away from the end. If the capacitive reactance is smaller than Z_{0}, the minimum moves toward the end. TERMINATION IN INDUCTANCE When the line is terminated in an inductance, both the current and voltage shift in phase as they arrive at the end of the line. When X_{L} is equal to Z_{0}, the resulting standing waves are as shown in figure 334, view F. The current minimum is located 1/8λ from the end of the line. When the inductive reactance is increased, the standing waves appear closer to the end. When the inductive reactance is decreased, the standing waves move away from the end of the line. TERMINATION IN A RESISTANCE NOT EQUAL TO THE CHARACTERISTIC IMPEDANCE (Z_{0}) Whenever the termination is not equal to Z_{0}, reflections occur on the line. For example, if the terminating element contains resistance, it absorbs some energy, but if the resistive element does not equal the Z_{0} of the line, some of the energy is reflected. The amount of voltage reflected may be found by using the equation: Where: ER = the reflected voltage Ei = the incident voltage RR = the terminating resistance Z_{0}= the characteristic impedance of the line If you try different values of R_{L} in the preceding equation, you will find that the reflected voltage is equal to the incident voltage only when R_{L} equals 0 or is infinitely large. When R_{L} equals Z_{0}, no reflected voltage occurs. When RL is greater than Z_{0}, E_{R} is positive, but less than E_{i}. As R_{L} increases and 345
approaches an infinite value, E_{R} increases and approaches E_{i} in value. When R_{L} is smaller than Z_{0}, E_{R} has a negative value. This means that the reflected voltage is of opposite polarity to the incident wave at the termination of the line. As R_{L} approaches zero, E_{R} approaches E_{i} in value. The smaller the value of E_{R}, the smaller is the peak amplitude of the standing waves and the higher are the minimum values. TERMINATION IN A RESISTANCE GREATER THAN Z_{0} When RL is greater than Z0, the end of the line is somewhat like an open circuit; that is, standing waves appear on the line. The voltage maximum appears at the end of the line and also at halfwave intervals back from the end. The current is minimum (not zero) at the end of the line and maximum at the odd quarterwave points. Since part of the power in the incident wave is consumed by the load resistance, the minimum voltage and current are less than for the standing waves on an openended line. Figure 334, view G, illustrates the standing waves for this condition. TERMINATION IN A RESISTANCE LESS THAN Z_{0} When R_{L} is less than Z_{0}, the termination appears as a short circuit. The standing waves are shown in figure 334, view H. Notice that the line terminates in a current LOOP (peak) and a voltage NODE (minimum). The values of the maximum and minimum voltage and current approach those for a shorted line as the value of R_{L} approaches zero. A line does not have to be any particular length to produce standing waves; however, it cannot be an infinite line. Voltage and current must be reflected to produce standing waves. For reflection to occur, a line must not be terminated in its characteristic impedance. Reflection occurs on lines terminated in opens, shorts, capacitances, and inductances, because no energy is absorbed by the load. If the line is terminated in a resistance not equal to the characteristic impedance of the line, some energy will be absorbed and the rest will be reflected. The voltage and current relationships for openended and shorted lines are opposite to each other, as shown in figure 334, views C and D. The points of maximum and minimum voltage and current are determined from the output end of the line, because reflection always begins at that end. Q26. A nonresonant line is a line that has no standing waves of current and voltage on it and is considered to be flat. Why is this true? Q27. On an open line, the voltage and impedance are maximum at what points on the line? STANDINGWAVE RATIO The measurement of standing waves on a transmission line yields information about equipment operating conditions. Maximum power is absorbed by the load when Z_{L} = Z_{0}. If a line has no standing waves, the termination for that line is correct and maximum power transfer takes place. You have probably noticed that the variation of standing waves shows how near the rf line is to being terminated in Z_{0}. A wide variation in voltage along the length means a termination far from Z0. A small variation means termination near Z_{0}. Therefore, the ratio of the maximum to the minimum is a measure of the perfection of the termination of a line. This ratio is called the STANDINGWAVE RATIO (swr) and is always expressed in whole numbers. For example, a ratio of 1:1 describes a line terminated in its characteristic impedance (Z_{0}). 346
