**From:** *Aubrey_Sparkman@Dell.com*

**Date:** Tue May 09 2000 - 06:16:57 PDT

**Next message:**Chris Rokusek: "RE: [SI-LIST] : May 9th Presentation: "Radiation from Edge Effects in Printe..."**Previous message:**Nadolny, Jim: "RE: [SI-LIST] : May 9th Presentation: "Radiation from Edge Effec ts in Printe..."**Maybe in reply to:**Doug Brooks: "[SI-LIST] : Trace Impedance Selection"**Next in thread:**John Spohnheimer: "RE: [SI-LIST] : Trace Impedance Selection"

John,

Thanks!

Aubrey Sparkman

Signal Integrity

Aubrey_Sparkman@Dell.com

(512) 723-3592

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

*> From: John Spohnheimer [mailto:John.Spohnheimer@dalsemi.com]
*

*> Sent: Monday, May 08, 2000 6:04 PM
*

*> To: 'si-list@silab.eng.sun.com'
*

*> Subject: RE: [SI-LIST] : Trace Impedance Selection
*

*>
*

*>
*

*> While reading the various posts to the original question and
*

*> the direction of some of the discussion, I can't help but
*

*> think we may be confusing ourselves...
*

*>
*

*> When I was first introduced to Network Analysis many years
*

*> ago, one of the first points made was that Maxwell's
*

*> equations (plus the Lorentz force equation) sum up all you
*

*> need to know about E&M. Network Analysis is just a VERY
*

*> useful approximation to the nasty differential equations that
*

*> result when attempting to analyze real circuits. Since it is
*

*> an approximation, you have to be aware of its assumptions,
*

*> and when those assumptions might not apply. In particular,
*

*> Network Analysis assumes that the size of the circuit is such
*

*> that all pertinent phenomena can be represented by lumped
*

*> elements, i.e. all circuit geometry sizes are much, much less
*

*> than any wavelength of interest.
*

*>
*

*> Well, that limitation was fine for our first course, but how
*

*> do you handle real-life situations with time delays and
*

*> distributed networks. That's where the T-line comes in. Not
*

*> only does the T-line have some very nice electrical
*

*> characteristics, but it also has some very convenient
*

*> mathematical characteristics that extend the domain of
*

*> network analysis. The T-line is a network analysis
*

*> approximation that embodies certain characteristics that
*

*> previously were only solvable with the full Maxwell's
*

*> equations - hence a VERY useful approximation.
*

*>
*

*> So far, so good. Where we seem to be running into difficulty
*

*> is when we mix modes of our discussion. Specifically:
*

*>
*

*> I claim that radiation from circuits is due to fundamental
*

*> wave phenomenon - the full Maxwell's equations are required
*

*> (at this point) to get believable results. Unfortunately,
*

*> all the network components that we work with (including
*

*> T-lines), have NO wave phenomenon associated with them.
*

*> Attempting to mix both network analysis models with
*

*> free-space wave propagation characteristics is, in my
*

*> opinion, doomed to failure. Mixing models conceptually will
*

*> almost assuredly lead to misunderstanding and weird,
*

*> non-physical results.
*

*>
*

*> A good example of this is the classic energy conservation
*

*> problem with two capacitors: Take two caps (each C), one
*

*> initially charged to V, the other to zero. Connect them at
*

*> time zero. The final voltage will be V/2 by charge
*

*> conservation, but then energy isn't conserved. Einitial =
*

*> ½*C*V^2, Efinal = 2*( ½*C*(V/2)^2) = ¼*C*V^2 Where'd half
*

*> the energy go? I don't buy "radiation" and I don't buy "it
*

*> disappeared". The real problem is that the model is
*

*> non-physical. You can't build a real circuit with two caps
*

*> without introducing some inductance and some resistance
*

*> (unless you use superconductors...). Once these real, but
*

*> previously neglected, physical components are added, the
*

*> conceptual problem disappears: Either half the energy is
*

*> dissipated in the finite resistance, or (for the case of the
*

