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inductance calculation of a coax
Posted Jul 21, 2012, 6:36 p.m. EDT Low-Frequency Electromagnetics 2 Replies
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Hi,
I am trying to calculate the inductance of a coax in MEF module, however it gives an error due to the insulator between the conductors.
How is it possible to calculate the inductance of a coax in COMSOL?
thank you
I am trying to calculate the inductance of a coax in MEF module, however it gives an error due to the insulator between the conductors.
How is it possible to calculate the inductance of a coax in COMSOL?
thank you
2 Replies Last Post Jul 22, 2012, 7:44 a.m. EDT
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Posted:
1 decade ago
There are a number of ways to do this. I've attached just one example (in version 4.3) that is done in 3D, and uses the fact that the stored magnetic energy = 0.5*LI^2, where L is the inductance. This model agrees with the analytic expression and it is also convenient to generalizing to more arbitrary 3D coax-like geometries. I've set it up to have a unit current.
(For the analytic expression, see, for example, www.physics.byu.edu/faculty/christensen/Physics 220/FTI/32 Inductance/32.11 The inductance of a coaxial cable.htm)
You could also do this in 2D axisymmetric mode.
And in any case, you could also go back to the definition of inductance in terms of flux and current, and integrate over a surface perpendicular to the B field to find the flux.
NOTE: To save space, the attached file still does not include the solution. So be sure to run it! Then look at "Inductance" under Results --- Derived Values.
(For the analytic expression, see, for example, www.physics.byu.edu/faculty/christensen/Physics 220/FTI/32 Inductance/32.11 The inductance of a coaxial cable.htm)
You could also do this in 2D axisymmetric mode.
And in any case, you could also go back to the definition of inductance in terms of flux and current, and integrate over a surface perpendicular to the B field to find the flux.
NOTE: To save space, the attached file still does not include the solution. So be sure to run it! Then look at "Inductance" under Results --- Derived Values.
Attachments:
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Posted:
1 decade ago
Thank you very much, Mr. Koslover.
My comsol's version is 4.2a. I cannot open your file. However I want to share some of my calculations. I think there is something wrong, but I cannot find it. My model is 3D.
First, the inductance formula:
mur*mur_o*L*log(r_o/r_i)/(2*pi) gives me a number of 3.3647e-10 H.
I'm trying to get the inductance numerically from the definition. So, I defined an integral called int_rad and selected an edge between the outer and inner metal cylinder. Then I typed the flux like this:
L*int_rad(mef.Hx*t1x+mef.Hy*t1y)
(L is the length of the coax)
then I defined an integral called int_circ which includes the edges at just one end of the outer cylinder. Then I typed the current as:
int_circ(mef.Hx*t1x+mef.Hy*t1y)/mur_o
(mur_o is the permeability of free space)
Then, inductance = -flux/current
this formulation gives me a number of: 9.37066e-10 H.
I don't know why they are so different.
Thirdly, I tried to do the calculation from the magnetic energy whose calculation is:
2*mef.intWm/(mef.I0_1^2)
and that gives me another different number: 8.6e-12 H
Now, if I describe my model briefly,
I expanded the Magnetic Insulation part in MEF physics. added a terminal which has a voltage of 10 V. This is the outer boundary of the outer cylinder. Then added a ground. That is the inner outer boundary of the inner cylinder.
my conductor is aluminum, insulator is some material whose conductivity is 1e-12 and rel.permitivitty: 2.4
So, what is that I'm doing wrong here?
Additionally, when I changed the insulator's conductivity to 0 (as in air), the program gives an error of "singular matrix". I do not understand that either.
I appreciate your help. thank you very much.
Ceren
My comsol's version is 4.2a. I cannot open your file. However I want to share some of my calculations. I think there is something wrong, but I cannot find it. My model is 3D.
First, the inductance formula:
mur*mur_o*L*log(r_o/r_i)/(2*pi) gives me a number of 3.3647e-10 H.
I'm trying to get the inductance numerically from the definition. So, I defined an integral called int_rad and selected an edge between the outer and inner metal cylinder. Then I typed the flux like this:
L*int_rad(mef.Hx*t1x+mef.Hy*t1y)
(L is the length of the coax)
then I defined an integral called int_circ which includes the edges at just one end of the outer cylinder. Then I typed the current as:
int_circ(mef.Hx*t1x+mef.Hy*t1y)/mur_o
(mur_o is the permeability of free space)
Then, inductance = -flux/current
this formulation gives me a number of: 9.37066e-10 H.
I don't know why they are so different.
Thirdly, I tried to do the calculation from the magnetic energy whose calculation is:
2*mef.intWm/(mef.I0_1^2)
and that gives me another different number: 8.6e-12 H
Now, if I describe my model briefly,
I expanded the Magnetic Insulation part in MEF physics. added a terminal which has a voltage of 10 V. This is the outer boundary of the outer cylinder. Then added a ground. That is the inner outer boundary of the inner cylinder.
my conductor is aluminum, insulator is some material whose conductivity is 1e-12 and rel.permitivitty: 2.4
So, what is that I'm doing wrong here?
Additionally, when I changed the insulator's conductivity to 0 (as in air), the program gives an error of "singular matrix". I do not understand that either.
I appreciate your help. thank you very much.
Ceren