[SI-LIST] Re: si-list Digest V3 #194
- From: <art_porter@xxxxxxxxxxx>
- To: <gigabit@xxxxxxxxxx>, <andrew.c.byers@xxxxxxxxxxxxxx>
- Date: Fri, 18 Jul 2003 15:54:34 -0600
As someone previously stated, inductance is defined as the ratio of the =
magnetic field to the current. BUT both of those are vector quantities, =
not single numbers. And there is a different quantity for each point in =
a field. So "single values" for inductance are obviously =
simplifications. My interpretation of "the path of least inductance" =
would be the set of connected points for which the value of inductance =
is least. =20
Art Porter=20
-----Original Message-----
From: Sainath Nimmagadda [mailto:gigabit@xxxxxxxxxx]
Sent: Thursday, July 17, 2003 5:01 PM
To: andrew.c.byers@xxxxxxxxxxxxxx
Cc: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: si-list Digest V3 #194
Andy,
Thanks. I appreciate the extra effort to explain detail of integration.
In short, you've explained the current loop formed by a signal path on=20
trace and signal return path beneath the trace and on the ground plane.=20
Such a return path, with its minimum loop area, is widely known to=20
provide the path of "least" inductance for high-frequency currents(for=20
example, Black Magic book). If inductance is thought of as one number,=20
what does "least inductance" refer to? Which is the path of "most"=20
inductance for the microstrip? No doubt, I'm missing somethig.
Sainath
---------Included Message----------
>Date: Thu, 17 Jul 2003 10:02:49 -0700
>From: <andrew.c.byers@xxxxxxxxxxxxxx>
>Reply-To: <andrew.c.byers@xxxxxxxxxxxxxx>
>To: <gigabit@xxxxxxxxxx>, <beneken@xxxxxxxxxxxx>
>Cc: <si-list@xxxxxxxxxxxxx>
>Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>
>Sainath,
>
>As Thomas pointed out, inductance is the ratio of magnetic flux to=20
current
>in the conductor. Magnetic flux is the integral of B dot dA, or the=20
magnetic
>field [dot product] the surface you are integrating over. The "dot=20
product"
>is the same as multiplying the B-field by the area by the cosine of=20
the
>angle between the B-vector and the normal to the area. So if the=20
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=20
1,
>and you simply multiply B*area. Here's an example to illustrate.=20
>
>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=20
the yz
>plane between the trace and the ground plane. Make it any length=20
(smaller if
>you are simulating with EM tool). If we assume perfect conductors (ie=20
no
>internal-conductor magnetic fields), then all of the magnetic field
>associated with that signal trace will pass through this rectangle. It=20
is
>kind of like a net. Magnetic field lines always have to end up in the=20
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 =3D B*A/I. In this case, you will actually have
>inductance per unit length because your net had a specific z-length.=20
>
>If you were to put your integrating surface on the other side of the=20
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=20
lines.
>By placing it between the signal line and the return path, you capture=20
all
>the field lines. So you have one number for inductance if you account=20
for
>all the B field lines. An inductance "distribution" would indicate that =
you
>are not catching all the magnetic field lines with your integrating=20
surface.
>
>
>This might open up a talk about internal inductance, when you have=20
magnetic
>field lines (ie current) INSIDE the conductors. As frequency increases, =
the
>current crowds to the surface, and the internal inductance diminishes.=20
But
>at lower or intermediate frequencies, this internal inductance can be=20
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=20
few
>microns high, the internal inductance might have to be considered up=20
to
>several GHz. Does this affect you? Do you electrical models consider=20
this
>effect? How about internal inductance of the ground plane? Interesting=20
stuff
>here.
>
>Salud,
>
>Andy Byers
>
>-----Original Message-----
>From: Sainath Nimmagadda [mailto:gigabit@xxxxxxxxxx]=20
>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=20
integration.=20
>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=20
>sense?=20
>
>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=20
>magnetic
>>flux. So far Your idea is ok. But calculating magnetic flux from=20
>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=20
>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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