RE: [SI-LIST] : Trace Impedance Selection

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From: Bilal Ahmad (bahmad@cisco.com)
Date: Tue May 16 2000 - 15:52:09 PDT


This is my 4th attempt at making this post (originally tried on May 08);
I think the server didn't like my attachment, which is now available on
a web-link. (I am assuming no one received the previous posts!)

---- Original message from May 08, 2000 ----

I think this problem will benefit a lot from experimental data, as it is
too complex to be
analyzed without direction from experiment. What structures are
responsible for the
majority of radiation? How much is their impedances affected by the
presence of other
structures nearby? Is the radiation from individual sources more
important, or is it the
coupled energy to efficient radiators on the board that is more
important in the overall radiation
budget? Etc....

Anyway, I want to mention a few points regarding the selection of Zo on
PCBs in regards to its
effect on radiated emissions. Please forgive me if I repeat somethings
already said here; I
just joined the list yesterday, and the archive on the internet seems to
be down since then, at
least.

Axiom: All radiating structures are electrically small thin wire
antennas.
Axiom: Individual radiators (primary radiation, not secondary emissions)
are responsible for
the majority of radiation.

The amount of power transfer from a source and transmission line
combination into an antenna
is determined by how well the impedances of the source/transmission-line
are matched (complex
conjugately) to that of the driving point impedance of the antenna. How
well the power
transferred to the antenna is transferred into air/space as radiation is
determined by the
radiation efficiency of the antenna, which depends on how much of the
resistance of the
antenna impedance is the radiation resistance (Rr) and how much is
attributed to ohmic losses
(R_loss).

(Aside: The 377 ohm impedance of free space is not directly relevant
here, I think. However,
Kraus has a very nice discussion of its significance in the case of very
large apertures---viz
a viz geometrical matching to plane wavefronts--- in the second chapter
of his book Antennas:
see section titled, "scattering by large apertures. And at some other
places in the book.)

Electrically small thin wire radiating structures have a small radiation
resistance. The total
driving point impedance of a electrically small antenna is a sum of the
radiation resistance
(Rr), a loss resistance (Rloss) and a large reactance (jX). For example,
Kraus-Antennas treats
the example of a center-fed dipole of length = 0.1*lambda, radius =
0.001*lambda, and made of
perfectly conducting material. The input impedance is calculated with a
simple application of
the method of moments, Za = 1.1 - j*1528 ohms. (In this case, Rloss =
0.)

So, let's say that our PCB has these little antennas hanging here and
there and connected to
sources of impedance Zo through transmission lines of characteristic
impedance Zo. A simple
configuration to look at would be where a small antenna is sitting at
the end of a
transmission line which is either terminated with Zo or left
open-circuited.

For Za = 1.4 - j*1000 ohms
V = 1 volt (rms)

Unterminated:

          Rs = Zo
                           -----------
    ------/\/\/\----------( Zo )--------------
    | ----------- |
    | |
    | ---
    | | |
    V | | Za
    | | |
    | ---
    | |
    | |
    -------------------------------------------------

Terminated:

          Rs = Zo
                           -----------
    ------/\/\/\----------( Zo )------------------------------
    | ----------- | |
    | | |
    | --- ---
    | | | | |
    V | | Za | |
Zo
    | | | | |
    | --- ---
    | | |
    | | |
    -----------------------------------------------------------------

The radiated power as a function of Zo is shown in this plot:

    http://www.employees.org/~bahmad/PrvsZo.jpg

So, with this simplistic picture alone, it appears that larger Zo is
very slightly better in containing
radiation, however, this decrease with increase in Zo is small,
especially for the terminated lines.

Bilal Ahmad

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