## 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
StepInstructionsInput
data/units
KeysOutput
data/units
stants into secondary for evalua-
tion of elliptic integrals (all
dimensions in m).
---
5Input coil spacing
After coil radii have been input
once, the variation of M with x
can be found as follows:
xAM
6Enter coil spacingxDM

 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-040RCL 1-080RCL A-
-STO 2x-x-1/x--
-R ----LN-
-STO 1R-x--x--
-R --8--+-
-STO 0r-x--P S-
-*LBL a----STO 9K(m)
-RCL 0-x---P S-
-RCL 1--RCL 6--RCL 7-
010----RCL A-
-STO 3 = r/R050EEX-090x-
-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-
0204--CHS--x2-
-x-060STO A-100x-
-RCL 0--P S--RCL 8-
-x--RCL 2--RCL A-
-RCL 1--RCL A--x-
-x--x--+-
-STO 7k2 = m-RCL 1--RCL A-
---+--1/x-
-STO 6k-RCL A--x-
-GSB E--x--x-
0301--RCL 0--+-
-RCL 7-070+-110P S-
-2--RCL 5--STO 8E(m)
---RCL A--RTN-
---x--* LBL D-
-RCL 9--RCL 4--STO 2-
-x--+--RCL 0-
-RCL 8--RCL A--GTO a-
---x-117RTN-
-RCL 0--RCL 3----
----+----