## QEX

From the above, the following are approximate rules which apply to the AWG system and they are easy to remember:

L An increase of three gauge numbers (say from No. 21 AWG to No. 18 AWG) doubles the area and weight, which consequently cuts in half the dc resistance.

2. An increase of six gauge numbers (say from No. 18 AWG to No. 12 AWG ) doubles the diameter.

3. An increase in ten gauge numbers (say from No. 12 AWG to No. 2 AWG) increases the area and weight by ten and this reduces the dc resistance by ten times.

4. A No. 10 AWG round copper wire has a diameter of about 0.10 inches, an area of about ten thousand circular mils and a dc resistance of approximately 1 Q per 1000 feet (standard annealed copper at 20° C).

5. The weight of No. 2 AWG copper wire is approximately 200 pounds per 1000 feet.

6. The diameter of No. 12 AWG is very close to 2 mm (exactly 2.05 mm).

7. The diameter of No. 18 AWG is very close to 1 mm (exactly 1.02 mm).

8. The diameter of No. 24 AWG is very close to 0.5 mm (exactly 0.511 mm).

9. The diameter of No. 30 AWG is very close to 0.25 mm (exactly 0.254 mm).

These approximate rules are easy to apply when winding coils, transformers or inductors for ham radio use. No consideration is given here to the insulation thickness, as this varies from manufacturer to manufacturer in the case of enamelled wire (ie, Formvar, a good thin insulating material). The insulating layer thickness also varies with the size of the wire. For demanding applications, the supplier's technical data should be carefully checked For example, see Note 8.

For those interested in obtaining the diameter of a round copper wire given its AWG number, without the use of tables or reference handbooks (Notes 2 and 3), I have written a short program for the popular HP-41 CV programmable calculator. Using a computer, I believe, is a bit of an overkill in this case. The actual program is shown in Table 1 and it is not to difficult to rewrite for other programmable

Table 1—HP-41 CV Program for Converting AWG into mils and mm.

01 LBL ALPHA WIRE ALPHA

02 LBL 01

03 ALPHA WIRE SIZE? ALPHA

04 XEQ ALPHA PROMPT ALPHA

05 XEQ ALPHA INT ALPHA

06 STO 01

07 51

08 STO 02

09 RCL 01

10 RCL 02

12 GTO 01

13 92

14 LN

15 39

17 STO 03

18 RCL 01

19 CHS

20 36

22 x

23 ex

24 5

25 x

27 0.0254

28 x

<program name> cbegins branch/loop>

<asks for AWG number> crnakes AWG integer>

cchecks if AWG<50> <if not start again> <calc of prog const>

<stores 1 n kawg> <calc geom progression;»

<diameter in mils>

machines. A very small error may appear in the calculated diameter when compared to the wire tables in Note 2, as these numbers are rounded off to reduce the decimal digits.

The following relation, derived from Eq 1, is used to convert an AWG number to diameter:

The above equation is used as the basis of the program shown in Table 1. You must load it first by setting the HP-41CV to "Prgm." Once loaded, it will stay in memory. To run this program, called "Wire," do the following:

a) Do XEQ ALPHA WIRE ALPHA. This invokes the WIRE program.

b) Press R/S: This will display a WIRE SIZE? prompt.

c) Enter the AWG number, then press R/S.

d)The display shows the diameter in mils. Press R/S again for mm.

e) Press RS to continue with another AWG computation.

Please note that for large wire sizes you can enter the numbers as:

No. 1/0 AWG: enter as "0" No. 2/0 AWG: enter as "-1" No. 3/0 AWG: enter as "-2" No. 4/0 AWG: enter as "-3", etc.

### Conclusion

The American Wire Gauge system has been briefly presented, with its basic properties and some easy rules to remember when building projects using round copper wire. A small error exists in the exact calculation of the diameter of the wire, as the insulation thickness of the enamel is ignored. This is a small error (about 0.001 inch or 1 mil) that does not greatly affect the practice of winding small coils, inductors or transformers for amateur radio use. The calculator program shown converts AWG numbers to diameters in mils and mm for any gauge of wire larger than or equal to No. 50 AWG.

Antonio L. Eguizabal is a graduate of the University of Santiago with a BSc (Hons) and MASe from the University of British Columbia, both in Electrical Engineering. He was first licensed as CE3ACO in 1967. His interestes include analog, digital, RF

circuits and telecommunication systems, as well as experimenting with novel antennas for professional and amateur work. Antonio is also a volunteer radio operator with the North and West Vancouver Emergency Program.

Notes

1Dwight, H.B , Professor at MIT, Electrical Coils and Conductors, Their Characteristics and Theory, Chapter 5, McGraw Hill 1945.

2Fink, D.G, and Beaty, H.W., Standard Handbook for Electrical Engineers, Chapter 4, Twelfth Edition, McGraw Hill, 1987. 3Staff of Siemens A G., Electrical Engineering Handbook, Chapters 1 and 8, John Wiley and Sons, 1990. aNBS Handbook 100, National Bureau of Standards, National Technical Information Service, US Department of Commerce, Washington, DC. 5Canadian Electrical Code, Section 2-116, Canadian Standards Association, 1990, Rexdale, Ontario. 6National Electrical Code Handbook, Article 110-6, National Fire Protection Association, 1990, Quincy, Massachussetts. 7Eguizabal, A.L., "Inductance of Solenoid Coils: A Radio Amateur View, Part II, The Canadian Amateur, February 1994, p 53. eBelden Wire and Cable Master Catalog, Cooper Industries, 1989, Richmond, Indiana. r-r-i