Evaluation of the discrete complex-image method for a NEC-like moment-method solution Page: 5 of 12
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The following text was automatically extracted from the image on this page using optical character recognition software:
Co / Re(k.2)
C - - s Re kp)
5 jk2 10 15
Fig. 2. Contours for evaluation of the Sommerfeld integrals: a) contours in the k2 plane, b) contours in the kp
plane, with branch cuts from k, and k2.
The remainders of the potentials after subtracting the quasistatic terms are
v22 = 2 Rv(kz2) kz2 Jo(kpp)k dkp
u22 = 2 Ru(kz2) Jo(kpp)k dkp
kz2 _ 1
Skkzk i+ kz2 k? +k3'
Ru(kz2)= kz2 -1.
kz + kz2 2.
The extracted quasistatic terms can be combined with the free space Green's function for
the image by applying the Sommerfeld identity,
o eikz2(z+z') e- jk2R1
0 kz2 Jo(kp)kp dkp = R1 '
The equations for the electric field components are then
Ev_- jwl"to 82
P 47rk2 apaz
= -jwIpo (02
z 47rk2 (az
EH_- -jWIeRo (82
EH jWIiJ (18a
z 47rk2 apaz
k1 + k2 G21
+kJ 22+ kG21) +S
+ k2 \G22 + 21 o#+ 3H
( - k2G_
+ G22- k2 G21) cosin + SP
+k G22 - k2 + G21 si 0 Sp o4
\22 k2 + k4
where the subscripts on E or S indicate the cylindrical component of the field and the superscript
indicates a vertical electric dipole (V) or horizontal dipole on along the x axis (H). G22 and G21
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Burke, G.J. Evaluation of the discrete complex-image method for a NEC-like moment-method solution, report, January 5, 1996; California. (https://digital.library.unt.edu/ark:/67531/metadc671246/m1/5/: accessed March 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.