[SI-LIST] Re: capacitor impedance in time domain
- From: Steve Weir <weirsi@xxxxxxxxxx>
- To: Dorin <dorin.oprea@xxxxxxxxxxx>
- Date: Mon, 31 Jan 2005 06:06:48 -0800
Dorin, yeah you got me there. I guess some people should sleep more often!
Regards,
Steve.
At 08:55 AM 1/31/2005 -0500, Dorin wrote:
>Nice try! (dv/dt)/[d(dv/dt)] is not equal with dv/dt.
>
>Thanks,
>Dorin
>
>
>
>Steve Weir wrote:
>
> > Steve, I am not sure why you would feel uncomfortable with Z = dv/dt /
> > di/dt. The miracle of linear superposition makes all the math that I am
> > familiar with work. One of the eye openers for me in much younger clothes
> > was looking at passive filter networks as feedback networks. This was
> > described in a feedback and control systems text by MacDonald. I'll dig it
> > out if you are interested. But basically we just end up with a Vo = Vin *
> > 1/( 1+G/H ) equation where Vin is the original pulse and Vo is the voltage
> > waveform at the tx-line capacitor junction. If you think about it, this is
> > pretty much what Peter's math is a simplified representation of.
> >
> > As to the derivation here we go:
> >
> > 1. i = C * dv/dt
> > 2. Z = dv/dt / di/dt
> >
> > Z = dv/dt * 1/( d/dt ( i ) )
> > Z = dv/dt * 1/ ( d/dt( C * dv/dt ))
> > Z = dv/dt * 1/(d(dv/dt)) * 1/C
> > Z = 1/( dv/dt * C )
> >
> > Now if we compare this to the frequency domain definition:
> >
> > Z = 1/jwC, recognizing that jw is just an expression of dv/dt, this all
> > works. It is just a matter of what representation is the most convenient
> > to work with.
> >
> > Regards,
> >
> > Steve.
> >
> > At 07:17 PM 1/30/2005 -0800, Steve Corey wrote:
> > >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>        
> 0; 
> > > >>>>>>>>-LIST] Re: capacitor impedance in time
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>>domain         
> ; 
> > > >>>>>>
> > > >>;&#=
> > > >>
> > > >>>>>>160;
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>60I          
>  
> > > >>>>>>
> > > >>=
> > > >>
> > > >>>>>>60;
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>          |
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>> >--------------------------------------------------------
> ------
> > > >>>>>>
> > > >>---=
> > > >>
> > > >>>>>>----
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>--  -----------------------------------------| >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.  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
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>----------------------------------------------------------------
> -- To
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>unsubscribe from si-list: si-list-request@xxxx with 'unsubscribe'
> > > >>>>>>>>inthe Subject field or to administer your membership from a web
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>page, go to:
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>//www.freelists.org/webpage/si-list For help:
> > > >>>>>>>>si-list-request@xxxx with 'help' in the Subject field List
> FAQ wiki
> > > >>>>>>>>page is located at:
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>>          
> 0;
> > > >>>>>>
> > > >>0;&=
> > > >>
> > > >>>>>>#160;
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>  http://si-list.org/wiki/wiki.pl?Si-List_FAQ List =
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>technical
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>documents are available at:
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>>          
>  
> > > >>>>>>
> > > >>=
> > > >>
> > > >>>>>>60;
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>> http://www.si-list.org List archives are viewable at:
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>>          
> 60;
> > > >>>>>>
> > > >>60;=
> > > >>
> > > >>>>>> 
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>          
> 60;htt
> > > >>>>>>
> > > >>p:/=
> > > >>
> > > >>>>>>/www.
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>freelists.org/archives/si-list or at our remote archives:
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>>          
>  
> > > >>>>>>
> > > >>=
> > > >>
> > > >>>>>>60;
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>          htt
> p://gr
> > > >>>>>>
> > > >>oup=
> > > >>
> > > >>>>>>s.yah
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>oo.com/group/si-list/messages Old (prior to June 6, 2001) list
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>archives are
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>viewable at:
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>>          
> 60;
> > > >>>>>>
> > > >>60;=
> > > >>
> > > >>>>>> 
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>          
> 60;htt
> > > >>>>>>
> > > >>p:/=
> > > >>
> > > >>>>>>/www.
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>
> > > >>>>>>>>qsl.net/wb6tpu
> > > >>>>>>>>--------------------------------------------------------------
> ----
> > > >>>>>>>>To unsubscribe from si-list:
> > > >>>>>>>>si-list-request@xxxx 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@xxxx 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
> > > >>>>>>>>
> > > >>>>>>>>
> > > >>>>>>>
> > > >>>>>>>=20
> > > >>>>>>>=20
> > > >>>>>>>------------------------------------------------------------------
> > > >>>>>>>To unsubscribe from si-list:
> > > >>>>>>>si-list-request@xxxx with 'unsubscribe' in the Subject field
> > > >>>>>>>=20
> > > >>>>>>>or to administer your membership from a web page, go to:
> > > >>>>>>>//www.freelists.org/webpage/si-list
> > > >>>>>>>=20
> > > >>>>>>>For help:
> > > >>>>>>>si-list-request@xxxx with 'help' in the Subject field
> > > >>>>>>>=20
> > > >>>>>>>List FAQ wiki page is located at:
> > > >>>>>>> http://si-list.org/wiki/wiki.pl?Si-List_FAQ
> > > >>>>>>>=20
> > > >>>>>>>List technical documents are available at:
> > > >>>>>>> http://www.si-list.org
> > > >>>>>>>=20
> > > >>>>>>>List archives are viewable at: =20
> > > >>>>>>> //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: =20
> > > >>>>>> //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
> > > >>>>>>=20
> > > >>>>>>
> > > >>>>>>------------------------------------------------------------------
> > > >>>>>>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
> > > >>>>>
> > > >>>>>
> > > >>>>>
> > > >>>>>
> > > >>>>
> > > >>>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
> > >
> >
> > 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
> >
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:
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Old (prior to June 6, 2001) list archives are viewable at:
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