=======================================================
Dmitri Kuznetsov, Ph.D.
Principal Engineer
ViewLogic Systems, Inc. e-mail: vdm@viewlogic.com
1369 Del Norte Rd. Tel: (805)278-6824
Camarillo, CA 93010 Fax: (805)988-8259
=======================================================
Raghu wrote:
>
> Dear Everybody:
>
> Thanks Ray for the results from ApsimRLGC. I have attempted to explain below why
> the results at 1MHz seem to be at variance from the values at other frequencies.
> It was also mentioned that at 1 MHz the skin depth is more than 2 mils and one
> should not see much skin effect in a 1 mil thick conductor. I have attempted to
> clarify this as well. Let me first reproduce Ray's results with more
> information.
>
>
> valuated @ Rs RS (ohms/m) RS+RDC
> (ohms/m)
> ----------- -------------------------------- -----------
> ---------------
> @1MHz 1.4874E-3 Ohms/(sqrt(Hz)*meter) 1.4874
> 6.8340
> @100MHz 1.0933E-3 Ohms/(sqrt(Hz)*meter) 10.933 16.280
> @1GHz 1.2272E-3 Ohms/(sqrt(Hz)*meter) 38.807 44.154
> @5GHz 1.3207E-3 Ohms/(sqrt(Hz)*meter) 93.387 98.734
>
> The value of Rs depends on the current distribution across the cross-section of
> the conductor. This in turn depends on
>
> 1. The variation across the width of the conductor. The width here is 6 mils and
> even at 1 MHz, there will be variation across the width.
>
> 2. The variation across the height of the conductor.
>
> 3. The current distribution across the width and height of the ground plane. The
> ground plane can contribute as much as 25% of the total resistance and this also
> needs to be accounted for. At low frequencies the current flows all across the
> ground plane. At high frequencies, it flows directly below the trace or
> conductor. A frequency of 1 MHz is in the transition region.
>
> A recent paper in IEE Transactions on Microwave Theroy and Techniques (July
> 1999, p. 979) titled "Internal Impedance of Conductors of Rectangular
> Cross-Section" by G. Antonini, A. Orlandi, and C. R. Paul has excellent figures
> of current distribution at different frequencies for a microstrip. It also makes
> the point that sqrt (f) variation at high frequencies is valid only for circular
> conductors. Also, the high frequency internal inductive reactance is not equal
> to the high frequency resistance for rectangular conductors.
>
> Coming back to my original point, the reason the value of Rs
> (ohms/(sqrt(Hz)*meter) at 1 MHz seems high can be attributed to the following:
>
> 1. The sqrt (f) variation is not valid for rectangular conductors and is not
> valid at frequencies where skin effect is not well established (as at 1 MHz for
> this example).
>
> 2. In the range 100 KHz - 10 MHz, a very big contributor to the variation in
> RTOTAL (i.e the derivative of RTOTAL with respect to frequency) is the reduction
> of the width of the current flow in the ground plane. This again, is not
> necessarily a sqrt (f) variation.
>
> 3. ApsimRLGC calculates the total R (RTOTAL) and then subtracts out the DC R
> (RDC) to get Rs. At 1 MHz, RTOTAL is close to RDC and this can lead to greater
> errors when Rs is separated out and divided by frequency.
>
> On a related issue, Dimitri has rightly pointed out that one cannot arbitrarily
> assign a value to Rs without suitably changing the inductance. Otherwise some
> fundamental principles such as causality may be violated. ApsimRLGC was
> originally designed to work with ApsimSPICE and its output is compatible with
> ApsimSPICE. ApsimSPICE avoids the problem of violating these principles by using
> physical models for its transmission line simulation.
>
> I think this email is long enough, espeically considering the increased traffic
> in the SI reflector, and I would be happy to supply more information on any of
> this offline to anybody who may be interested
>
> --
>
> ************************************************************************
> Raj Raghuram
> Applied Simulation Technology
> 1641 N. First Street, Suite 170
> San Jose, CA-95112.
> Tel: (408) 436-9070 ext.101
> Fax: (408) 436-9078
> e-mail: raghu@apsimtech.com
> ************************************************************************
>
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