From: Jay Chesavage (jayc@cisco.com)
Date: Thu Jan 06 2000  05:40:48 PST
Adrian:
Thank you for your considered reply, and especially for the additional
information that this chaos theory application comes from optimizing
radiation, rather than minimizing it. I can see much more fruit from an
effort where you tinker with optimizing radiation at one frequency, or one
set of frequencies, rather than minimizing radiation at ALL frequencies.
Take a very simple 2D example like this:
3 isotropic sources of An*exp(jwt) are located on a line, with
separation d1 and d2. If the measured field at a point x,y is
the sum of these sources, and 0 is located on a perpendicular
axis coincident with s2, we get:
Y
\

S1=A1*exp(jwt)

 *(x,y)
d1


S2=A2*exp(jwt)y=0X


d2


S3=A3*exp(jwt)


(x=0)
So, the radiation at *(x,y) is
I(x,y) = A1*exp(jwt(z1)) + A2*exp(jwt(z2)) + A3*exp(jwt(z3))
z1=sqrt{(d1y)^^2 + x^^2}
z2=sqrt{y^^2 + x^^2}
z3=sqrt{(d2y)^^2 + x^^2}
The case for d1=d2=...dn has been modeled extensively for the case
of a radiating array. Fiddling with d1...dn in arbitrary ways seems
relatively new. (I only know of regular and logarithmic arrays)
So the statement of the problem for _maximizing_ at a few frequencies
is "Tinker with d1 & d2 with w fixed until I(x,y) is maximized".
This amounts to optimizing a function where 2 variables have to be
fiddled with.
Contrast this with the statement of the _minimization_ problem:
"Tinker with d1 & d2 to minimize I(x,y) for ALL frequencies".
A reasonable number of frequency points to evaluate, say from 100Mhz to
10Ghz might be 1000 points spaced logarithmically apart. If we decide we
are going to look at 1000 frequencies, the second minimization problem
requires 1000X more calculations, and each new degree of
freedom multiplies the complexity of the problem by an additional 1000X!
If we change the problem from 3 radiators to 6, the minimization problem
now requires 10^9 times more calculations than the maximization problem!
A factor of 9 orders of magnitude here, a factor of a billion there,
pretty soon you think you're either the late Carl Sagan, or you work for
the senate appropriations committee!
So if I have to choose which problem to optimize, I would go for
the maximize radiation problem, and leave the minimization problem
to someone with 10^9 X more time on their hands.
So, for the chaos experts out there, for a 10 hole problem (we're still in
TWO dimensions, remember: square everything again for THREE!) how do I
reduce the _factor of_ 10^21 additional calculations I just introduced
compared to the maximization of radiation problem?
The proposition of following functions to local maxima or minima is the
domain of gradients and tensors. If chaos theory is the proposition of
using old results to infer new ones, then it is a great tool (and sounds
in this context remarkably like linear programming). My point was that
the number of calculations for the general proposition of minimizing over
all state space compared to one state space is truly staggering, and being
a practical person, I'm still wondering how one could use Chaos Theory in
this context to produce a practical result.
Jay
On Wed, 5 Jan 2000, Adrian Shiner wrote:
> In answer to your question at the end of your email..maybe to probably.
>
> Consider these points and then let us expand the discussion .. it is just
> costing me nothing ..this is my professional and personal interest being
> applied in my leisure time.
>
> 1. There is ample evidence that radio antennae (aerials) designed on
> principles derrived from Chaos Theory are both smaller and have wider
> bandwidth for a given standing wave ratio than classical approaches. Getting
> the screening right is just a matter of designing a poor antenna!!!!!!!!
>
> 2. Chaos Theory is by no means limited to time dependant phenomena. All you
> need is a non linear system where the next state of the the system is
> nonlinearly linked to the previous state.
>
> 3. Radio astronomers are using the power of wave interference to discover
> new knowledge about the nature of the universe. Most physical phenomena in
> physics tend to provide insights on the very large and very small physical
> scales at the same time (not thinking classical physics). I have not seen
> anyone yet thinking about interference effects applied to screening
> (although I do not have enough time in my life to read everything). Steering
> microwave beams for radar uses interference but in a different way to energy
> passing through 2 adjacent slots.
>
> 4. Background reading on, around and thought on the subject of interest
> always pays dividends. It has been shown very recently that the classical
> Gaussian statistical distribution of real physical phenomena is incorrect in
> a big way. The distribution is skewed towards to origin. An example is the
> demagnetisation of magnets at high temperatures ( You could consider this as
> an example of Chaos Theory. Does the skew relate to a bifurcation
> characteristic?). The same curve applies in biological processes. This was
> in a report in the (UK) Financial Times. Check their web site for the exact
> article.
>
> 5. There is a world of difference between the thought needed to sustain the
> status quo in support of a business & that needed to maximise the
> development of the art. Unfortunately, the Universities and Military (these
