Copper Wire, Toroids, and Transformers
Wire and its Uses
Wire and its Uses
Conductive wire has many uses, this page is mostly
concerned with its uses in electronics, specifically in
amateur radio design and construction.
There is a metric standard for wire measurement,
and of course, it is very simple.
And, as you might expect, the system used in the U.S. is
enormously complicated and nonintuitive.
But if you don’t live in the U.S. with its peculiar wire
gauge system you will still see designs using inductors
and transformers constructed with U.S.specific wire sizes.
So, we need to look at the specifics of the American Wire Gauge
or AWG system, and some handy rules of thumb for working
with it.
Then, some details about making inductors and transformers
with that wire!
Toroidal inductors have many advantages,
so we’ll look at the toroidal cores commonly used
in ham designs.
American Wire Gauge
The American Wire Gauge or AWG is used in the U.S. and Canada for electrically conducting wire. Steel wire uses various different wire gauges — one for the type of wire you would use to repair a fence or hang a picture, another for that used on musical instruments, and so on.
The electrical current capacity depends on the crosssectional area and not the diameter. This means that the formulas are more complicated than you might expect for diameter versus wire gauge number or for the relationship between the diameters of two different gauge numbers.
Counterintuitively, larger gauge numbers mean smaller wire.
Why?
This comes from the production process. The wire is formed by drawing the original copper stock material through a series of increasingly smaller dies. A smaller final diameter requires more passes through the dies. The final gauge number isn’t exactly the number of die passes, but generally speaking, the higher gauge numbers mean larger numbers of die passes and therefore smaller final diameters.
There is a gauge 0, which is large, plus increasingly larger multiplezero sizes up to 0000 which is also written as 4/0. Power distribution conductors larger than 4/0 are usually identified by their area in thousands of circular mils, but if you’re doing industrial work or designing and building power distribution networks you shouldn’t need this page to tell you how to do that!
The formal notation is the number followed by “AWG” as in 12 AWG However, you will also see #12, Number 12 or No. 12, No. 12 AWG, and 12 gauge or 12 ga.
For the large multizero sizes the formal notation is something like 0000 AWG. But you will also see 4/0 (pronounced “four aught”), 4/0 AWG, #0000 AWG, and #4/0.
AWG Rules of Thumb
We’ll get to the formulas and tables in a moment, but let’s start with some simple rules of thumb. All these are approximate but still useful.
If you double the diameter the AWG decreases by 6. Or, half the diameter means the AWG increases by 6.
If you double the crosssectional area the AWG decreases by 3. Or, twice the area means the AWG increases by 3.
If you decrease the AWG by ten gauge numbers (e.g., #24 to #14) the area and weight are multiplied by about 10 and the resistance is divided by about 10.
Aluminum wire has a conductivity of about 60% that of copper, so the aluminum wire has about the same resistance as copper wire 2 gauge sizes smaller.
Stranded wire is also described by AWG, where it also defines the crosssectional area. Since about 10% of the crosssection of the multistranded wire is air, the stranded version will be about 5% thicker than the solid wire of the same AWG. Stranded wire will be described with three numbers indicating the overall AWG of the bundle, the number of strands, and the AWG of the individual strands. 22 AWG 7/30 is the result of using seven strands of 30 AWG wire to create one 22 AWGstranded wire bundle.
AWG Formulas
The way that AWG works is that #4/0 AWG and #36 AWG are defined by diameter.
#4/0 AWG = 0.46 inches
#36 AWG = 0.005 inches
All the other gauges are defined mathematically. The ratio of those two diameters is 1:92, and the gauges are 39 steps apart. The diameters are then very geometrically. Formally, the ratio of two consecutive gauge diameters is the 39th root of 92, or approximately 1:1.1229322. But the ASTM B 25802 standard says don’t go overboard on numerical precision! Use no more than 4 significant digits, with no finer than 0.0001 inches or 0.1 mil precision for #44 AWG and larger (which will cover almost everything most of us will ever use), and no finer than 0.00001 or 0.01 mil for smaller wires.
Equations provide a straightforward way of calculating diameters, areas, and gauge numbers. For multiaught M/0 wire, use N = 1–M in the following equations. For example, for 4/0 use 3 for N.
