[SI-LIST] Re: capacitor impedance in time domain

  • From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
  • To: si-list@xxxxxxxxxxxxx
  • Date: Sun, 30 Jan 2005 19:17:47 -0800

Steve -- perhaps I'm missing the point of your analysis, or not 
understanding how you're using Z.  If I combine your equation below [Z = 
1/( dv/dt * C )] with the defining equation for the capacitor 
i=C*(dv/dt), I get Z=1/i.  Perhaps you have a typo in there.

Typos aside, I'm uncomfortable calling f = (dv/dt)/(di/dt) an impedance. 
    It's obviously time-dependent, but I would only feel comfortable if 
the time-dependent impedance transforms to the frequency-domain 
impedance.  Furthermore, the above funtion f is input-dependent, so it's 
not an intrinsic function of the device, which a system function such as 
impedance should be.  For example, consider a 1 farad capacitor.  If we 
excite it with v=sin(t), we get i=cos(t), and f=-cos(t)/sin(t).  If we 
excite it with v=cos(t), get i=-sin(t), and f=sin(t)/cos(t).

The preceding arguments are really just nomenclature, about whether f 
should be called impedance, which obviously isn't important to solving 
the problem.  I may have missed the point of your prior analysis when I 
read it the first time by getting tripped up on the impedance part of 
it, so what I'm really interested in knowing is the following:

Given a device's description (for example, i=C*(dv/dt)) how would you 
use f=(dv/dt)/(di/dt) to solve the problem of that device within a 
circuit such as that postulated in the initial post of this thread?  Or 
maybe more along the lines of your earlier analysis, how would f be used 
to lend rapid insight short of solving the problem rigorously (as was 
done by another list member)?

I'm not trying to be contrary here -- just trying to understand if 
you're pointing out a circuit analysis technique to which I haven't been 
exposed.

   -- Steve

-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Analysis Company."
http://www.tdasystems.com

email: steven.corey@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax:   (503) 246-2282
-------------------------------------------


