hp-15c Program Index and documentation

This program calculates solutions to common reactance problems and also allows an inductor to be specified. Solver is not needed to do reactance calculations. The equations can be solved directly. The advantage with using Solver is that programs can be shorter. An example is here.

The equations which follow are all used in this program. An unknown variable C, L or f can be calculated by entering it as zero.

- C = 1/((2πf)
^{2}L) capacitance in farads - L = 1/((2πf)
^{2}C) inductance in henrys - f = 1/(2π√(LC)) frequency in hertz
- Xc = 1/(2πfC) capacitive reactance in ohms
- Xl = 2πfL inductive reactance in ohms
- T = 5040√((18*d +40*l)L)/d calculate coil turns given inductance L (henrys), coil diameter d (mm) and coil length l (mm).

- T ≈ 45000√(L/d) for coils with a 2:3 ratio of diameter d (mm) to length. L is in henrys.

set unknown to zero. Its value will be calculated.

R/S

The reactances are now in registers 4 and 5. At resonance the values are the same. New values of C, L and f can be stored in registers 1, 2 and 3.

GSB 4 for capacitive reactance Xc and GSB 5 for inductive reactance Xl.

If you wish you can enter C, L and f directly in registers 1, 2 and 3. Store 0 for the unknown variable.

Press GSB B to calculate the value for the unknown variable.

You can calculate an approximate number of turns for an inductor using the Wheeler formula. See also the ARRL Handbook.

Turns = 5040*√((18*d +40*l)L)/d where L is in henrys, d is the diameter of the winding in mm, l is the length of the winding in mm. The factor 5040 in front of the standard Wheeler formula corrects for henrys instead of microhenrys (1000) and mm instead of inches (5.04).

d ENTER l ENTER GSB 8

An approximation or rough check for the Wheeler formula is T = 40√(aL)/d where a is the average of the coil length l and diameter d. L is in microhenries. For a 10 microhenry, 20 mm diameter, 30 mm long coil the Wheeler formula shows 31.5 turns and the approximation shows 31.6 turns. With more extreme size ratios the error is greater.

For coils with a 2:3 diameter to length ratio an even simpler formula is T = 45 √(L/d). This formula shows 31.8 turns.

Using the inductance stored in register 2, enter the coil diameter d GSB 9 to test this simplified formula. In this program the factor is 45000 since L in register 2 is in henrys.

0 ENTER 1 EEX CHS 6 ENTER 1 EEX 6 GSB A

R/S

RCL 4 Xc = 6.28 ohms

RCL 5 Xl = 6.28 ohms

1 EEX 7 STO 3 - The frequency is increased 10 times to 10 Mhz.

GSB 4 Xc = 0.63 ohms

GSB 5 Xl = 62.83 ohms

0 ENTER RCL 2 RCL 3 GSB A

For resonance at 10 MHz the capacitor should now be 253 picofarads.

For a coil, diameter d = 20 mm and length l = 20 mm:

2 0 ENTER 2 0 GSB 8

8.6 turns are required. This inductor is loaded with a lot of capacitance. Reducing capacitance to 15 picofarads requires a 17 microhenry inductor of 35 turns.

Name | Description | Name | Description | ||
---|---|---|---|---|---|

A | Enter capacitance, Inductance and frequency. Unknown value is entered as zero. | 2 | * RCL3, x^2, 1/x code fragment | ||

B | Calculate unknown | 4 | Calculate capacitive reactance Xc | ||

C | Get capacitance | 5 | Calculate inductive reactance Xl | ||

D | Get inductance | 8 | Calculate number of turns using the Wheeler formula | ||

E | Get frequency | 9 | Simple turns calculator using 45000 √(L/d), L is in henrys | ||

1 | 1/(2π)^2 code fragment |

Name | Description | |
---|---|---|

1 | Capacitance C farads | |

2 | Inductance L henrys | |

3 | Frequency f hertz | |

4 | Capacitive reactance Xc ohms | |

5 | Inductive reactance Xl ohms | |

6 | 2π temporary storage | |

7 | Inductor length l mm | |

8 | Inductor diameter d mm |

Line | Display | Key Sequence | Line | Display | Key Sequence | Line | Display | Key Sequence | |||
---|---|---|---|---|---|---|---|---|---|---|---|

