tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 72

Electromagnetic Field Theory: A Problem Solving Approach Part 72. 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. | Point Dipole Arrays 685 b End-fire Array If however for the same half wavelength spacing the currents are out of phase x 7r the fields add along the x axis but cancel along the y axis. Here even though the path lengths along the y axis are the same for each dipole because the currents are out of phase the fields cancel. Along the x axis the extra tt phase because of the half wavelength path difference is just canceled by the current phase difference of ir so that the fields due to each dipole add. The radiation pattern is called end-fire because the power is maximum in the direction along the array as shown in Figure 9-7e. c Arbitrary Current Phase For arbitrary current phase angles and dipole spacings a great variety of radiation patterns can be obtained as illustrated by the sequences in Figures 9-7 and 9-8. More power lobes appear as the dipole spacing is increased. 9-3-2 An N Dipole Array If we have 2N 1 equally spaced dipoles as shown in Figure 9-9 the nth dipole s distance to the far field point is approximately lim rn r na sin 0 cos 8 r na so that the array factor of 4 generalizes to AF în dln nasin 9 -N where for symmetry we assume that there are as many dipoles to the left negative n as to the right positive n of the z axis including one at the origin n 0 . In the event that a dipole is not present at a given location we simply let its current be zero. The array factor can be varied by changing the current magnitude or phase in the dipoles. For simplicity here we assume that all dipoles have the same length dl the same current magnitude Io and differ in phase from its neighbors by a constant angle Xo so that în Ioe inXo -N n N 10 and 9 becomes AF Iodl N sin e cos -x-0 -N 11 686 Radiation Sr acos2 ttcos 0 X 4 2 5 acos2 jr cos0 X - it 8 4 Sf acos2 7TCOS 0 W 1 d Figure 9-8 With a full wavelength dipole spacing 2a A there are four main power lobes. Point Dipole Arrays 687 Defining the parameter ft _ gi l a sin 0 cos - 0 12 the geometric series in 11 can be .