The diameter of #N AWG wire is:
d_{N} = 0.005 × 92^{(36N)/39} inch
d_{N} = 0.127 × 92^{(36N)/39} mm
The AWG gauge N of a wire of diameter d inch is:
N = –39 × log_{92}(d/0.005) + 36
The AWG gauge N of a wire of diameter d mm is:
N = –39 × log_{92}(d/0.127) + 36
The crosssectional area of #N AWG wire is:
A_{N} = 0.000019635 × 92^{(36N)/19.5} inch^{2}
A_{N} = 0.012668 × 92^{(36N)/19.5} mm^{2}
As with most everything else, the metric version is much simpler. The Metric Gauge is 10 times the diameter in millimeters. However, metric wire sizes are usually specified simply by their diameter in millimeters.
Copper Wire Tables
AWG  Diameter  Resistance  
inch  mm  ?/1000 ft  ?/1000 m  
0000  0.4600  11.684  0.04901  0.1608 
000  0.4096  10.405  0.06180  0.2028 
00  0.3648  9.266  0.07793  0.2557 
0  0.3249  8.251  0.09827  0.3224 
1  0.2893  7.348  0.1239  0.4066 
2  0.2576  6.544  0.1563  0.5127 
3  0.2294  5.827  0.1970  0.6465 
4  0.2043  5.189  0.2485  0.8152 
5  0.1819  4.621  0.3133  1.028 
6  0.1620  4.115  0.3951  1.296 
7  0.1433  3.665  0.4982  1.634 
8  0.1285  3.264  0.6282  2.061 
9  0.1144  2.906  0.7921  2.599 
10  0.1019  2.588  0.9989  3.277 
11  0.0907  2.305  1.260  4.132 
12  0.0808  2.053  1.588  5.211 
13  0.0720  1.828  2.003  6.571 
14  0.0641  1.628  2.525  8.286 
15  0.0571  1.450  3.184  10.45 
16  0.0508  1.291  4.016  13.17 
17  0.0453  1.150  5.064  16.61 
18  0.0403  1.024  6.385  20.95 
AWG  Diameter  Resistance  
inch  mm  ?/1000 ft  ?/1000 m  
19  0.0359  0.912  8.051  26.42 
20  0.0320  0.812  10.15  33.31 
21  0.0285  0.723  12.80  42.00 
22  0.0253  0.644  16.14  52.96 
23  0.0226  0.573  20.36  66.79 
24  0.0201  0.511  25.67  84.22 
25  0.0179  0.455  32.37  106.2 
26  0.0159  0.405  40.81  133.9 
27  0.0142  0.361  51.47  168.9 
28  0.0126  0.321  64.90  212.9 
29  0.0113  0.286  81.84  268.5 
30  0.0100  0.255  103.2  338.6 
31  0.00893  0.227  130.1  426.9 
32  0.00795  0.202  164.1  538.3 
33  0.00708  0.180  206.9  678.8 
34  0.00630  0.160  260.9  856.0 
35  0.00561  0.143  329.0  1079 
36  0.00500  0.127  414.8  1361 
37  0.00445  0.113  523.1  1716 
38  0.00397  0.101  659.6  2164 
39  0.00353  0.0897  831.8  2729 
40  0.00314  0.0799  1049  3441 
The U.S. National Electric Code or NEC specifies ampacity or current limits for wires. These are for individual wires and not wires bundled into Romex or other sheathed multiconductor cables where the allowed current limits are much lower. The limits depend on the insulation’s temperature rating to 60°C, 75°C, and 90°C.
AWG  Ampacity for insulation 

60°C  75°C  90°C  
0000  195  230  260 
000  165  200  225 
00  145  175  195 
0  125  150  170 
1  110  130  150 
2  95  115  130 
3  85  100  110 
4  75  85  95 
6  55  65  75 
8  40  50  55 
10  30  35  40 
12  25  25  30 
14  20  20  25 
16  —  —  18 
14  —  —  14 
Toroidal Inductors
Toroidal inductors are wound with magnet wire on a toroidal core as seen here. This toroid shape is like a donut or bagel, so the resulting inductor is shaped like a simple solenoid or springshaped inductor that has been wrapped almost into a complete circle.
