[SI-LIST] Re: Question on EMI radiated power
- From: "Dr. Edward P. Sayre" <esayre@xxxxxxxx>
- To: chuck@xxxxxxxxxxx, <Andrew.Burnside@xxxxxxxxxxxxxxxxxxx>, <a.ingraham@xxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Sun, 06 Nov 2005 15:22:56 -0500
All:
The question of input resistance and reactance follows from the definition
of voltage and current at the input terminals of any electromagnetic
structure. It does not detail of the energy once it flows into the antenna
or other electromagnetic structure but is a simple way to discuss the
properties of energy as it flow from one region to another. Reflection and
transmission at a planar interface can be equally well explained in terms
of terminal impedances as an antenna or scatterer.
Regarding the interpretation of radiation resistance and reactance, the
energy leaving a sphere in a radiation sense (distance -> infinity) will be
TEM in ordinary material, that is, the electric and magnetic field will be
transverse to the radial vector of the radiation sphere. Since the
radiation resistance is strictly a steady state sinusoidal defined term,
each Fourier component of the signal will have a unique radiation
resistance. The total power radiated in a specific direction from each
Fourier power component can be totaled using Parseval's Theorem over the
frequency range in question of the Poyntyng vector components.
But since radiation resistance is a terminal property related to total
radiated power, the total power at the input for a digital time signal can
similarly be computed for each Fourier component and summed. However,
neither the radiation resistance nor this summed quantity relates to
radiation in a specific direction or path. If for some reason, energy is
conducted away from the feed point by coupling to an adjacent structure,
then this must be included when the radiation resistance is computed.
With regard to the input reactance, it relates, as others have said, to the
sinusoidal voltage and current components which are pi/2 or 90 degrees out
of phase whatever the reason. It just happens that Maxwell's equations
when applied to the near field (distances on the order of the applied
wavelength) end up with imaginary components which fall off rapidly with
distance. Input reactance is, like input (radiation) resistance always a
function of frequency and so has a different value for each Fourier
component. For electrically small components (wavelength big compared to
some length metric) dipole reactance is always capacitive and closed loops
are always inductive. After the first resonance (i.e. where the reactance
passes through zero) the reactance changes sign so what was capacitive
becomes inductive and visa-versa.
The bigger question of relating time signal behavior to steady state
sinusoidal theory is complicated and not one-to-one with any frequency or
data rate. One must therefore be very careful with throwing around matrix
S-Parameter behavior as if any one value vs frequency or even a string of
values determines time signal behavior.
Personally I have a big problem with specifications that only discuss the
magnitude vs. frequency of an interconnect (e.g. XAUI). It's as if the
phase doesn't count where it is in fact very important but a little hard to
get your head around. For instance the phase determines the group velocity,
the quantity that tells you how fast the energy in a sinusoid is conducted
along an interconnect. If the group velocity is a strong function of
frequency, it is likely that a time signal will be distorted and show up as
a component of deterministic jitter.
Well enough preaching for now -
Sincerely,
ed sayre
====================
At 12:21 PM 11/6/2005 -0700, Charles Hill wrote:
>Andrew,
>
>We were discussing the feedpoint impedance of an antenna which is a complex
>scalar quantity and how a portion of that, the radiation resistance,
>represents the power transfer.
>
>When dealing with coupled structures a matrix quantity is used which has the
>off-diagonal terms of mutual impedance. The phase angle of the mutual
>impedance relates to the phase shift in the coupling. The feedpoint
>impedance of a coupled structure has to be computed from the matrix along
>with the self-impedances of the coupled elements; the feedpoint impedance is
>not a diagonal term of the matrix. So even with a coupled structure, the
>radiation resistance is a portion of the feedpoint impedance which
>represents the radiated power and it is always real valued.
>
>If it helps, consider another case of coupled inductors--a transformer. The
>only power that is transferred is a portion of that where the input voltage
>and input current are in phase--right?
>
>Charles
>
>
>-----Original Message-----
>From: si-list-bounce@xxxxxxxxxxxxx
>[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Andrew Burnside
>Sent: Sunday, November 06, 2005 4:44 AM
>To: chuck@xxxxxxxxxxx; a.ingraham@xxxxxxxx; si-list@xxxxxxxxxxxxx
>Subject: [SI-LIST] Re: Question on EMI radiated power
>
>
>Chuck
>:My interpretation of a reactive component is energy storage in the near
>:field surrounding the antenna, and of course there will be no power
>transfer
>:due to this. This is completely consistent with energy storage in
>::capacitors and inductors. Therefore, there is no such thing as a complex
>::radiation impedance.
>
>
>However, the reactive component may relate to any (partial) mutual
>inductance/capcitance there is to other structures in the near field.
>Therefore, we don't have an ideal antenna due to the near field loading.
>When considering EMI, we may well be within the near field range.
>
>If we consider digital circuits only for a moment, then the majority of the
>emissions are likely to be due to clocks / and current dumped down the power
>supply network. Yes, there may be some direct emissions from interconnects,
>but these are usually fairly small compared to the PSN, as we aren't talking
>power electronics here.
>
>If we are considering the far field only, then yes it is possible to get
>away with a resistance only if we are only interested in power transfer.
>However, I would have thought though that the emission phase is becoming
>signficant, considering the rise times of some of the signals present.
>
>Regards
>
>Andrew
>
>
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