Steve Weir wrote:
> Steve, actually the equation Z = 1/( dv/dt * C ) holds just fine in the 
> time domain.  You just have to remember that V and therefore dv/dt at the 
> node depends on Z.  The feedback equation using Z for the capacitor yields 
> the correct result whether we ground the capacitor, or simply use it to 
> couple two transmission line segments as is commonly done in a SERDES 
> backplane application
> 
> Regards,
> 
> 
> Steve.
> At 11:54 PM 1/29/2005 -0800, Steve Corey wrote:
> 
>>In my opinion, the easiest way to solve the problem is to think of what
>>you would expect when TDR'ing an ideal 50-ohm T-Line of delay Td
>>terminated by an ideal capacitance C, using an ideal 50-ohm TDR with a
>>total voltage step of vstep.  The capacitor initially appears as a short
>>circuit (voltage goes to zero, gamma=-1) and finally appears as an open
>>circuit (voltage goes to vstep, gamma=+1).  Now think of the view from
>>the perspective of the capacitor.  When it looks up the line, all it
>>sees is 50 ohms to ground, tline energy storage notwithstanding -- the
>>capacitor doesn't care if it's a terminated tline or a resistor.  As a
>>result, the controlling time constant to charge the capacitor is
>>(C*50ohms).  When we mix all this together, we come up with a TDR
>>waveform that starts at zero, steps up to vstep/2, is flat for 2*Td,
>>steps instantaneously to zero, then "decays" up to vstep with a time
>>constant given by C*50ohms.
>>
>>We review this case, and a number of related cases, in our TDR quick
>>guide, although the pictures do include parasitic effects such as finite
>>risetime and a nonideal capacitor:
>>http://www.tdasystems.com/library/appnotes/tdr_iconnect_quick_guide.PDF
>>
>>For a actual measurements on a power/ground plane pair, you can take a
>>look at figure 4 in the following app note:
>>http://www.tdasystems.com/library/appnotes/PDNA-0703.pdf
>>
>>Regarding Steve's earlier post -- replacing jw with dv/dt to map Z =
>>1/jwC to Z = 1/(dv/dt * C) is really no different from a frequency
>>domain analysis since the latter expression is only valid for a
>>single-frequency sinusoidal v.  Looking for flat and steep places in a
>>non-sinusoidal v and applying that relationship will not give valid results.
>>
>>   -- Steve
>>
>>-------------------------------------------
>>Steven D. Corey, Ph.D.
>>Time Domain Analysis Systems, Inc.
>>"The Interconnect Analysis Company."
>>http://www.tdasystems.com
>>
>>email: steven.corey@xxxxxxxxxxxxxx
>>phone: (503) 246-2272
>>fax:   (503) 246-2282
>>-------------------------------------------
>>
>>
>>Steve Weir wrote:
>>
>>>Alan, well if we short a transmission line at the far end with a 
>>
>>capacitor,
>>
>>>then Z still equals 1/( dv/dt * C ).  Hopefully this is obvious as a
>>>reexpression the sinewave response Z = 1/jwC.  With a big "perfect"
>>>capacitor, this will just look like a shorted line with a -1 reflection
>>>coefficient. As the capacitor gets smaller, the pulse top reflection will
>>>decay, and with further reductions in C the edge reflections will decay.
>>>
>>>The problem with viewing this as an RC is the stored energy in the line.
>>>
>>>Regards,
>>>
>>>
>>>Steve
>>>At 03:04 PM 1/28/2005 -0800, Alan Hilton-Nickel wrote:
>>>
>>>
>>>>Steve, I don't think you and Chris are talking about the same topology. My
>>>>understanding is that Chris is looking at
>>>>"a lossless transmission line terminated with a lossless capacitor", which
>>>>to me looks like:
>>>>
>>>>driver => txline => capacitor => GND
>>>>
>>>>I believe Arpad is correct in looking at this topology as an RC
>>>>connection, especially in the lossless case.
>>>>
>>>>Alan
>>>>
>>>>Steve Weir wrote:
>>>>
>>>>
>>>>
>>>>>Arpad, this would be a good time to use Jon Powell's si-draw tool.  But
>>>>>let me try this without:
>>>>>
>>>>>driver => txline => coupling cap => txline => terminator
>>>>>
>>>>>Now, let's suppose the driver has a Tr of 100ps, a Tf of 100ps, and a
>>>>>pulse width of 2.4ns, an output impedance of 0.0001 ohms, and a drive
>>>>>level of 2.5V.  Let's try three different values of coupling capacitors,
>>>>>all in the same 0402 body and 50 ohm txlines.
>>>>>
>>>>>10pF
>>>>>1nF
>>>>>100nF
>>>>>
>>>>>Now, what sort of wave form do you expect to see at each point?
>>>>>
>>>>>I know what my answers are:  10pF lots of reflection towards the source
>>>>>and droop towards the terminator.  1nF and 100nF very little reflection
>>>>>or droop.  Plug it into your favorite simulator and see what you get.
>>>>>
>>>>>Regards,
>>>>>
>>>>>
>>>>>Steve
>>>>>At 02:03 PM 1/28/2005 -0800, Muranyi, Arpad wrote:
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>You will get full reflection, because the impedance
>>>>>>you need to use for the equation you quoted is the
