TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 61

Electromagnetic Field Theory: A Problem Solving Approach Part 61. 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. | The Transmission Line Equations The surface charge per unit length q and magnetic flux per unit length A are 2tTEV MW f6 ui b A dr In - Jo 2tt a so that the capacitance and inductance per unit length of this structure are v In b a i 2ir a where we note that as required LC Efi Substituting Er and into 12 yields the following transmission line equations dEr dHj dv di 1JL dz dt dz dt dH dEr di dv dz dt dz dt 8-1-3 Distributed Circuit Representation Thus far we have emphasized the field theory point of view from which we have derived relations for the voltage and current. However we can also easily derive the transmission line equations using a distributed equivalent circuit derived from the following criteria i The flow of current through a lossless medium between two conductors is entirely by displacement current in exactly the same way as a capacitor. ii The flow of current along lossless electrodes generates a magnetic field as in an inductor. Thus we may discretize the transmission line into many small incremental sections of length Az with series inductance L Az and shunt capacitance C Az where L and C are the inductance and capacitance per unit lengths. We can also take into account the small series resistance of the electrodes R Az where R is the resistance per unit length ohms per meter and the shunt conductance loss in the dielectric G Az where G is the conductance per unit length siemens per meter . If the transmission line and dielectric are lossless R 0 G 0. 576 Guided Electromagnetic Waves The resulting equivalent circuit for a lossy transmission line shown in Figure 8-5 shows that the current at z Az and z differ by the amount flowing through the shunt capacitance and conductance i z t i z Az t CAzMz G Az v z t 26 dt Similarly the voltage difference at z Az from z is due to the drop across the series inductor and resistor v z 0- v z Az t T Az Z Az i z Az t R Az 27 dt By dividing 26 and 27 through by Az and taking the limit as Az- 0 we obtain the lossy .

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