**From:** Sainath Nimmagadda (*sainath@lsil.com*)

**Date:** Mon Mar 26 2001 - 09:21:54 PST

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Dear all,

Remember this recent thread? Following up on this somewhat complex

topic, I went to select experts, thru personal communication, across the

globe. Let us share the responses received so far.

First response is from Dr. Franzon and the second from Dr. Wong. (Well,

that is the order in which I received them)

Dr. Franzon and Dr. Wong, we appreciate your taking time and thank you

for your valuable inputs.

Best regards,

Sainath

-------------------------------------------------------

Quite humbly, I simply reflect Howards first point (minimum energy).

The

Universe is lazy and current will take the path of least Impedance (ie.

complex power P=VI = ZI^2, so minimum power = miniumum Z), so that it

has

to do the least work.

Z=sqrt(R+jwL/G+jwC). Assuming current path does not affect C much, then

the current path takes the path of lowest R+jWL. If R is low, then that

becomes path of least L. Note, we are referring to total loop

inductance.

Note that if R is high (e.g. on chip) then current does NOT take the

path

of lowest L, but least R+jwL - the current distn changes with frequency.

Also, note that this also explains the skin effect. When wL is high,

because w is high, then the current spreads to the skin to drop L at

the expense of R.

I hope that clarifies. Feel free to forward this to the list. I am

travelling and in a touch of a rush.

Regards

Paul

----------------------------------------------------------------

Sainath,

In generally, current will flow through the path with the lowest

IMPEDANCE.

At low frequencies when the capacitors are open circuits and the

inductors

are short circuits, current will flow through the path with the lowest

RESISTANCE. This leads to problem such as current crowding around

corner.

At high frequencies when the capacitors and inductance can longer be

ignored, the path with the lowest IMPEDANCE may depend on the signal

frequency. For example, cross-talk capacitance may become low impedance

path and short out the current path, whereas inductive line may become

high

impedance and prevent current flow. To further complicate the issue,

inductance depends on the dimension of the current loop (i.e., the

signal

line and the return path) and may be a function of frequency if the path

with the lowest impedance changes.

In principle, if one can generate the resistance, capacitance (including

self and cross-talk) and inductance (including self and mutual) matrixes

for the entire interconnect network, one can solve for the current

path. In practice, it will be too complex to model the entire chip.

One

can only model a small section of the chip at a time. This is

acceptable

for the capacitance matrix since electric field is typically terminated

at

neighboring structures. Magnetic field, on the other hand, can reach

structures few hundred microns away, and hence greatly complicates the

inductance matrix.

At even higher frequencies, the lumped element approach (i.e., treating

the

interconnect as R, L and C) begins to breakdown, one will need to solve

the

Maxwell equations with EM solver. Phenomenon such as skin effect,

substrate loss can no longer be ignored.

I hope this explanation helps.

Regards,

Simon

----------------------------------------------------------

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**Next message:**Aubrey_Sparkman@Dell.com: "RE: [SI-LIST] : internal timestep too small in transient analysis"**Previous message:**Kim Helliwell: "Re: [SI-LIST] : internal timestep too small in transient analysis"**Next in thread:**Aubrey_Sparkman@Dell.com: "RE: [SI-LIST] : Re: approximations for partial self inductance"**Maybe reply:**Aubrey_Sparkman@Dell.com: "RE: [SI-LIST] : Re: approximations for partial self inductance"**Maybe reply:**Reid, Chris: "RE: [SI-LIST] : Re: approximations for partial self inductance"**Maybe reply:**Reid, Chris: "RE: [SI-LIST] : Re: approximations for partial self inductance"**Maybe reply:**Grossman, Brett: "RE: [SI-LIST] : Re: approximations for partial self inductance"

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