>>>>>>small signal (AC) impedance.  Referring to my previous
>>>>>>posting a short time ago, the constant current source
>>>>>>equivalent during the ramping portion of your trapezoid
>>>>>>waveform has a (finite dV) / (dI =3D 0) =3D> infinite impedance.
>>>>>>
>>>>>>The question I have for you is this:  where do you mean
>>>>>>that your waveform is trapezoid?  At the beginning of
>>>>>>the T-line, or at the end, where the capacitor is?
>>>>>>If the first, be prepared for a non trapezoid waveform
>>>>>>at the capacitor, because the T-line and the cap forms
>>>>>>an RC circuit, who's response is an exponential waveform.
>>>>>>If the ramp is faster the RC constant you will see
>>>>>>an exponential waveform, if it is slower, you will see
>>>>>>a more or less trapezoid waveform.
>>>>>>
>>>>>>I hope this helps,
>>>>>>
>>>>>>Arpad
>>>>>>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= 
>>>>>
>>3D=3D=
>>
>>>>>>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= 
>>>>>
>>3D=3D=
>>
>>>>>>=3D=3D=3D=3D=3D
>>>>>>
>>>>>>
>>>>>>-----Original Message-----
>>>>>>From: si-list-bounce@xxxxxxxxxxxxx 
>>>>>
>>[mailto:si-list-bounce@xxxxxxxxxxxxx] =
>>
>>>>>>On Behalf Of group_delay
>>>>>>Sent: Friday, January 28, 2005 1:48 PM
>>>>>>To: si-list@xxxxxxxxxxxxx
>>>>>>Subject: [SI-LIST] Re: capacitor impedance in time domain
>>>>>>
>>>>>>
>>>>>>hi all,
>>>>>>what i really want to do is find out how much waveform gets reflected
>>>>>>
>>>>>>
>>>>>
>>>>>>from the end of a lossless transmission line terminated with a
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>lossless capacitor, assuming the input waveform is a trapezoidal
>>>>>>signal. I know this can be computed using: gamma =3D (Zl-Zo)/(Zl+Zo),
>>>>>>but this requires you to calculate Zl for the time domain signal. If I
>>>>>>wanted to avoid it and use time domain analysis, how would I setup the
>>>>>>equation?
>>>>>>
>>>>>>thanks,
>>>>>>chris
>>>>>>
>>>>>>
>>>>>>--- In si-list@xxxxxxxxxxxxxxx, steve weir <weirsp@xxxx> wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>matthias, in the time domain we would solve the differential
>>>>>>>
>>>>>>
>>>>>>equations for=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>the network, or more likely using a computer program we would solve =
>>>>>>>
>>>>>>
>>>>>>the=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>difference equations over a series of discrete time steps.  Now in
>>>>>>>
>>>>>>
>>>>>>either=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>case we could express impedance as dv/dt / di/dt.  But I don't know =
>>>>>>>
>>>>>>
>>>>>>how=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>useful it would be towards either visualizing behavior, or solving the =
>>>>>>>
>>>>>>>
>>>>>>>equations.  Let's take the trapezoidal wave for instance.  An =
>>>>>>>
>>>>>>
>>>>>>effective=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>impedance is pretty easy to come by on each:  the rising, and falling=20
>>>>>>>portions of the waveform from the capacitance expression C =3D
>>>>>>>
>>>>>>
>>>>>>i/dv/dt, Z =3D=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>dv/dt / di/dt =3D 1/(dv/dt * C ).  The flat portions are troublesome
>>>>>>>
>>>>>>
>>>>>>as are=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>the vertices, since dv/dt theoretically goes to zero and the
>>>>>>>
>>>>>>
>>>>>>impedance from=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>the formula jumps to an infinite value.  Intuition should tell us
>>>>>>>
>>>>>>
>>>>>>that this=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>is wrong, as
>>>>>>>
>>>>>>
>>>>>>coupling capacitors routinely pass high frequency pulses.
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>=20
>>>>>>>In the frequency domain, we have this nailed.  We don't have=20
>>>>>>>discontinuities at the vertices.  The vertices and flat portions =
>>>>>>>
>>>>>>
>>>>>>follow=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>curves formed by the frequency components, and rather than a flat
>>>>>>>
>>>>>>
>>>>>>section=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>containing DC and no HF, quite the opposite is true:  the flatter we
>>>>>>>
>>>>>>
>>>>>>want=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>the pulse tops to be, the higher the frequency content required.  This =
>>>>>>>
>>>>>>>
>>>>>>>aligns with our intuition.  But when we transform the representation
>>>>>>>
>>>>>>
>>>>>>back=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>to the time domain, those piecewise linear segments are now curved
>>>>>>>
>>>>>>
>>>>>>solving=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>the discontinuities at the vertices and eliminating the flat slopes
>>>>>>>
>>>>>>