Toroidal cores have advantages over simple solenoid inductors. To start with, they’re selfshielding. Their magnetic field goes around and stays largely within the core. You can place them close to each other with much less unwanted coupling. You can also place them close to conducting surfaces without worrying about inducing currents in those surfaces and suffering the associated loss.
Also, the toroid cores themselves are made from mixes of iron powder and other chemicals. This material has a much higher permeability than air, so it takes much less looping wire to create the same amount of inductance. The inductors are physically much smaller and they have far less loss than an aircore equivalent.
You form the inductor with magnet wire, which is made from electrolytically refined copper and is coated with a flexible insulating surface. We traditionally call this “enameled wire”. However, modern magnet wire is not coated with any enamel material. It instead is coated with one to four layers of polymer film insulation.
Polyvinyl formal (also called Formvar) is used for applications with the lowest temperature range. Polyurethane, polyamide, and polyester are used for increasing temperatures, and then polyesterpolyimide, polyamidepolyimide, and finally polyimide for operation up to 250°C.
The newer magnet wire insulation acts as a flux when it is heated by molten solder, meaning that we don’t have to scrape or sand the ends. But the old stuff we get in surplus needs mechanical cleaning to get a good solder joint.
You want the turns to occupy about 5/6 to 9/10 of the circumference of the core, evenly spaced.
For optimal Q or quality factor, you would like for the wire to be as large as possible while still fitting all the turns with no overlap around the inner circumference. The insulated turns around the inside may all touch each other or at least come very close.
You can see that on the toroidal inductor seen here. You count one turn for each pass through the center. It has 27 turns. It may be easier to count the full loops around the exterior and then add one.
Toroidal Cores
There are two major classes of toroidal core material: ferrite and powdered iron.
Ferrite toroids are used to fabricate larger inductances used to filter out or block higher frequency signals. They are lossy at higher frequencies and that’s exactly what you want. The cylindrical bulge near each end of a computer video cable is a barrelshaped ferrite core that the entire bundle passes through. It blocks “commonmode” signals, highfrequency signals that would be radiated by the cable if they flowed basically in unison on the bundle.
Powdered iron toroids are used to fabricate fairly precise inductances to be used in filters or other tuned circuits up to 100 MHz.
Ferrite toroids are designated FTsst and powdered iron toroids as Tsst where ss is a two or threedigit number indicating outer diameter in hundreds of an inch, and t is a one or twodigit number indicating the material mix.
A T50 toroid is 0.50″ in outer diameter, a T130 is 1.30″ in outer diameter, and so on. They range from a tiny T12 (which actually is 0.125″ across) up to the 2″ T200.
The material mix specifies the core’s permeability, stability, and appropriate frequency range. Micrometals manufacture most of the powdered iron toroidal cores used by amateurs, and they paint the cores to indicate the material.
As you see from this table, some of the mix numbers increase with both frequency range and permeability or ?, but many do not.
Stability is in partspermillion per degree C.
Micrometals Toroidal Cores  
Mix  Color  Freq (MHz)  Stability  ?  Material 
3  grey  0.05–0.5  370  35  Carbonyl HP 
15  red/white  0.1–2  190  25  Carbonyl GS6 
1  blue  0.5–5  280  20  Carbonyl C 
2  red  2–30  95  10  Carbonyl E 
7  white  3–35  30  9  Carbonyl TH 
6  yellow  10–50  35  8  Carbonyl SF 
10  black  30–100  150  6  Powdered iron W 
17  blue/yellow  40–180  50  4  Carbonyl 
12  green/white  50–200  170  4  Synthetic oxide 
Alinco and other vendors use a handy inductance index A_{L} which is ?H per 100 turns for powdered iron cores.
