## APPENDIX A MUTUAL INDUCTANCE OF TWO COAXIAL COILS

This program computes the mutual inductance of a pair of coaxial circular coils as a function of the two radii and their axial separation (see tables 2-4). All units are MKS. The geometry of the coils is shown below:

TABLE 2.- INSTRUCTIONS FOR USE
Step Instructions Input
data/units
Keys Output
data/units
1 Load sides 1 and 2 - - -
2 Load data card containing con-
stants into secondary for evalua-
tion of elliptic integrals (all
dimensions in m).
- - -
3 Enter first coil radius r ENT -
4 Enter second coil radius R ENT -
5 Input coil spacing
After coil radii have been input
once, the variation of M with x
can be found as follows:
x A M
6 Enter coil spacing x D M
 RO First coil radius R1 SEcond coil radius R2 Coil spacing R3 Ratio of coil spacing R6 k R7 m=k3 R8 E(m), elliptic integral of first kind R9 K(m), elliptic integral of second kind RA m1 = 1- m SO 1.3862944 S1 0.1119723 S2 0.0725296 S3 0.5 S4 0.1213478 S5 0.0288729 S6 0.4630151 S7 0.1077812 S8 0.2452727 S9 0.0412496

M = mutual inductance pf coil pair (henries)

where

Complete elliptic integrals of the first and second kind are

The test case is: r = 0.2, R = 0.25, and x = 0.1, which should be inserted as follows: 0.2 [ENT ] 0.25 [ENT ] 0.1 [A] 2.4877X10-7 at x = 0.2 m, 0.2 [D] 1,23945X10-7. Rational approximations to K(m) and E(m) are from reference 14.

TABLE 4.- CALCULATOR PROGRAM FOR MUTUAL INDUCTANCE OF TWO COAXIAL COILS
001 *LBLA - 040 RCL 1 - 080 RCL A -
- STO 2 x - x - 1/x - -
- R - - - - LN -
- STO 1 R - x - - x- -
- R - - 8 - - + -
- STO 0 r - x - - P S -
- *LBL a - - - - STO 9 K(m)
- RCL 0 - x - - - P S -
- RCL 1 - - RCL 6 - - RCL 7 -
010 - - - - RCL A -
- STO 3 = r/R 050 EEX - 090 x -
- RCL 0 - - CHS - - RCL 6 -
- RCL 1 - - 7 - - + -
- + - - x - - RCL A -
- x2 - - RTN - - x -
- RCL 2 - - *LBL E - - 1 -
- x2 - - RCL 7 - - + -
- + - - 1 - - RCL 9 -
- 1/x - - - - RCL A -
020 4 - - CHS - - x2 -
- x - 060 STO A - 100 x -
- RCL 0 - - P S - - RCL 8 -
- x - - RCL 2 - - RCL A -
- RCL 1 - - RCL A - - x -
- x - - x - - + -
- STO 7 k2 = m - RCL 1 - - RCL A -
- - - + - - 1/x -
- STO 6 k - RCL A - - x -
- GSB E - - x - - x -
030 1 - - RCL 0 - - + -
- RCL 7 - 070 + - 110 P S -
- 2 - - RCL 5 - - STO 8 E(m)
- - - RCL A - - RTN -
- - - x - - * LBL D -
- RCL 9 - - RCL 4 - - STO 2 -
- x - - + - - RCL 0 -
- RCL 8 - - RCL A - - GTO a -
- - - x - 117 RTN -
- RCL 0 - - RCL 3 - - - -
- - - - + - - - -

Appendix B