000 | 035 | 43 32 | g RTN | 070 | 44 5 | STO 5 | |||||

001 | 42,21,11 | f LBL A | 036 | 42,21,15 | f LBL E | 071 | 43 32 | g RTN | |||

002 | 44 3 | STO 3 | 037 | 32 1 | GSB 1 | 072 | 42,21, 8 | f LBL 8 | |||

003 | 33 | R⬇ | 038 | 45,20, 2 | RCL × 2 | 073 | 44 7 | STO 7 | |||

004 | 44 2 | STO 2 | 039 | 45,20, 1 | RCL × 1 | 074 | 33 | R⬇ | |||

005 | 33 | R⬇ | 040 | 11 | √x̅ | 075 | 44 8 | STO 8 | |||

006 | 44 1 | STO 1 | 041 | 15 | 1/x | 076 | 1 | 1 | |||

007 | 32 12 | GSB B | 042 | 44 3 | STO 3 | 077 | 8 | 8 | |||

008 | 43 32 | g RTN | 043 | 31 | R/S | 078 | 20 | × | |||

009 | 42,21,12 | f LBL B | 044 | 43 32 | g RTN | 079 | 45 7 | RCL 7 | |||

010 | 45 3 | RCL 3 | 045 | 42,21, 1 | f LBL 1 | 080 | 4 | 4 | |||

011 | 43 20 | g x=0 | 046 | 2 | 2 | 081 | 0 | 0 | |||

012 | 32 15 | GSB E | 047 | 43 26 | g π | 082 | 20 | × | |||

013 | 45 2 | RCL 2 | 048 | 20 | × | 083 | 40 | + | |||

014 | 43 20 | g x=0 | 049 | 44 6 | STO 6 | 084 | 45,20, 2 | RCL × 2 | |||

015 | 32 14 | GSB D | 050 | 43 11 | g x² | 085 | 11 | √x̅ | |||

016 | 45 1 | RCL 1 | 051 | 43 32 | g RTN | 086 | 45,10, 8 | RCL ÷ 8 | |||

017 | 43 20 | g x=0 | 052 | 42,21, 2 | f LBL 2 | 087 | 5 | 5 | |||

018 | 32 13 | GSB C | 053 | 20 | × | 088 | 0 | 0 | |||

019 | 32 4 | GSB 4 | 054 | 45 3 | RCL 3 | 089 | 4 | 4 | |||

020 | 32 5 | GSB 5 | 055 | 43 11 | g x² | 090 | 0 | 0 | |||

021 | 43 32 | g RTN | 056 | 20 | × | 091 | 20 | × | |||

022 | 42,21,13 | f LBL C | 057 | 15 | 1/x | 092 | 43 32 | g RTN | |||

023 | 32 1 | GSB 1 | 058 | 43 32 | g RTN | 093 | 42,21, 9 | f LBL 9 | |||

024 | 45 2 | RCL 2 | 059 | 42,21, 4 | f LBL 4 | 094 | 45 2 | RCL 2 | |||

025 | 32 2 | GSB 2 | 060 | 45 6 | RCL 6 | 095 | 34 | x↔y | |||

026 | 44 1 | STO 1 | 061 | 45,20, 3 | RCL × 3 | 096 | 10 | ÷ | |||

027 | 31 | R/S | 062 | 45,20, 1 | RCL × 1 | 097 | 11 | √x̅ | |||

028 | 43 32 | g RTN | 063 | 15 | 1/x | 098 | 4 | 4 | |||

029 | 42,21,14 | f LBL D | 064 | 44 4 | STO 4 | 099 | 5 | 5 | |||

030 | 32 1 | GSB 1 | 065 | 43 32 | g RTN | 100 | 26 | EEX | |||

031 | 45 1 | RCL 1 | 066 | 42,21, 5 | f LBL 5 | 101 | 3 | 3 | |||

032 | 32 2 | GSB 2 | 067 | 45 6 | RCL 6 | 102 | 20 | × | |||

033 | 44 2 | STO 2 | 068 | 45,20, 3 | RCL × 3 | 103 | 43 32 | g RTN | |||

034 | 31 | R/S | 069 | 45,20, 2 | RCL × 2 |