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

TABLE 3.- REGISTERS USED IN
MUTUAL INDUCTANCE PROGRAM

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

Step	Key entry	Comments	Step	Key entry	Comments	Step	Key entry	Comments
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

Return to III-1

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