Question about Inductance

Hi all

Just got a nagging question about Inductance that I need clearing up :slight_smile:
Basically I going / trying to make my own air wound inductor, I don't have an oscilloscope measure - so I've found an equation to help me build the coil to an approximate Inductance.

The formula states that L = (n^2 * r^2) / (9r + 10x)
Where:
n - Number of turns in the coil
r - Radius
x - Length

My nagging question is, does the thickness (diameter) of the wire itself play a part in all of this? If so how would I factor it in?

That same formula is in my 1949 Reference Data for RF engineers and is said to be correct to 1%.
Wire size is not discussed, but in the previous paragraph it says:
"The formula is based on the assumption of a uniform current sheet, but the correction due to the use of spaced round wires is usually negligible for practical purposes. "

So, as long as the wire is relatively small compared to the diameter and length * n, you should be OK.

Depending on the frequency and inductance you are trying to get, interwinding capacitance may or may not be a factor. Thicker wire increases the interwinding capacitance, but we're talking about a few 10s of pF if using large wire closewound. So if this is for a tuned circuit, figure on having some way to adjust the capacitance.

polymorph:
Depending on the frequency and inductance you are trying to get, interwinding capacitance may or may not be a factor. Thicker wire increases the interwinding capacitance, but we're talking about a few 10s of pF if using large wire closewound. So if this is for a tuned circuit, figure on having some way to adjust the capacitance.

Assuming that you aren't swamping this capacitance somewhere else.

Or the frequency of interest is low enough that the self-resonance frequency is way above it.

So yes, that formula is fairly accurate. What are you trying to build?

KeithRB:
That same formula is in my 1949 Reference Data for RF engineers and is said to be correct to 1%.

I had no idea it was that accurate - sounds very reassuring :slight_smile:
The wire I’m using is .65mm so I guess in the grand scheme of things it will be ok.

polymorph:
Depending on the frequency and inductance you are trying to get

I’m actually building it for a FM transmitter so anywhere between 87KHz - 108Hz.

I’ve been looking at a few tutorials online but the problem I’ve found is that it’s more of a “get the parts and assemble them” approach as opposed to “here’s how it works”. While I am a fan of first approach I very much prefer the latter because I’m actually learning something :slight_smile:

That said I managed to find a site that went in to the theory a bit more which is where I got the equation from, I was just curious about the wire gauge because in every tutorial I’ve seen they all seem to feature different gauges.

Self-capacitance will make some difference at those frequencies. If the wire is spaced about the thickness of the wire itself between windings, it shouldn't be a problem.

Although I think you meant 87MHz to 108MHz.... ;')

polymorph:
I think you meant 87MHz to 108MHz.... ;')

Opps!! I thought I double checked my post too lol
Tired eye syndrome must have been kicking in :slight_smile:

lilsancho:
My nagging question is, does the thickness (diameter) of the wire itself play a part in all of this? If so how would I factor it in?

Yes it does, most of the inductance of a straight wire is due to the field immediately
at the surface of the wire, thinner wire is higher inductance.

With a coil the amplifying effect of the coil will mean the main source of inductance
is the coiling, so the wire thickness is less important in proportion but it will still matter.

At those frequencies skin-effect is important so you want to reduce the losses in the
coil as much as possible which means thick wire is required, and the usual thickness
used is about the same as the gap between adjacent turns.

Thick wire reduces microphony too.

The inductance of the coil cannot be taken in isolation at those frequencies as
stray capacitance and inductance of other parts of the circuit are not easily
calculated or characterised, so RF design always involves some trial and error
or a tuning component to get the circuit to resonate at the desired frequency.