[SI-LIST] Re: Inductance vs. Impedance
- From: "Scott McMorrow" <scott@xxxxxxxxxxxxx>
- To: andrew.c.byers@xxxxxxxxxxxxxx
- Date: Fri, 18 Jul 2003 16:03:53 -0700
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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--
Scott McMorrow
Teraspeed Consulting Group LLC
2926 SE Yamhill St.
Portland, OR 97214
(503) 239-5536
http://www.teraspeed.com
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