RE: [SI-LIST] : Trace Impedance Selection

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


Aubrey Sparkman
Signal Integrity
(512) 723-3592

> -----Original Message-----
> From: John Spohnheimer []
> Sent: Monday, May 08, 2000 6:04 PM
> To: ''
> 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 =
> *C*V^2, Efinal = 2*( *C*(V/2)^2) = *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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