There are two programs available for specifying inductors -- one for air-core coils and the other for toroid-wound inductors. Each one is an independent, stand-alone, executable Microsoft Windows program. No installation is required. Just download and run. I have used these programs on several different computers running a variety of operating systems including Windows XP, 2000, and 98 with no problems.

To keep things manageable, this software only handles coils whose diameter-to-length ratio is between one-tenth and ten. This gives a 100:1 range for diameter/length and should cover just about any air-core inductors hand-wound by homebrew builders. Sifting through engineering handbooks of various ages and descriptions. I was surprised to find that there is no single formula that covers solenoidal cylindrical air-core inductors over this range. The most common equation for inductance is:

L = n²∗d²/(18d + 40h) where: L = inductance in microhenries n = number of turns d = mean diameter in inches h = height of winding in inches

This is known as the Wheeler formula. You can find it in many handbooks, including most editions of the *ARRL Handbook for Radio Communications*. This formula is accurate to about 1%, but is limited to coils with a diameter/height ratio of less than about 0.8 (long, skinny coils).

For shorter and fatter coils (i.e., where diameter/height is more than 0.8), there is no analytical formula that I could find for the inductance. Most handbooks use an alternative approach for these inductors that references graphs or tables of numbers3. The computer program I'm describing here includes this data and is suitable for inductors where the diameter is up to ten times the height of the winding.

"Diameter" in this formula refers to the mean diameter of the winding. The mean diameter is actually the outside diameter of the coil form plus the diameter of the wire being wound on it. The problem, of course, is that you probably don't know what wire size you'll be using until you have finished applying the formula. Ignoring this little complication can lead to a sizeable error in the computed inductance, especially for a small-diameter coil wound with heavy-gauge wire.

Another issue that raises its ugly head is that of parasitic capacitance. Each turn of the coil exhibits a small amount of capacitance to its neighboring turns. The net capacitance resulting from the series combination of all these stray capacitors, small as it is, acts as if it were in parallel with the inductor, and will actually form a resonant circuit at some frequency. The impedance of the coil increases rapidly as the operating frequency approaches this point. Above self-resonance the coil starts to behave like a capacitor. It's therefore helpful, when designing an inductor, to have an idea of what the self-resonant frequency will be, since this sets a limit on the maximum frequency of use.

A straightforward method of estimating the parasitic capacitance of a coil is described in a paper published by the IEEE4. The method is included in this program in order to find the capacitance and self-resonant frequency.

The air-core inductor calculator software includes features that handle some of these headaches, so that you don't have to. For instance:

- The appropriate method for inductance calculation is automatically selected, based on the diameter/height ratio,
- After you have entered coil form diameter and winding height, the program automatically factors in the diameter of the wire,
- Based on wire size, coil diameter and number of turns, the program attempts to calculate total stray capacitance and displays this figure along with an estimate of the self-resonant frequency. These are necessarily only rough estimates, since the capacitance depends on a number of factors like coil form material, proximity of nearby conductors, etc.,
- The program assumes that the coil is wound with solid copper enamel-coated magnet wire. Spacing of the turns is assumed to be as close as possible. In calculating inductance and stray capacitance, a small correction is made to allow for insulation thickness and irregularities due to hand winding,
- The maximum wire size that will fit into the space you specify is calculated and displayed using AWG units,
- For convenience, the total length of wire required to wind the coil is determined. Thus, you don't have to guess how much wire you need before you start winding. For a coil with many turns, this saves a lot of frustration (and wasted wire).

This program has a few built-in limitations worth mentioning:

- No allowance is made for lead lengths when calculating inductance or total wire length,
- Coil diameter/height ratio must be between one-tenth and ten,
- The number of turns must be more than one and less than 16384,
- The calculated inductance is the true, or low-frequency, inductance and is most accurate at frequencies well below the self-resonant frequency of the coil,
- The coil is assumed to be far away from other conductors. If you place a shield around the coil, the inductance can drop by a significant amount. This effect is worse for long, thin inductors. As an example, for an air-core coil whose winding height is ten times its diameter, the inductance can be reduced by up to 20% when enclosed in a shield that is twice the diameter of the coil.

Toroid cores commonly used in amateur radio work are of two basic types. Iron-powder cores are manufactured from fine particles of iron mixed with a binder, forming, in effect, a distributed air gap. This technique decreases the inductance that can be obtained compared to a solid iron core, but also markedly lowers the losses and allows high frequency and VHF usage. Ferrites cores are made of exotic ceramic-like materials having a chemical composition of manganese-zinc or nickel-zinc. Both materials are formed into toroidal (and other) shapes with sizes ranging from a fraction of an inch to several inches in diameter.

The magnetic properties of both types of core depend on the material of which they are made. This is sometimes referred to as the *mix*. The inductance that can be realized by winding a given number of turns on a toroid depends on the mix and the physical size. Powdered iron toroids manufactured by Micrometals, Inc.5 - and this is mostly the case in ham radio circles - are painted with a standard color code to indicate the mix. Ferrite cores are usually not color-coded, making identification difficult.

The advantage of using toroidal cores is that the magnetic fields are almost entirely confined to the core. Inductors made this way rarely require shielding and can be mounted close to other components. This is in marked contrast to air-core cylindrical inductors.

The main disadvantage of metal toroid core inductors (especially ferrites) is that they will become magnetically saturated at high power levels, causing the inductance to drop drastically. This effect is non-existent in air-core coils.

This calculator program lets you select the type of toroid you are working with (powdered iron or ferrite) and then lets you choose from a list of industry-standard sizes and materials using pull-down menus. Not all combinations of toroid size and material are valid ones, and the program will display an informational message box if you choose a non-existent combination.

From here on, things are similar to the air-core calculator. Enter inductance value or number of turns, click on the **Solve for** button for the parameter you want and the program goes to work, gathering the manufacturer's data for the core you have chosen, calculating the inductance or number turns and displaying the results. Recommended frequency range is displayed and the core dimensions are listed (you can select metric or English units) along with the maximum wire size and required length.

The wire size is the heaviest gauge wire that can fit into the winding area, given the size of the core and the number of turns. It is recommended that the winding area should not occupy the full toroid circumference - rather, a gap of about 30 degrees should be left between the start and end of the winding. This practice is claimed to reduce stray capacitance. A drawing in the **winding information** frame illustrates this.

- The color codes shown for powdered iron cores follow Micrometals' standard.
- This program makes no allowance for external lead length when calculating inductance or wire length.
- The program displays a suggested range of operating frequency for the type of core selected. Ferrite cores have two suggested ranges: one for narrow-band operation as for tuned circuit and a different one for wide-band applications like filters.
- The maximum number of turns that the program can handle is 65535. The number of turns must also be greater than 1.
- The largest number you can enter into the inductance box (regardless of the units selected in the pull-down menu) is 65535.
- A goodly amount of user-input error checking is built in to the program, but it doesn't check everything. If you enter ridiculous numbers (like saying you want to wind 20,000 turns in a T-12 core) it will give ridiculous answers (like calling for a wire size of 90 AWG).