[SI-LIST] Re: Inductance vs. Impedance
- From: Vinu Arumugham <vinu@xxxxxxxxx>
- To: scott@xxxxxxxxxxxxx
- Date: Fri, 18 Jul 2003 17:19:42 -0700
To tweak that a little more, current will flow through all available
paths. The bulk of it will follow the path of least impedance.
Thanks,
Vinu
Scott McMorrow wrote:
>Andy,
>To be a bit more clear, current will follow the path of least impedance,
>and not always the path of least inductance. If a capacitive element
>in a circuit, or geometry, provides a lower impedance path, the current
>will tend to follow that path, instead of the inductive one. This is
>especially important to consider when working with non-TEM or
>non-uniform 3D structures at high frequencies (>3 GHz). Even more
>generally, current will always follow the path of least energy.
>
>best regards,
>
>scott
>
>
>andrew.c.byers@xxxxxxxxxxxxxx wrote:
>
>
>
>>Inductance is the ratio of magetic flux (not field) to current. Flux is not
>>a vector, it is a scalar. So is the magnitude of the current in a wire
>>(closed integral of H dot dl). So you will get single inductance number for
>>a specific interconnect cross section.
>>
>>See pg. 81-83 of "Fields and Waves in Communications Electronics (3rd ed)",
>>Ramo,Whinnery,and Van Duzer.
>>
>>As you progress down the interconnect, the current will want to flow
>>wherever this inductance in the smallest. The path that the current follows
>>will be this path of "least inductance".
>>
>>Happy Weekend!
>>
>>Andy
>>
>>
>>
>>-----Original Message-----
>>From: art_porter@xxxxxxxxxxx [mailto:art_porter@xxxxxxxxxxx]
>>Sent: Friday, July 18, 2003 2:55 PM
>>To: gigabit@xxxxxxxxxx; Byers, Andrew C
>>Cc: si-list@xxxxxxxxxxxxx
>>Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>>
>>
>>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.
>>
>>Art Porter
>>
>>-----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
>>trace and signal return path beneath the trace and on the ground plane.
>>Such a return path, with its minimum loop area, is widely known to
>>provide the path of "least" inductance for high-frequency currents(for
>>example, Black Magic book). If inductance is thought of as one number,
>>what does "least inductance" refer to? Which is the path of "most"
>>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
>>>
>>>
>>>
>>>
>>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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>
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