*> superconductor) the tank circuit oscillates forever.
*

*>
*

*> So, you're probably asking: is this guy foolish enough to say
*

*> you can't model these effects? Absolutely not. I'm just
*

*> warning you to be careful about how the models are
*

*> constructed and interpreted. If you want to model radiation
*

*> from a T-line, your network should consist of the T-line
*

*> (with your favorite embedded model) plus a parasitic resistor
*

*> that models the amount of the signal coupled into the
*

*> surrounding media. The energy dissipated into this resistor
*

*> is not lost as heat, but rather radiated into free space
*

*> (i.e. from the antenna characteristics of the circuit). This
*

*> "radiation" resistor is just a bookkeeping means of
*

*> accounting for the energy loss from the circuit - i.e. it
*

*> keeps the circuit simulator honest.
*

*>
*

*> Accounting for the value of this resistor is a bit tricky.
*

*> The best way that comes to mind would be to treat the T-line
*

*> as a 3-port circuit (the third port being the radiated field)
*

*> and calculate what the energy lost into the field really is
*

*> from your port1 and port 2 measurements (energy into port1
*

*> minus energy rec'd at port2 = energy radiated into port3).
*

*> This term would then appear in parallel to the standard input
*

*> impedance of the T-line model. I'd fully expect that this
*

*> term would vary with frequency and depend strongly on the
*

*> surrounding structures. I think a similar measurement
*

*> technique can be used to estimate the single port input
*

*> impedance of an antenna when modeling the load on a
*

*> transmitter. The real question at hand would then be if
*

*> anyone has a theoretical model for the input impedance seen
*

*> for an arbitrary antenna structure. I'm sure such models
*

*> exist for dipoles and such, but general board layout isn't
*

*> anywhere near as symmetrical or consistent.
*

*>
*

*> This discussion thread seems to assume that since free space
*

*> has an impedance of 377 ohms, the "radiation" resistor would
*

*> also appear as 377 ohms. I disagree strongly. The value of
*

*> the "radiation" resistor has to account for the all the
*

*> various coupling efficiencies and the loading due to near
*

*> field structures. Even a well designed half-wave dipole can
*

*> be designed with an input impedance of 50 ohms (i.e.
*

*> VSWR=1.0), and it still has to couple into free space at 377
*

*> ohms. A better way to conceptually look at an antenna is as
*

*> an impedance transformer, not just a straight resistance.
*

*>
*

*> Now I'll be the first to admit that I may be full of it since
*

*> I haven't actually tried to correlate to real life with this
*

*> technique, but it seems to be a much cleaner way of thinking
*

*> about the problem.
*

*>
*

*> John Spohnheimer
*

*>
*

*>
*

*>
*

*>
*

*> Vinu Arumugham wrote:
*

*> >
*

*> > If you were able to connect a transmitter to a receiver
*

*> using a 377 ohm
*

*> > transmission line, this line would be in parallel to the
*

*> "transmission
*

*> > line" between the two formed by free space. Therefore, one half the
*

*> > transmitted power would go through free space and the other
*

*> half through
*

*> > the line. As the line impedance is lowered, more power would be
*

*> > transmitted through the line and less through space.
*

*> >
*

*> > What's wrong with this scenario?
*

*> >
*

*> > Thanks,
*

*> > Vinu
*

*>
*

*>
*

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*>
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**Next message:**Chris Rokusek: "RE: [SI-LIST] : May 9th Presentation: "Radiation from Edge Effects in Printe..."**Previous message:**Nadolny, Jim: "RE: [SI-LIST] : May 9th Presentation: "Radiation from Edge Effec ts in Printe..."**Maybe in reply to:**Doug Brooks: "[SI-LIST] : Trace Impedance Selection"**Next in thread:**John Spohnheimer: "RE: [SI-LIST] : Trace Impedance Selection"

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