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:

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 xcan 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=k^{3} |

R8 | E(m), elliptic integral of first kind |

R9 | K(m), elliptic integral of second kind |

RA | m_{1} = 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.

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 | - |

- | x^{2} | - | - | RTN | - | - | x | - |

- | RCL 2 | - | - | *LBL E | - | - | 1 | - |

- | x^{2} | - | - | RCL 7 | - | - | + | - |

- | + | - | - | 1 | - | - | RCL 9 | - |

- | 1/x | - | - | - | - | RCL A | - | |

020 | 4 | - | - | CHS | - | - | x^{2} | - |

- | 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 | k^{2} = 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 | - | - | - | - |

- | - | - | - | + | - | - | - | - |