The formula for the inductance of a piece of wire of diameter d and length l

[htg]

Can someone give me the formula for the inductance of a piece of wire of diameter d and length l?
I found a formula which disagrees with the data given by manufacturers regarding inductance of RF MOSFET leads, so I wonder if it is correct.

 

[Prototyp_V1.0]

Re: Inductance of a wire

That will give no sense anyway. It also depends of distance between cable pairs and if those is straight parallell, is spunded.

Also capasitance is a factor and will have a great influence in a cables behaviour.

 

[htg]

Re: Inductance of a wire

This is the first thing I need. Inductance of a twin lead is also of interest.

 

[FvM]

Re: Inductance of a wire

I agree with Prototype_V1.0. The inductance of a wire can't be measured without knowing the return path. For the inductance of a wire pair, you can simply refer to the basic transmission line formulas in RF and theoretical electrical engineering text books.

I have this formula in my book:

L = µ/pi * ln(d/r) (in H/m)
µ is 1.256e-6, d is the wire (center) distance, r is the wire radius, the formula is said to be valid for d > 5*r.

For complex geometries, I prefer to calculate inductances with FastHenry form freefieldsolvers.com.

Some manufacturers have also package parasitics specifications for RF and power devices together with SPICE models.

 

[htg]

Re: Inductance of a wire

Thanks. This gives the inductance of a twin lead per unit length. I have this formula in my book, but there is a comment that you need to add inductances of both single leads to it. So I still would like to see the formula for the inductance of a single wire.

 

[Prototyp_V1.0]

Re: Inductance of a wire

. . . . So I still would like to see the formula for the inductance of a single wire.

Without a return path (second wire) you've now made yourself an antenna.

 

[htg]

Re: Inductance of a wire

Not necessarily. You can have two unipolar capacitors at the ends of the wire, plus something to control the current (e.g. a MOSFET).

 

[FvM]

Re: Inductance of a wire

but there is a comment that you need to add inductances of both single leads to it.

I guess, the comment is referring to the inner inductance of the conductor. It's a frequency and resistivity dependant term that appears together with the skin effect. In relation to the characteristic inductance of typical conductance geometries, it can be neglected.

 

[htg]

Re: Inductance of a wire

My book gives formulas for the inner and outer inductance of a single wire, so probably the comment at the formula for the inductance of twin lead refers to both inner and outer inductance. I want to verify if other sources give the same formula for the inductance of a single wire.

 

[FvM]

Re: Inductance of a wire

As I said, the "outer inductance" of a single wire is an undefined quantity in my opinion. I wonder, how the respective formula is derived?

 

[htg]

Re: Inductance of a wire

Unfortunately, I do not know how it is derived.

 

[FvM]

Re: Inductance of a wire

Perhaps the more interesting question is, which physical problem the formular is representing? In my field of vision, the inductance of a wire is mainly a practical design problem for getting a good estimation of circuit behaviour. Unless antennas and radiation resistance come into play, conductors are always wire loops or parallel wires with finite distance. Procceding from the previously mentioned expression for the parallel wire case with it's ln(d/r) term, the inductance of a single wire would be infinite. Possibly it isn't, but it must be expected a large value compared to a two wire geometry.

I understood, that you're targetting to the calculation of circuit inductances rather than solving general EM problems. It seems obvious to me, that the discussed single wire problem is meaningless in this relation.

 

[123jack]

Re: Inductance of a wire

don't quote me on this but I suspect this issue is of interest when designing
equipment for remotely induced oscilation over large distances (i.e. very large comapared to general apps ...you can perhaps estimate the applications yourselves)

jack

 

[htg]

Re: Inductance of a wire

My book give the following formulas for the external and internal inductance of a single wire:

Lext = (µ*l/(2*pi)) * (ln(2*l/r)-1)

Lint = µ*l/(8*pi)

 

[shane123]

Re: Inductance of a wire

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---------- Post added at 11:17 ---------- Previous post was at 11:16 ----------

very nice ppst