Use the below table to find A_{L} for the core size and material, and then apply these formulas to calculate the required number of turns N for the desired inductance in ?H or the resulting inductance in ?H for a given number of turns N:
N = 100 × sqrt ( L_{?H} / A_{L} )
L_{?H} = A_{L} × N^{2} / 10000
A_{L} Values for Micrometals Iron Powder Toroidal Cores  
Size  Mix/Color / Frequency (MHz)  
3 / grey 0.05–0.5 
15 / red/wht 0.1–2 
1 / blue 0.5–5 
2 / red 2–30 
7 / white 3–35 
6 / yellow 10–50 
10 / black 30–100 
17 / blu/yel 40–180 
12 / grn/wht 50–200 

T12  60  50  48  20  18  17  12  7.5  7.5 
T16  61  55  44  22  —  19  13  8  8 
T20  76  65  52  27  24  22  16  10  10 
T25  100  85  70  34  29  27  19  12  12 
T30  140  93  85  43  37  36  25  16  16 
T37  120  90  80  40  32  30  25  15  15 
T44  180  160  105  52  46  42  33  18.5  18.5 
T50  175  135  100  49  43  40  31  18  18 
T68  195  180  115  57  52  47  32  21  21 
T80  180  170  115  55  50  45  32  22  22 
T94  248  200  160  84  —  70  58  32  — 
T106  450  345  325  135  133  116  —  —  — 
T130  350  250  200  110  103  96  —  —  — 
T157  420  360  320  140  —  115  —  —  — 
T184  720  —  500  240  —  195  —  —  — 
T200  425  —  250  120  105  100  —  —  — 
Now you have selected a core size and mix, and calculated how many turns of wire are required, you can use the first table below to estimate the largest size of wire that can make that many singlelayer turns. Estimate it as it will depend on coating thickness and precisely how you wind the coil.
You can find tables for even finer wire, but even this table goes beyond the limit of practicality for most applications.
These should cover almost all the inductances you would ever need for practical circuits for resonant circuits or for bandpass and high and lowpass filters when used in combination with practical capacitor values through the HF and into the low VHF range.
Maximum Turns  
AWG  T12  T25  T37  T50  T68  T80  T94  T106  T130  T200 
12  –  –  3  6  9  14  16  16  25  43 
14  –  1  5  8  13  18  21  21  32  54 
16  –  2  7  13  17  24  28  28  41  69 
18  1  4  10  18  23  32  37  37  53  88 
20  1  6  14  23  29  41  47  47  67  111 
22  2  9  19  30  38  53  60  60  86  140 
24  4  13  25  39  49  67  77  77  109  177 
26  7  17  33  50  63  85  97  97  137  223 
28  9  23  42  64  80  108  123  123  173  281 
30  13  29  54  81  101  136  154  154  217  355 
32  17  38  68  103  127  171  194  194  272  439 
34  23  49  88  132  162  218  247  247  346  557 
A_{L} Values for Ferrite Toroidal Cores in mH/1000 turns  
Core  63/67 mix ? = 40 
61 mix ? = 125 
43 mix ? = 850 
77/72 mix ? = 2000 
J/75 mix ? = 5000 
FT23  7.9  24.8  188  396  980 
FT37  19.7  55.3  420  884  2196 
FT50  22.0  68.0  523  1100  2715 
FT82  22.4  73.3  557  1170  — 
FT114  25.4  79.3  603  1270  3170 
For the last of the toroid tables, here are the A_{L} values for ferrite toroids. Note that A_{L} is in mH per 1000 turns for ferrite toroids!
Apply these formulas to calculate the required number of turns N for the desired inductance in mH or the resulting inductance in mH for a given number of turns N:
N = 1000 × sqrt ( L_{mH} / A_{L} )
L_{mH} = A_{L} × N^{2} / 1000000
Ferrite toroids are not colorcoded, so it’s hard to tell what an unlabeled one really is. You could quickly wind a simple coil, count the turns and measure its inductance, and then solve for A_{L} to see which of these mixes was used. You often use ferrite cores in situations where you aren’t concerned with the precise value anyway. Slipping ferrite beads onto power supply lines, or slipping the larger barrelshaped ones salvaged from old computer video cables onto the outside of coaxial feedlines to block commonmode currents at an HF dipole feed.
Power Transformers
Typical power transformers use these wiring color codes. Be careful!
Primary:
If not tapped, two black leads.
If tapped, black and black/red striped with a black/yellow tap.
High voltage:
If not tapped, two red leads. Centertap would be red/yellow striped.
Rectifier filament winding:
If not tapped, two yellow leads. Centertap would be yellow/blue striped.
Filament winding #1:
If not tapped, two green leads. Centertap would be green/yellow striped.
Filament winding #2:
If not tapped, two brown leads. Centertap would be brown/yellow striped.
Filament winding #3:
If not tapped, two grey leads. Centertap would be grey/yellow striped.
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