With TJ Byers

## Winding Single-Layer Air Coils

### Question:

Why does the inductance get bigger as the diameter of the coil grows larger? It would seem that the larger the coil, the weaker the magnetic field, hence the smaller the inductance ... wouldn't it? I'm trying to wind a 250µH coil for a project I'm building, and all this is getting very confusing.

**Dennis Friedman**

via Internet

### Answer:

Of all the disciplines associated with electronics, inductance is probably the most perplexing. Unlike Ohm's Law and, which contains just two variables, inductance is a mixture of physical sizes, shapes, and voodoo magic. To answer your question, all we have to do is look at the equation for calculating inductance.

where:

L is the inductance in microhenrys (µH)

N is the number of turns

A is the radius of the coil in inches

B is the length of the coil in inches

If we plot this equation on a graph, it looks like this.

As you can plainly see, inductance increases as the diameter increases. Strange but true. Now as for winding a 250µH coil, the formula for this is

If A equals 1 inch (2 inches dia.), B equals 4 inches, and L equals 250µH, then you need 111 turns of wire. The next step it to determine what size (AWG) wire. This is done by looking up the Turns Per Linear Inch ratings for enamel covered magnet wire. For 250µH you need 111 turns spread over 4 inches.

**Wire Gauge** |
**Ohms Per 1000 ft.** |
**Turns Per Linear Inch** |

14 |
2.52 |
15.2 |

16 |
4.02 |
19.0 |

18 |
6.39 |
23.9 |

20 |
10.1 |
29.9 |

22 |
16.2 |
37.5 |

24 |
25.7 |
46.8 |

26 |
41.0 |
58.8 |

28 |
65.3 |
73.3 |

30 |
104.0 |
91.7 |

34 |
261.0 |
145 |

**TABLE 1.** Wire Resistance and Turns Per Linear Inch

Cross referencing the table shows us that 111 turns of 20-gauge wire (or thinner) suits our needs exactly. If this is more math than you care to deal with, use the handy-dandy coil calculator at **www.vwlowen.demon.co.uk/java/coil.htm**. This is a JavaScript utility written for metrics, so you have to convert from inches to millimeters. (Hint: 1 inch » 25mm; conversely, 1mm = .04 inches.)

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