PURPOSE: to calculate the mutual impedance between filamentary monopoles.
METHOD: In the induced emf formulation, the mutual impedance of coupled dipoles is
where I2(t) denotes the current distribution (normalized to unit terminal current) on dipole 2, and E1(t) is the field of dipole 1 when it transmits with unit terminal current. Distance along the axis of dipole 2 is denoted by the cordinate t. E1 may be expressed as the sum of the fields from each of the monopoles comprising dipole 1. Furthermore, the integral is the sum of the integrations over each of the monopoles comprising dipole 2. Thus, the dipole-dipole mutual impedance may be expressed as the sum of four monopole-monopole impedances.
It may be convenient to draw the above figure in terms of monopoles with the current distribution shown as dotted lines. (The monopole letters remain the same.)
The surface impedance is calculated just above statement 2. B01 denotes J0 / J1 where J0 and J1 are the Bessel functions of order zero and one with complex argument, ZARG. It is assumed that all the wire segments have the same radius, conductivity and surface impedance.
In the DO LOOP ending with statement 3, SGANT calculates the segment lengths D(J). DMIN and DMAX denote the lengths of the shortest and longest segments. If the wire radius or the segment lengths are clearly beyond the range of thin-wire theory, N is set to zero at statement 4 followed by RETURN to the main program to abort the calculation.
At statement 5, the program selects a segment K, and a few statements below this it selects another segment L. K is a segment of test dipole I, and L is a segment of expansion mode J. The mutual impedance between segments K and L is obtained by calling subroutine GGS or GGMM. In statement 18, this impedance is lumped into C(MMM). The mutual impedance Zij between dipoles I and J is the sum of four segment-segment impedances, The variables IFLAG and JFLAG are used if a ground plane is present for the calculation of the mutual impedance elements. If IFLAG is equal to JPLAG, the mutual impedance terms will not have the effects of a ground plane since both monopoles lie on the same side of the ground interface. If the monopoles are on the opposite sides of the interface (IFLAG not equal to JFLAG), the reflection coefficient correction must be applied to the mutual impedance elements. This same technique is applied in subroutines GNFLD and GFFLD.
In SGANT, segment K has endpoints KA and KB, and segment L has endpoints LA and LB. It is convenient to think of KA and KB as points 1 and 2 on segment K, and LA and LB as points 1 and 2 on L. The four segment-segment impedances can be defined as P(IS,JS). The first subscript IS refers to the terminal point on segment K, and the second subscript JS refers to the terminal point on L. Thus IS=1 or 2 if dipole I has its terminal point I2(I) at KA (point 1) or KB (point 2), respectively. Similarly, JS=l or 2 if mode J has its terminal point I2(J) at LA or LB. The impedances P(IS,JS) are defined with the following reference directions for current flow: from point 1 toward point 2 on each segment. If dipole I has this same reference direction on segment K, FI = 1; otherwise FI = -1. Similarly FJ = 1 or -1 in accordance with the reference direction for mode J on segment L. In statement 18, P(IS,JS) is multiplied by FI and FJ before its contribution is added to Zij.
Subroutine GGMM calculates the impedances Q(KK,LL) which are like the P(IS,JS) but have different conventions for reference directions and subscript meaning. The transformation from the Q impedances to the P impedances is accomplished in the DO LOOP ending with statement 13.
If the wire has finite conductivity, the appropriate modification is applied to the impedance matrix just above statement 15. The terms arising from the dielectric shell on an insulated segment are obtained from subroutine DSHELL just above statement 16. Finally, the lumped loads, ZLD, are added to the diagonal elements of the impedance matrix in the DO LOOP ending at statement 23.
K is a segment of test dipole I, and L is a segment of expansion node J. when the segment numbers K and L are equal, SGANT calls GGMM to obtain the mutual impedance between two filamentary electric monopoles. These monopoles are parallel and have the same length. monopole K is positioned on the axis of the wire segment, and monopole L is on the surface of the sane wire segment. Thus, the displacement is equal to the wire radius. The two monopoles are side-by-side with no stagger.
When segments K and L intersect, SGANT again calls GGMM for the mutual impedance between the two filamentary monopoles. monopole K is situated on the axis of wire segment K, and monopole L is on the surface of wire segment L. The axes of segments K and L define a plane P, and monopole K lies in this plane, monopole L is parallel with plane P and is displaced from it by a distance equal to the wire radius.
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Last modified on: 3 Nov 2007