>>>>>>with=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>theoretically infinite Z between the edges.
>>>>>>>=20
>>>>>>>So if someone wanted to look only at the rising and falling edges, an=20
>>>>>>>impedance in the time domain is reasonable, and possibly even
>>>>>>>
>>>>>>
>>>>>>useful.  But=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>it really gets awkward when dealing with the whole waveform unless
>>>>>>>
>>>>>>
>>>>>>we first=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>perform frequency limiting operations, most easily performed in the=20
>>>>>>>frequency domain.
>>>>>>>=20
>>>>>>>I am not an expert on algorithms, so I really can't say from an error=20
>>>>>>>analysis and computational efficiency standpoint what is really the
>>>>>>>
>>>>>>
>>>>>>best=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>way to perform a transient analysis.  But in my naivete, I would be=20
>>>>>>>inclined to transform everything into the frequency domain, compute =
>>>>>>>
>>>>>>
>>>>>>the=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>solution and transform back.  In my feeble mind, this would avoid
>>>>>>>
>>>>>>
>>>>>>some of=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>the discontinuity and convergence problems in SPICE and more closely=20
>>>>>>>follows nature.  But since people a whole lot better at math than I
>>>>>>>
>>>>>>
>>>>>>have=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>worked long and hard on those algorithms, I suspect either the=20
>>>>>>>computational overhead, or error build-up of my naive approach would =
>>>>>>>
>>>>>>
>>>>>>be=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>unacceptably high.  Maybe what this world needs is a five cent, 256 =
>>>>>>>
>>>>>>
>>>>>>bit=20
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>floating point, matrix solver!
>>>>>>>=20
>>>>>>>Steve.
>>>>>>>=20
>>>>>>>At 10:13 PM 1/26/2005 +0100, Matthias Bergmann wrote:
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>>Hello, I don`t understand why impedance should be limited to =
>>>>>>>>
>>>>>>>
>>>>>>Frequency
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>domain. What impedance are we speaking about ? For example the
>>>>>>>>characteristicimpedance Z of a transmission line also exists in
>>>>>>>>
>>>>>>>
>>>>>>time domain.
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>If you look along a transmission line, v(t) / i(t) have got
>>>>>>>>
>>>>>>>
>>>>>>singularities
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>(undefined, infinite), these are called short and open ?!?!?
>>>>>>>>
>>>>>>>
>>>>>>Furthermore
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>mostof the simulation programs use the time domain because it permits
>>>>>>>>non-linearities. I don`t know how what happens when your impulse is
>>>>>>>>trapezoidal, but if it was a rectangular and your load is a
>>>>>>>>
>>>>>>>
>>>>>>capacitance, you
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>are answer would look like an exponential function, with your
>>>>>>>>
>>>>>>>
>>>>>>reflection
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>co-efficient as initial value. Regards, Matthias Bergmann P.S.:
>>>>>>>>
>>>>>>>
>>>>>>Yes, use
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>SPICE or ADS ! _m |---------+---------------------------------->
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
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>>>>>>>>
>>>>>>>>-list@xxxx>&#160;&#160;&#160;&#160;&#160;&#160;&#160&#160;&#160;&#160
>>>>>>>>-LIST] Re: capacitor impedance in time
>>>>>>>>
>>>>>>>
>>>>>>>domain&#160;&#160;&#160;&#160;&#160;&#16&#160;&#160;&#160;&#160;&#160 
>>>>>>
>>;&#=
>>
>>>>>>160;&#1
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>60I&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; 
>>>>>>
>>&#1=
>>
>>>>>>60;&#16
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;|
>>>>>>>>
>>>>>>>
>>>>>>>&#160;>-------------------------------------------------------------- 
>>>>>>
>>---=
>>
>>>>>>----
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>-- &#160;-----------------------------------------| >I could be
>>>>>>>>
>>>>>>>
>>>>>>wrong >but
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>tome >impedance is a concept strongly related to Frequency domain.
>>>>>>>>It is
>>>>>>>>meaningful just in that domain. Absolutely. If you define impedance =
>>>>>>>>
>>>>>>>
>>>>>>as
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>voltage/current, then you run into great difficulties if you try to
>>>>>>>>
>>>>>>>
>>>>>>do it in
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>the time domain.&#160; In general, with any complex impedance,
>>>>>>>>
>>>>>>>
>>>>>>v(t)/i(t) has
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>singularities (undefined, infinite). I consider impedance =3D
