I have a spool of magnet wire and several round forms on which to wind coils. If I know the gauge of wire, and the diameter of the coil form, is there a way to calculate the number of turns required to receive the AM band? ….or any other bands?
My air-variable cap is from an old Hallicrafters and I believe it’s appx 500pf.
By far the easiest way to design a coil to resonante on a specific frequency is using a Grid Dip Oscillator. These are largely forgotten these days, but to the RF designer, they are as useful as a multimeter is to an electrician. By using a similar capacitor to what the radio will use, either fixed or variable, a coil is wound, temporarily connected to the capacitor and "dipped" with the GDO. This will give the frequency range, high and low, and also an indication of the "Q" or quality factor by noting the depth and width of the dip indication. By adding or removing turns, the resonant freq can be changed as well as guaging the effect of different tuning slugs. Both solenoid and torroids can be measured, coupled coils can also be designed , and the degree of coupling also found, from under coupled, to over coupled double humping. The GDO will also detect an oscillating circuit , either by accident or design,and indicate the frequency. The GDO can also inject a frequency into a circuit to test operation, similar to a signal generator.
The GDO is a quick way to design coils and unlike claculators, will take into account stray capacitances, losses, and other real world variables.
Here's what I did. I bought an inexpensive LCR meter, Proster, and used this Resonant Frequency Calculator
You can buy a better one if you like, they have better resolution.
Then I start winding on whatever core that Googling or the folks here, suggested to use. Any core will work, air , ferrite, iron, cardboard, etc. I start winding the coil with extra long wire, more than is needed, and keep it hooked up to the meter until I get to the exact micro Henryc, uH that I want. The extra wire off the coil impacts the measurements very little. Then once I get close, I trim the wire and make it exact. That get's me the uH. Using a chart is OK, but using a meter will show you that just a few turns make a huge difference.
Keep in mind, performance is a different issue. Litz wire vs solid wire for AM (Medium) band. Iron toroid for short wave vs air or cardboard, even when the uH measurement is the same for all cores.. I realized quickly that an air core, at the correct uH, will work, but requires an outside antenna or a lot of gain.
Using a meter makes it way easier to experiment. And just because the Resonant Frequency Calculator says a combo will work, it might not in your circuit for many reasons, like it won't oscillate at the frequency you are going for. At least the coil value won't be a problem.
Just goes to show you the imagination and genius of people like Marconi, who only had themselves, math, books, and intuition.
I think the on-line calculators are easier. https://www.crystalradio.net/professorcoyle/index.shtml
Lots of good crystal radio resources on this site.
There are formulas for doing that, and even online web pages that let you calculate L and C for resonant circuits. HOWEVER ...
I have an old book with what is known as a nomogram to do the same with just a ruler. I use it all the time. Here is a scan of the nomogram, short explanation below:
Assuming your capasitor goes from 50pF to 500pF. Follow the dotted line, from 500pF on the right, up to 200uH on the left hand side. The line crosses the frequency at approximately 500 kHz.
The same thing goes for 50pF. It crosses the frequency line at about 1600kHz. So - 50pF to 500pF, together with 200uH, covers the AM band from 500kHz to 1600kHz.
If you find this nomogram helpful, I can post a nomogram for designing coils too if you are interested.