Voltage StandingWave Ratio The ratio of maximum voltage to minimum voltage on a line is called the VOLTAGE STANDING WAVE RATIO (vswr). Therefore: The vertical lines in the formula indicate that the enclosed quantities are absolute and that the two values are taken without regard to polarity. Depending on the nature of the standing waves, the numerical value of vswr ranges from a value of 1 (ZL = Z0, no standing waves) to an infinite value for theoretically complete reflection. Since there is always a small loss on a line, the minimum voltage is never zero and the vswr is always some finite value. However, if the vswr is to be a useful quantity, the power losses along the line must be small in comparison to the transmitted power. Power StandingWave Ratio The square of the voltage standingwave ratio is called the POWER STANDINGWAVE RATIO (pswr). Therefore: This ratio is useful because the instruments used to detect standing waves react to the square of the voltage. Since power is proportional to the square of the voltage, the ratio of the square of the maximum and minimum voltages is called the power standingwave ratio. In a sense, the name is misleading because the power along a transmission line does not vary. Current StandingWave Ratio The ratio of maximum to minimum current along a transmission line is called CURRENT STANDINGWAVE RATIO (iswr). Therefore: This ratio is the same as that for voltages. It can be used where measurements are made with loops that sample the magnetic field along a line. It gives the same results as vswr measurements. Q28. At what point on an opencircuited rf line do voltage peaks occur? Q29. What is the square of the voltage standingwave ratio called? Q30. What does vswr measure? 347
SUMMARY This chapter has presented information on the characteristics of transmission lines. The information that follows summarizes the important points of this chapter. TRANSMISSION LINES are devices for guiding electrical energy from one point to another. INPUT IMPEDANCE is the ratio of voltage to current at the input end of a transmission line. OUTPUT IMPEDANCE is the ratio of voltage to current at the output end of the line. TWOWIRE OPEN LINES are parallel lines and have uses such as power lines, rural telephone lines, and telegraph lines. This type of line has high radiation losses and is subject to noise pickup. TWIN LEAD has parallel lines and is most often used to connect televisions to their antennas. A TWISTED PAIR consists of two insulated wires twisted together. This line has high insulation loss. 348
A SHIELDED PAIR has parallel conductors separated by a solid dielectric and surrounded by copper braided tubing. The conductors are balanced to ground. RIGID COAXIAL LINE contains two concentric conductors insulated from each other by spacers. Some rigid coaxial lines are pressurized with an inert gas to prevent moisture from entering. Highfrequency losses are less than with other lines. FLEXIBLE COAXIAL LINES consist of a flexible inner conductor and a concentric outer conductor of metal braid. The two are separated by a continuous insulating material. WAVEGUIDES are hollow metal tubes used to transfer energy from one point to another. The energy travels slower in a waveguide than in free space. 349
COPPER LOSSES can result from power (I^{2} R) loss, in the form of heat, or skin effect. These losses decrease the conductivity of a line. DIELECTRIC LOSSES are caused by the heating of the dielectric material between conductors, taking power from the source. RADIATION and INDUCTION LOSSES are caused by part of the electromagnetic fields of a conductor being dissipated into space or nearby objects. A transmission line is either electrically LONG or SHORT if its physical length is not equal to 1/4λ for the frequency it is to carry. LUMPED CONSTANTS are theoretical properties (inductance, resistance, and capacitance) of a transmission line that are lumped into a single component. DISTRIBUTED CONSTANTS are constants of inductance, capacitance and resistance that are distributed along the transmission line. 350
Introduction to Matter, Energy, and Direct Current, Introduction
to Alternating Current and Transformers, Introduction to Circuit Protection,
Control, and Measurement, Introduction to Electrical Conductors, Wiring Techniques,
and Schematic Reading, Introduction to Generators and Motors,
Introduction to Electronic Emission, Tubes, and Power Supplies,
Introduction to SolidState Devices and Power Supplies,
Introduction to Amplifiers, Introduction to
WaveGeneration and WaveShaping Circuits, Introduction to Wave Propagation, Transmission
Lines, and Antennas, Microwave Principles,
Modulation Principles, Introduction to Number Systems and Logic Circuits, Introduction
to Microelectronics, Principles of Synchros, Servos, and Gyros,
Introduction to Test Equipment, RadioFrequency
Communications Principles, Radar Principles, The Technician's Handbook,
Master Glossary, Test Methods and Practices, Introduction to Digital Computers,
Magnetic Recording, Introduction to Fiber Optics
