[SI-LIST] Re: si-list Digest V3 #194
- From: andrew.c.byers@xxxxxxxxxxxxxx
- To: gigabit@xxxxxxxxxx, beneken@xxxxxxxxxxxx
- Date: Thu, 17 Jul 2003 10:02:49 -0700
Sainath,
As Thomas pointed out, inductance is the ratio of magnetic flux to current
in the conductor. Magnetic flux is the integral of B dot dA, or the magnetic
field [dot product] the surface you are integrating over. The "dot product"
is the same as multiplying the B-field by the area by the cosine of the
angle between the B-vector and the normal to the area. So if the B-vector is
perpendicular to the area surface, then the B-vector is parallel to the unit
normal vector of the area surface, cosine of this zero degree angle is 1,
and you simply multiply B*area. Here's an example to illustrate.
You have a rectangular metal trace over a ground plane, length in the
z-direction, height in the y, width in the x. Stretch a rectangle in the yz
plane between the trace and the ground plane. Make it any length (smaller if
you are simulating with EM tool). If we assume perfect conductors (ie no
internal-conductor magnetic fields), then all of the magnetic field
associated with that signal trace will pass through this rectangle. It is
kind of like a net. Magnetic field lines always have to end up in the same
place they started, completing the circle. Also, in this configuration, all
your field lines are perpendicular to the integrating rectangle. So
inductance is flux/I = B*A/I. In this case, you will actually have
inductance per unit length because your net had a specific z-length.
If you were to put your integrating surface on the other side of the trace,
extending up from the top of the trace, you theoretically would have to make
the area of the surface extend to infinity to "catch" all the field lines.
By placing it between the signal line and the return path, you capture all
the field lines. So you have one number for inductance if you account for
all the B field lines. An inductance "distribution" would indicate that you
are not catching all the magnetic field lines with your integrating surface.
This might open up a talk about internal inductance, when you have magnetic
field lines (ie current) INSIDE the conductors. As frequency increases, the
current crowds to the surface, and the internal inductance diminishes. But
at lower or intermediate frequencies, this internal inductance can be a
contributing factor. For PCB's, this is typically in the low MHz range. But
for square conductors on silicon, measuring a few microns wide and a few
microns high, the internal inductance might have to be considered up to
several GHz. Does this affect you? Do you electrical models consider this
effect? How about internal inductance of the ground plane? Interesting stuff
here.
Salud,
Andy Byers
-----Original Message-----
From: Sainath Nimmagadda [mailto:gigabit@xxxxxxxxxx]
Sent: Thursday, July 17, 2003 9:25 AM
To: beneken@xxxxxxxxxxxx
Cc: si-list@xxxxxxxxxxxxx; gigabit@xxxxxxxxxx
Subject: [SI-LIST] Re: si-list Digest V3 #194
Thomas,
Thank you. I agree, you get one value of inductance for one integration.
If you repeat this for a number of 'concentric spheres', you will get a
number of inductances- ranging from minimum to maximum. Does that make
sense?
Sainath
---------Included Message----------
>Date: Thu, 17 Jul 2003 12:04:57 +0200
>From: "Thomas Beneken" <beneken@xxxxxxxxxxxx>
>Reply-To: <beneken@xxxxxxxxxxxx>
>To: <si-list@xxxxxxxxxxxxx>
>Subject: [SI-LIST] Re: si-list Digest V3 #194
>
>Hello Sainath,
>
>inductance is the proportional factor between the current and the
magnetic
>flux. So far Your idea is ok. But calculating magnetic flux from
magnetic
>field requires an integration across a closed surface surrounding the
>conductor carrying the current. So - as You see - You will not get a
>inductance distribution over conductor length but only an integral
value for
>the conductor enclosed in the chosen sphere.
>
>Sorry,
>Thomas
>
>> Msg: #12 in digest
>> Date: Wed, 16 Jul 2003 11:55:35 -0800
>> From: "Sainath Nimmagadda" <gigabit@xxxxxxxxxx>
>> Subject: [SI-LIST] Microstrip Inductance
>>
>> Hello experts:
>>
>> For a microstrip, we know the magnetic field distribution(for
>> example,
>> Fig. 2.3 Stephen Hall's book) and current density
>> distribution(Fig. 4.5
>> same book). Given these, how would you obtain the inductance
>> distribution?
>>
>> Thanks in advance,
>> Sainath
>
>
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