>>>>>>>>
>>>>>>>
>>>>>>v(s)/i(s) or
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>v(f)/i(f), which makes it a strictly frequency domain parameter.
>>>>>>>>
>>>>>>>
>>>>>>Regards,
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>Andy
>>>>>>>>
>>>>>>>
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>>>>>>
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>>
>>>>>>#160;
>>>>>>
>>>>>>
>>>>>>
>>>>>>
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>>>>>>>>
>>>>>>>
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>>>>>>
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>>>>>
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>>>>>List FAQ wiki page is located at:
>>>>>              http://si-list.org/wiki/wiki.pl?Si-List_FAQ
>>>>>
>>>>>List technical documents are available at:
>>>>>              http://www.si-list.org
>>>>>
>>>>>List archives are viewable at:
>>>>>               //www.freelists.org/archives/si-list
>>>>>or at our remote archives:
>>>>>               http://groups.yahoo.com/group/si-list/messages
>>>>>Old (prior to June 6, 2001) list archives are viewable at:
>>>>>               http://www.qsl.net/wb6tpu
>>>>>
>>>>>
>>>>>
>>>>>
>>>>
>>>The weirsp@xxxxxxxxxx e-mail address will terminate March 31, 2005.
>>>Please update your address book with weirsi@xxxxxxxxxx
>>>
>>>
>>>------------------------------------------------------------------
>>>To unsubscribe from si-list:
>>>si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
>>>
>>>or to administer your membership from a web page, go to:
>>>//www.freelists.org/webpage/si-list
>>>
>>>For help:
>>>si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
>>>
>>>List FAQ wiki page is located at:
>>>                http://si-list.org/wiki/wiki.pl?Si-List_FAQ
>>>
>>>List technical documents are available at:
>>>                http://www.si-list.org
>>>
>>>List archives are viewable at:
>>>              //www.freelists.org/archives/si-list
>>>or at our remote archives:
>>>              http://groups.yahoo.com/group/si-list/messages
>>>Old (prior to June 6, 2001) list archives are viewable at:
>>>              http://www.qsl.net/wb6tpu
>>>
>>>
>>>
>>>
>>
>>
>>
>>------------------------------------------------------------------
>>To unsubscribe from si-list:
>>si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
>>
>>or to administer your membership from a web page, go to:
>>//www.freelists.org/webpage/si-list
>>
>>For help:
>>si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
>>
>>List FAQ wiki page is located at:
>>                http://si-list.org/wiki/wiki.pl?Si-List_FAQ
>>
>>List technical documents are available at:
>>                http://www.si-list.org
>>
>>List archives are viewable at:
>>                //www.freelists.org/archives/si-list
>>or at our remote archives:
>>                http://groups.yahoo.com/group/si-list/messages
>>Old (prior to June 6, 2001) list archives are viewable at:
>>                http://www.qsl.net/wb6tpu
>>
> 
> 
> The weirsp@xxxxxxxxxx e-mail address will terminate March 31, 2005.
> Please update your address book with weirsi@xxxxxxxxxx
> 
> 
> ------------------------------------------------------------------
> To unsubscribe from si-list:
> si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
> 
> or to administer your membership from a web page, go to:
> //www.freelists.org/webpage/si-list
> 
> For help:
> si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
> 
> List FAQ wiki page is located at:
>                 http://si-list.org/wiki/wiki.pl?Si-List_FAQ
> 
> List technical documents are available at:
>                 http://www.si-list.org
> 
> List archives are viewable at:     
>               //www.freelists.org/archives/si-list
> or at our remote archives:
>               http://groups.yahoo.com/group/si-list/messages
> Old (prior to June 6, 2001) list archives are viewable at:
>               http://www.qsl.net/wb6tpu
>   
> 
> 
> 


------------------------------------------------------------------
To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field

or to administer your membership from a web page, go to:
//www.freelists.org/webpage/si-list

For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field

List FAQ wiki page is located at:
                http://si-list.org/wiki/wiki.pl?Si-List_FAQ

List technical documents are available at:
                http://www.si-list.org

List archives are viewable at:     
                //www.freelists.org/archives/si-list
or at our remote archives:
                http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
                http://www.qsl.net/wb6tpu
  

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