[SI-LIST] Re: R L & C extraction
- From: andrew.c.byers@xxxxxxxxxxxxxx
- To: a.ingraham@xxxxxxxx, si-list@xxxxxxxxxxxxx
- Date: Mon, 18 Aug 2003 11:46:26 -0700
For transmission lines in the PCB environment, the decrease in L will indeed
happen in the 10's of KHz to MHz range. Because the change is due to the
changing "internal inductance", the percentage change in total inductance is
dependent on the distance to the reference plane and the thickness of the
trace. (search on internal inductance to learn about why total inductance
decreases). In a differential setup, the distance between the lines also
affects this parameter (read "proximity effect").
But when the dimensions of the line shrink and the transition to the skin
effect region is higher in frequency, the total inductance won't start
decreasing until much higher in frequency also. For a typical transmission
line on chip (say 10um wide and 3um thick), this transition region can occur
in 100's of MHz up to the GHz region. So if you are trying to accurately
model transmission lines on chip at these frequencies, you have to consider
this frequency dependent inductance. It follows that tlines on package will
have transition regions somewhere in between chips and PCBs. Frequency
dependent behaviour is a major reason why broadband modeling and design is
difficult - and why many of us have jobs!
As Andy Ingraham pointed out, most closed form equations for inductance only
give you the high-frequency inductance that does not consider the
frequency-dependent internal inductance. But there is some good literature
out there with equations to use, some of it done decades ago. Another
approach is to use a good 2D field solver (seems like some threads here are
overlapping). The one I used was Ansoft spicelink, which used to be called
SI2D. Gives you the change in L accurately, and shows the nuances on the
curves of R and L due to the square shape of conductors. It does not account
for dielectric loss in the R curve though - for that you need the full 3D
HFSS port solve or apply your favorite dielectric loss correction after the
fact.
Regards,
Andrew Byers
-----Original Message-----
From: Ingraham, Andrew [mailto:a.ingraham@xxxxxxxx]
Sent: Monday, August 18, 2003 10:17 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: R L & C extraction
In most transmission lines, L decreases slightly with increasing frequency.
This happens at a moderately low frequency, in the vicinity of kilohertz to
a megahertz; and I believe the inductance change is on the order of ten
percent or so. Most field solvers and formulas give you the high frequency
inductance, above the region where it changes.
Capacitance should be pretty constant up to frequencies where the dielectric
constant changes; this is highly dependent on the insulating materials used.
If you need to make circuit transformations to change from one equivalent
circuit to another, then you will end up with values for R, L, and C that
can vary strongly with frequency. That might also happen if you are dealing
with a 3-dimensional structure that gets simplified into 2-D transmission
line parameters or a simple L/R/C lumped "equivalent" circuit.
Regards,
Andy
> I have found something i.e.
>
> 1) R : Skin effect will be more at higher frequencies and resistance of a
net will be more
> at higher frequency (when skin effect is pre dominant)
>
> 2) L: How is L related with frequency ?
>
> 3) C: How is C related with frequency?
>
> Thanks in Advance...
>
> Regards
> Karan
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