tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 65

Electromagnetic Field Theory: A Problem Solving Approach Part 65. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Figure 8-20 a The load impedance at z 0 reflected back to the source is found using the 6 Smith chart for various line lengths. Once this impedance is known the source current is found by solving the simple series circuit in c . 615 616 Guided Electromagnetic Waves 8-4-4 Standing Wave Parameters The impedance and reflection coefficient are not easily directly measured at microwave frequencies. In practice one slides an ac voltmeter across a slotted transmission line and measures the magnitude of the peak or rms voltage and not its phase angle. From 6 the magnitude of the voltage and current at any position z is i z v i r z i z l r0 v i-r z 23 From 23 the variations of the voltage and current magnitudes can be drawn by a simple construction in the T plane as shown in Figure 8-21. Note again that V is just a real number independent of z and that T z 1 for a passive termination. We plot l F z and 11-F z since these terms are proportional to the voltage and current magnitudes respectively. The following properties from this con- figure 8-21 The voltage and current magnitudes along a transmission line are respectively proportional to the lengths of the vectors HT z and 11 F z in the complex r plane. Arbitrary Impedance Terminations struction are apparent i The magnitude of the current is smallest and the voltage magnitude largest when T z 1 at point A and vice versa when T z 1 at point B. ii The voltage and current are in phase at the points of maximum or minimum magnitude of either at points A or B. iii A rotation of T z by an angle 17 corresponds to a change of A 4 in z thus any voltage or current maximum is separated by A 4 from its nearest minima on either side. By plotting the lengths of the phasors 11 T z as in Figure 8-22 we obtain a plot of what is called the standing wave pattern on the line. Observe that the curves are not sinusoidal. The minima are sharper than the maxima so the minima are usually located in position more precisely by measurement than the .

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