Radio Propagation Past a Pair of Dielectric Interfaces
Radio Propagation Past a Pair of Dielectric Interfaces
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„_ ic ox (H) (-Tt^*^' ♦£i-4)'i = 0, 'lE^ T — 2 y > y - 0, X - 5 - We seek a solution of the form (12) u(x, y) = u. (x, y) + u (x, y) and add the condition that u (x, y) and its first derivatives be bounded and continuous in any finite nei ::hborhood of the origin. In Section 3 this condition will be shown to be sufficient to guarantee that the origin behaves neither as a source nor a sink. The solution of this problem will occupy our attention for the balance of the report. 2. Solution Introdu...ce the complex v-plane 19 V » p e in which we define the radical (1) R(v) = v4^-v^ as follows: Assume k to have a vanishingly small ima?;inary part e |k| ie ind draw the branch cuts from ♦k and -k to infinity along the rays • = e and 9 = n + e respectively (cf. Figure 3)» If we choose v-k-pe, -2n+e^^^^ ^ ^ (v -k cos e^) Z'(v) dv -lU - where we recall the definitions (2) r- ^^'-P') 2ni P*(k cos e^) (3) a = z'(k cos 9) - sin e + A* - b' cos^ 9 5 2 ' 2 It is convenient to make the transformations (5) V » k cos ^ and (6) X = p cos 9 y «= p sin © so that (l) becomes P^kcog0) e^^P^°^ ^'^-^^ sin^d) (7) u (p, 9) = -Y ^ y^ (cos - cos e^) z'(k cos 0) where the contour C is taken as shown in Figure 5.
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You can find similar books in the "Read Also" column, or choose other free books by Julian Kane to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
„_ ic ox (H) (-Tt^*^' ♦£i-4)'i = 0, 'lE^ T — 2 y > y - 0, X - 5 - We seek a solution of the form (12) u(x, y) = u. (x, y) + u (x, y) and add the condition that u (x, y) and its first derivatives be bounded and continuous in any finite nei ::hborhood of the origin. In Section 3 this condition will be shown to be sufficient to guarantee that the origin behaves neither as a source nor a sink. The solution of this problem will occupy our attention for the balance of the report. 2. Solution Introdu...ce the complex v-plane 19 V » p e in which we define the radical (1) R(v) = v4^-v^ as follows: Assume k to have a vanishingly small ima?;inary part e |k| ie ind draw the branch cuts from ♦k and -k to infinity along the rays • = e and 9 = n + e respectively (cf. Figure 3)» If we choose v-k-pe, -2n+e^^^^ ^ ^ (v -k cos e^) Z'(v) dv -lU - where we recall the definitions (2) r- ^^'-P') 2ni P*(k cos e^) (3) a = z'(k cos 9) - sin e + A* - b' cos^ 9 5 2 ' 2 It is convenient to make the transformations (5) V » k cos ^ and (6) X = p cos 9 y «= p sin © so that (l) becomes P^kcog0) e^^P^°^ ^'^-^^ sin^d) (7) u (p, 9) = -Y ^ y^ (cos - cos e^) z'(k cos 0) where the contour C is taken as shown in Figure 5.
What to read after Radio Propagation Past a Pair of Dielectric Interfaces?
You can find similar books in the "Read Also" column, or choose other free books by Julian Kane to read onlineMoreLess
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