. The Bell System technical journal . Fig. 1—Spherical coordinates. The positive directions of r-, 9-, and vp-coniponentsof a vector are, respectively, the directions of increasing r, 6, and tp. and the impedance in the direction of increasing (p are ~ ~ir~H: 7 _ ^r _ _ jEfl In cyHndrical coordinates we have (Fig. 2): ^^ //. /J 7 = Z. = Fig. 2—Cylindrical coordinates. The positive directions of p-, v?-, and s-coniponentsof a vector are, respectively, the directions of increasing p, , and z. IMPEDANCE CONCEPT AND APPLICATION 27 Usually it is only one of the entire set of three-dimensional
. The Bell System technical journal . Fig. 1—Spherical coordinates. The positive directions of r-, 9-, and vp-coniponentsof a vector are, respectively, the directions of increasing r, 6, and tp. and the impedance in the direction of increasing (p are ~ ~ir~H: 7 _ ^r _ _ jEfl In cyHndrical coordinates we have (Fig. 2): ^^ //. /J 7 = Z. = Fig. 2—Cylindrical coordinates. The positive directions of p-, v?-, and s-coniponentsof a vector are, respectively, the directions of increasing p, , and z. IMPEDANCE CONCEPT AND APPLICATION 27 Usually it is only one of the entire set of three-dimensional imped-ances that is of particular importance, the preferred direction beingfrequently the direction of the wave under consideration. When theratios involved in the above definitions are unequal, it is expedient toresolve the field into component fields for which the ratios are equaLWe shall now consider some special examples. The field of the spherical electromagnetic wave emitted by a Hertziandoublet is known to be £,. = 5ffZ:(l+^)cos<,, (7) lirr^ \ (xr J ^ ^ ^^ ^ alle- /. , 1 \ • . /// = —i 1 + — sin 6, ^ 47rr \ err I where: // is the moment of the doublet in ampere-meters, r is thedistance from the doublet, d the angle made by a typical direction inspace with the axis of the doublet, and ^ is the angle between
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
