Neven,
The phenomenon you describe is pretty well understood and covered in the
literature. What follows is from memory but is essentially the idea, so
check the literature! Basically what you have, with a small opening, is a
waveguide operating below its cutoff frequency. While it is true that power
incident on the input port of such a waveguide does not propagate through
it, in the sense of a propagating mode, electromagnetic fields will exist
within the guide and will decay exponentially along the length of the
guide. These are referred to as cutoff or evanescent modes. Unfortunately,
when the evanescent mode reaches the other end of the waveguide, it will
propagate in the space beyond, albeit attenuated significantly. Propagation
through a waveguide is proportional to the complex exponential e^(-jBz). In
a waveguide operating below it's cutoff frequency, beta (B), the
propagation constant becomes negative-imaginary, B=-jA. The result is an
exponential decay of the field strength as e^(-Az). The amount of
attenuation is then dictated by the position within the guide, z, as
measured from the input, and the value of A.
Beta, B is the propagation constant and is computed for rectangular wave
guide as:
B = sqrt(k^2 -kc^2)
k = 2*pi*freq*sqrt(ue)
kc = sqrt( (m*pi/a)^2 + (n*pi/b)^2)
a = long dimension of waveguide cross section
b = short dimension of waveguide cross section
m and n are the mode indices
When kc > k the guide is in cutoff and B = -j(kc^2 - k^2) = -jA. In the
case of a rectangular waveguide operating in cutoff we are only interested
in the lowest frequency mode, TE10, The others operate at much higher
attenuations and we want worst case. In this case m=1 and n=0. So my best
guess is your attenuation should be something like 20log(e^(-Az)) dB, for a
single rectangular waveguide, of length z, operating below cutoff. This
could be easily extended to circular waveguide as well, if you have round
holes.
Well, that's my WAG at your question. As I said, this is covered in the
literature. Any EM text or microwave engineering text will have the
governing equations. One of my favorites is Microwave Engineering by David
Pozar. Perhaps others can suggest more.
Simulation could be done quite effectively using a field solver. We use
Ansoft's HFSS. There are others as well. I would not dismiss simulation
completely, but like you, I appreciate an analytical understanding. It
keeps you out of trouble! Well most of the time anyway...
I hope this helps.
Cheers,
-Rob Hinz
Consulting Engineer
SiQual, Signal Quality Engineering
18735 SW Boones Ferry Road
Tualatin, OR 97062-3090
(503) 885-1231
http://www.siqual.com/
At 09:16 AM 6/5/2001 -0700, Neven Pischl wrote:
I would appreciate if anyone could let me know if there are any references
(books, application notes, anythig ..) that deal with shielding
efectivness in cases when a source is close to an (electrically small)
opening in a shield (enclosure). In such a situation, the field will
penetrate through the hole and leak even if the size is much smaller than
the wavelength. I am particularly interested in situation when
high-frequency source, such as a PCB edge or a component operating at
(say) 1 GHz and above is in proximity of the venting holes, "small" gaps
in the chassis etc.
All references that I have deal with uniform plane wave propagating
incident to a metal plane with a slot or hole, in which case it is enought
o have electrically small size of the opening (e.g. lambda/10) to
efficiently block any field propagation through the barrier. I can't find
any useful reference that deals in any analytical way with the situation I
am intersted in.
I believe I might get some answers using some of the simulation programs,
but at the moment I am more intersted in the analysis of the problem than
in simulating it.
Thank you,
Neven Pischl
Rob Hinz
SiQual Corporation
r...@siqual.com
phone (503)885-1231 x30
fax (503)885-0550
