Calculating the inductance of a cylinder

[tonykoral]

Hi

I have an aluminum cyclinder, say 500 mm tall, diameter, say 200mm with a 3mm wall. Does anyone know the formula for calculating the inductance of that cylinder please?

Thanks

Tony

 

[Prototyp_V1.0]

A pure cylinder is usually an object that any inductance from wherever you measure is not important compared with other physical properties.
Especially since you doesn't mention any windings, only it's outer dimensions.

What are you intend to use it for anyway?

 

[tonykoral]

The inductance will be very low - (of the order of 0.05 microhenries or so) but I need to know it fairly accurately as I want to resonate the cylinder with a capacitance in the range 100pF to 400pF or so to get a tank circuit with very high Q.

Tony

 

[kak111]

Do you mean Coaxial Resonator

Coaxial Resonators

 

[FvM]

Inductance can be only calculated for closed current loops. You can't determine the inductance of the cylinder without defining the current return path.
P.S.:

I know there are formulae for Co-axial lines and resonators, but these do not give the inductance value.

If you refer to a coaxial (double) cylinder geometry, the inductance can be easily derived from transmission line formulas. It's not quite exact, because it would ignore the end pieces of the shorted coaxial line.

 

[tonykoral]

Not exactly,

I want to use the circuit as an oscillator Tank Circuit. Although it is a coaxial resonator of sorts, I do need to calculate just the inductance of the cylinder - that is why I am stuck trying to find the formula.

I know there are formulae for Co-axial lines and resonators, but these do not give the inductance value. I believe that there is a 1962 book "Inductance Calculations", by FW Grover which may have the formula I need in it.

Tony

 

[jesterahs]

I am wondering: Can you find the impedance of the cylinder? I believe it would be Z = R + jwL and from this result you can get L. Is this correct? I am new myself... I belive the impedance of a cylinder can be found - the formula includes some complicated Bessel functions though...

 

[tonykoral]

Hi

Yes, you could probably calculate it from the impedance Z, but the question still is how to measure or calculate the impedance.

It is quite frustrating as I already know a way of calculating the inductance for a rectangular tube or a straight strip, but not for a round cylindrical section. I would have thought that there was a straightforward formula around somewhere.

Regards

Tony

 

[KerimF]

Hi Tony,

You may like to build first the resonant tank (cylinder and a capacitor in parallel).
I guess you will need two disks for the edges and the resonant capacitor could be connected between their centres.

About the formula, maybe one can start, as a rough approximation, with the one of a wire with skin effect:

Lw=0.2H[Ln(4*H/D)-1]
Lw in uH
H in mm
D in mm

Of course, this formula assumes that H>>D and there is no return current inside the cylinder and both are not valid here. The latter could be made true if the capacitor is connected outside the cylinder but this may not be desirable.

The other related formula could be of two concentric cylinders.
In your case, the inner cylinder diameter (d) is of the wire connecting the two terminals of the resonant capacitor with the edge disk centres.

Lc = 4π*10-7 * [Ln(D/d) + 1/4]
Lc in H/m
D and d could be in mm

Also this formula assumes that the cylinder length >> D which is not the case here.

Lw gives 130 uH (I think the value is rather too high)
Lc gives 33 uH assuming the inner wire diameter is 1mm

It will be interesting to find out empirically the right value of L by measuring the resonant frequency of the tank with a known C and inner wire diameter.

Kerim