> people have their own career agendas) establishments cannot and will not be
> the founts of all progress. Independant thinking helps all!!!!
>
> Best wishes
>
> Adrian
>
>  Original Message 
> From: Jay Chesavage <jayc@cisco.com>
> To: <silist@silab.eng.sun.com>
> Sent: 04 January 2000 21:23
> Subject: Re: [SILIST] : Chassis hole opening and frequencies
>
>
> > Last time I checked, chaos theory had to do with temporally varying
> > phenomenon, rather than spatially fixed phenomenon. Chaos theory, for
> > example, may be used to study weather, but doesn't work to well to figure
> > out where to put telephone poles. Unless the holes in your sheet metal
> > chase each other around a lot more than mine do, or you can convince
> > someone that EMI measurements need to be made while the antenna moves
> > randomly, I can't imagine chaos theory being applicable here.
> >
> > Is there a class of Chaos theory which has to do with optimizing fixed,
> > static structures? Sounds more like linear programming to me (explore
> > state space for minimum radiation at frequency f, where the variable is
> > hole placement), and then go repeat the process for each and every f, and
> > each and every hole placement(!).
> >
> > This seems on the surface to pay far less dividends for much more effort
> > than does, for example, quadrupling the number of holes, while quartering
> > the area of each one (assuming the aspect ratio has already been reduced
> > to 1 wherever possible).
> >
> > Am I missing something?
> >
> > Jay
> >
> >
> >
> > On Tue, 4 Jan 2000, Adrian Shiner wrote:
> >
> > > Do Douglas' results provide yet another elegant demonstration of the
> > > interference effect of transmission of electromagnetic energy through
> (in
> > > this case imperfect) parallel slots?
> > > If so, then surely room for further development...chaotic hole spacing
> or
> > > narrow short slots at chatotic angular orientations and lengths. Read up
> on
> > > Chaos Theory for the use of chaotic in the sentence above.
> > > Bet wishes for the new year
> > >
> > > Adrian
> > >  Original Message 
> > > From: Douglas McKean <dmckean@corp.auspex.com>
> > > To: <silist@silab.eng.sun.com>
> > > Sent: 04 January 2000 18:02
> > > Subject: Re: [SILIST] : Chassis hole opening and frequencies
> > >
> > >
> > > > Hi Doug,
> > > >
> > > > Henry Ott has a bunch of relationships regarding
> > > > holes. Namely circular, rectangular, an array of
> > > > circular holes, an array of rectangular holes.
> > > >
> > > > He begins discussing cutoff frequencies for
> > > > individual types of holes. Circular hole cut
> > > > off frequency is based on the diameter.
> > > > Rectangular hole cut off frequency is based on
> > > > longest side. I have an Excel spreadsheet where
> > > > I translated these equations for ease of use. The
> > > > actual relationships I can look up for you.
> > > >
> > > > The following results are linear so I'll use
> > > > 1 inch and the result for 1/10 of an inch is
> > > > simply 1/10 the result for the 1 inch and so on ...
> > > >
> > > > 1 inch Circular Hole: cut off freq = 6.90E+09
> > > > 1 inch Rectangular Hole: cut off freq = 5.90E+09
> > > >
> > > > Mr. Ott continues the discussion with Shielding
> > > > Effectiveness (SE) for the geometry of a particular
> > > > hole, i.e. circular and rectangular and the
> > > > thickness to diameter ratio. Again, the
> > > > relationships are linear so I'll normalize them
> > > > for you at 1:1 for thickness:diameter
> > > >
> > > > SE for circular hole 1:1 (thick:dia) = 32dB
> > > > (Thus, a ratio of 1:10 = 3.2 dB)
> > > > SE for rectangular hole 1:1 (thick:dia) = 27.2dB
> > > > (Thus, a ratio of 1:10 = 2.7 dB)
> > > >
> > > > Intuitively, it should become obvious that the
> > > > length of the hole forces the "hole" whatever
> > > > geometry it is the deciding as to how much the
> > > > of a cavity effect begins to dominate.
> > > >
> > > > Mr. Ott also discusses the "pattern effectiveness"
> > > > of an array of holes (circular or rectangular IIRC).
> > > > I'll give some results from my little spreadsheet.
> > > >
> > > > A 4x4 inch array of 1/4 inch diameter holes with
> > > > a 1 inch center to center separation in 18 gage
> > > > sheet metal (thickness =0.0478 in)
> > > >
> > > > SE = 52.1 dB
> > > >
> > > > Same array of holes as above changing only
> > > > the separation to 1/2 inch,
> > > >
> > > > SE = 40 dB
> > > >
> > > > It works out with this relationship that halving
> > > > or doubling the separation of holes results in
> > > > changing the SE by about 12 dB. IOW, a 2 inch
> > > > separation of the above array gives an SE = 64 dB
> > > > or 12 dB added to the 52 dB for the 1 inch.
> > > >
> > > > Keep in mind that there are many assumptions
> > > > made with these results. And the rules of thumb
> > > > regarding linearity or changing results by 12 dB
> > > > are merely theoretical.
> > > >
> > > > One further note, Dr. Hubing at an EMC presentation
> > > > here in Santa Clara two summers ago, discussed
> > > > results from mucho research on his behalf about
> > > > holes in covers. The bottom line is that slots
> > > > are the thing to worry about and not holes. And
> > > > with that conclusion I wholeheartedly agree.
> > > >
> > > > Regards, Doug McKean
> > > >
> > > >
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