Standing Waves PDF

Standing Waves Transmission Media and Antenna System (EST 131) Prepared by: Engr. Rochelle M. Sabarillo Standing Waves When a signal is applied to a transmission line, it appears at the other end of the line some time later because of the propagation delay....

Standing Waves Transmission Media and Antenna System (EST 131) Prepared by: Engr. Rochelle M. Sabarillo Standing Waves When a signal is applied to a transmission line, it appears at the other end of the line some time later because of the propagation delay. If a resistive load equal to the characteristic impedance of a line is connected at the end of the line, the signal is absorbed by the load and power is dissipated as heat. If the load is an antenna, the signal is converted to electromagnetic energy and radiated into space. If the load at the end of a line is an open circuit or a short circuit or has an impedance other than the characteristic impedance of the line, the signal is not fully absorbed by the load. When a line is not terminated properly, some of the energy is reflected from the end of the line and actually moves back up the line, toward the generator. This reflected voltage adds to the forward or incident generator voltage and forms a composite voltage that is distributed along the line. This pattern of voltage and its related current constitute what is called a standing wave. Standing waves are not desirable. The reflection indicates that the power produced by the generator is not totally absorbed by the load. In some cases, e.g., a short-circuited or open line, no power gets to the load because all the power is reflected back to the generator. Department of Electrical Engineering & Technology 2 Relationship Between Reflections and Standing Waves Once the signal reaches the right end of the line, a reverse charging effect takes place on the capacitors from right to left. The effect is as if a signal were moving from output to input. This moving charge from right to left is the reflection, or reflected wave, and the input wave from the generator to the end of the line is the incident wave. Department of Electrical Engineering & Technology 3 Matched Lines Ideally, a transmission line should be terminated in a load that has a resistive impedance equal to the characteristic impedance of the line. This is called a matched line. When the load impedance and the characteristic impedance of the line match, the transmission goes smoothly and maximum power transfer—less any resistive losses in the line—takes place. The line can be any length. One of the key objectives in designing antenna and transmission line systems is to ensure this match. Alternating-current voltage (or current) at any point on a matched line is a constant value (disregarding losses). A correctly terminated transmission line, therefore, is said to be flat. Department of Electrical Engineering & Technology 4 Matched Lines If the load impedance is different from the line characteristic impedance, not all the power transmitted is absorbed by the load. The power not absorbed by the load is reflected back toward the source. The power sent down the line toward the load is called forward or incident power; the power not absorbed by the load is called reflected power. The signal actually on a line is simply the algebraic sum of the forward and reflected signals. When the mismatch between load resistive impedance and line impedance is great, the reflected power can be high enough to damage the transmitter or the line itself. Department of Electrical Engineering & Technology 5 Shorted Lines In the case of a short at the end of a line, the voltage is zero when the current is maximum. All the power is reflected back toward the generator. Department of Electrical Engineering & Technology 6 Open Lines With an infinite impedance load, the voltage at the end of the line is maximum when the current is zero. All the energy is reflected, setting up the stationary pattern of voltage and current standing waves shown. Department of Electrical Engineering & Technology 7 Mismatched (Resonant) Lines Most often, lines do not terminate in a short or open circuit. Rather, the load impedance does not exactly match the transmission line impedance. Furthermore, the load, usually an antenna, will probably have a reactive component, either inductive or capacitive, in addition to its resistance. Under these conditions, the line is said to be resonant. Such a mismatch produces standing waves, but the amplitude of these waves is lower than that of the standing waves resulting from short or open circuits. Department of Electrical Engineering & Technology 8 Calculating Standing Wave Ratio The magnitude of the standing waves on a transmission line is determined by the ratio of the maximum current to the minimum current, or the ratio of the maximum voltage to the minimum voltage, along the line. These ratios are referred to as the standing wave ratio (SWR). Department of Electrical Engineering & Technology 9 Calculating Standing Wave Ratio and Reflection Coefficient The ratio of the reflected voltage wave Vr to the incident voltage wave Vi is called the reflection coefficient. The reflection coefficient provides information on current and voltage along the line. Other formulas used are: Department of Electrical Engineering & Technology 10 Calculating Standing Wave Ratio The importance of the SWR is that it gives a relative indication of just how much power is lost in the transmission line and the generator. The curve here shows the relationship between the percentage of reflected power and the SWR. The percentage of reflected power is also expressed by the term return loss and is given directly in watts or decibels (dB) Naturally, when the standing wave ratio is 1, the percentage of reflected power is 0. But as a line and load mismatch grows, reflected power increases. When the SWR is 1.5, the percentage of reflected power is 4 percent. This is still not too bad, as 96 percent of the power gets to the load. Department of Electrical Engineering & Technology 11 Quiz: 1. A 52-Ω coaxial cable has a 36-Ω antenna load. What is the SWR? 2. If the load and line impedances of the cable in Prob. 1 are matched, what is the SWR? 3. The maximum voltage along a transmission line is 170 V, and the minimum voltage is 80 V. Calculate the SWR and the reflection coefficient. 4. The reflection coefficient of a transmission line is 0.75. What is the SWR? 5. A transmission line has an SWR of 1.65. The power applied to the line is 50 W. What is the amount of reflected power? Department of Electrical Engineering & Technology 12 Reminder Prepare for oral recitation. Department of Electrical Engineering & Technology 1 6 Thank You for Listening :) Do you have any questions? Email me at [email protected] or you may post a message in our Google Classroom.