# Re: [SI-LIST] : Oscillation in lumped circuits and transmission l ines

Fred Balistreri (*fred@apsimtech.com*)

*Fri, 05 Feb 1999 09:52:40 -0800*

Dima Smolyansky wrote:

*> *

*> Although, it could be noted that the propagation delay of a transmission line Pd is related to L and C as*

*> Pd = (LC)^1/2. In addition, the factor of 2*pi is just a conversion between linear and angular frequency, and therefore for even-handed comparison must be dropped. Then, the factor of 4 is apparently due to assumption of quarter*

*> wavelength oscillation. But then, there will be a similar high-order oscillation for an LC circuit. I think this implies good correlation between the two models. The choice between the two comes down to a standard*

*> lumped-distributed type analysis.*

*> *

*> Hope this helps.*

*> --*

*> Thanks,*

*> *

*> -Dima*

*> *

*> =========================*

*> Dima Smolyansky*

*> TDA Systems, Inc.*

*> 7465 SW Elmwood St.*

*> Portland OR 97223*

*> 503-977-3629*

*> 503-245-5684 (FAX)*

*> dima@tdasystems.com*

*> http://www.tdasystems.com*

*> *

*> Peterson, James F (FL51) wrote:*

*> *

*> > Good question Arani,*

*> > I have often wondered the same thing (every time someone uses the term*

*> > ringing and reflection to describe the same phenomenon). The more I study*

*> > the SI area of engineering the more I notice that people can be describing*

*> > things differently based on different perspectives but still be correct.*

*> > That said, I believe that a lumped LRC circuit's behavior is not related to*

*> > a transmission line reflection. One good reason is that the period of the*

*> > lumped circuit's oscillation will be 2*pi*(LC)^1/2, whereas the period of a*

*> > reflection will always be 4*Pd (where Pd is the 1 way prop. time of the*

*> > signal). In fact this is a great way to tell the difference. If the period*

*> > of a measured signal is much larger than 4 * Pd, then it's a lumped LRC*

*> > problem (add some series r to get rid of it).*

*> > Hope this helps,*

*> > Jim*

*> >*

*> >*

*> > -----Original Message-----*

*> > From: Arani Sinha [mailto:sinha@poisson.usc.edu]*

*> > Sent: Friday, February 05, 1999 3:02 AM*

*> > To: si-list@silab.Eng.Sun.COM*

*> > Cc: sinha@poisson.usc.edu*

*> > Subject: [SI-LIST] : Oscillation in lumped circuits and transmission*

*> > lines*

*> >*

*> > Hi,*

*> >*

*> > I have the following question.*

*> >*

*> > We can model an interconnect as either a lumped circuit or a*

*> > transmission line. By means of lumped modeling, we can say that*

*> > it has an oscillatory response if its damping factor is less*

*> > than 1. By means of transmission line modeling, we can say that*

*> > it has an oscillatory response if the signal reflection*

*> > co-efficients at source and load satisfy certain conditions.*

*> >*

*> > My question is whether oscillation in a lumped circuit and*

*> > signal reflection in a transmission line are actually the same*

*> > phenomenon. If so, there should be a correlation between*

*> > conditions for oscillation in a lumped circuit and those for*

*> > oscillation in a transmission line.*

*> >*

*> > After many discussions and much thought, I have not been able*

*> > to determine a correlation. I am also ambivalent about whether*

*> > they are the same phenomenon.*

*> >*

*> > I understand that the damping factor in a lumped circuit is*

*> > equivalent to the attenuation constant in a transmission line*

*> > and that condition of no reflection is equivalent to the*

*> > maximum power transfer theorem.*

*> >*

*> > I will really appreciate help in this regard.*

*> >*

*> > Thanks,*

*> >*

*> > Arani*

*> >*

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*> *

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It should be noted that Oscillation due to LC lumped parameters and

transmission line behavior are NOT the same thing and there is NO

correlation between the damping resistor used in lumped LC circuits and

attenuation in transmission lines. Theoritical (lossless) transmission

lines (distributed, not lumped) will NOT oscillate when properly

terminated with the known characteristic impedance. This is independent

of the length used since this case is theoritical. Lumped circuit

parameters should NOT be used in place of transmission lines. Lumped

LCR parameters can approximate a transmission line once enough RLC

segments are used. However such a model is NOT dynamic and will

oscillate once the stimulus is made fast enough. Then more RLC

segments will be needed. But the important fact is that the resistance

used to dampen the oscillation bears no relationship to the attenuation

due to copper losses at DC or skin effect losses at higher frequencies.

This is a different issue altogether.

Distributed RC lines used at the IC level work because of the geometries

involved and the fact that aluminum has been used which is not as good

a conductor as copper. That is changing. Even as shrinking occurs the

IC sizes and level of integration is dramatically increasing. This means

the RC approximation is already breaking down. Transmission lines will

have to be used in the not so distant future even for IC's especially

systems on a chip.

Best Regards,

--
Fred Balistreri
fred@apsimtech.com
http://www.apsimtech.com

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