ReactanceP

J E Patterson - jepspectro.com - 20231119

Description

J E Patterson - jepspectro.com - 20180610

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)²L) capacitance in farads
L = 1/((2πf)²C) 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.

Usage:

C ENTER L ENTER f GSB A
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.

Example:

C is unknown, L = 1E-6 henrys, the frequency f is 1 MHz.
0 ENTER 1 EEX CHS 6 ENTER 1 EEX 6 GSB A

Result:

C = 25.33 nanofarads
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.

Program Resources

Labels

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

Storage Registers

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

Program

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