|
[SI-LIST] Re: capacitor impedance in time domain
- From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Tue, 01 Feb 2005 08:50:50 -0800
Steve -- while I don't understand the details yet of your approach to
the original problem, it looks like it may rely on applying a feedback
equation such as Vo = Vin *1/( 1+G/H ) when Vo and Vin are time-domain
signals. While this type of equation is used for frequency-domain
analysis, it's not generally applicable in the time domain unless G and
H are constant, which would clearly not be the case for a transmission
line terminated by a capacitor. As you know, multiplication and
division of frequency-domain transfer equations become convolution and
deconvolution, respectively, in the time domain. In order to apply in
the time domain an equation derived in the frequency domain, you not
only have to transform the signals, you also have to transform the
operators.
This is the same reason why you can't compute what is commonly called an
impedance by dividing two time-domain signals along the lines of
Z=(dv/dt)/(di/dt). At least it won't be closely related to impedance as
the term is used in standard circuit theory.
Please let me know if I'm misinterpreting your approach to solving the
original problem, but as I understand it so far, it doesn't look like it
will give the right results or valid insight into the problem.
-- 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:
>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
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>>>>>>>>>>>>
>>>>>>>>>>page, go to:
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>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
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>>>>>>>>>>>>http://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:
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>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>          
>>>>>>>>>>>
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>>60;
>>
>>
>>>>>>60;=
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>> 
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>          
>>>>>>>>>>>
>>>>>>>>>>>
>>60;htt
>>
>>
>>>>>>p:/=
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>>/www.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>>freelists.org/archives/si-list or at our remote archives:
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>> 
>>
>>
>>>>>>=
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>>60;
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>          htt
>>>>>>>>>>>
>>>>>>>>>>>
>>p://gr
>>
>>
>>>>>>oup=
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>>s.yah
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>>oo.com/group/si-list/messages Old (prior to June 6, 2001) list
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>archives are
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>>>>>>>>>>>>
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>>>>>>>>>>>
>>>>>>>>>>>
>>60;
>>
>>
>>>>>>60;=
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>> 
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>          
>>>>>>>>>>>
>>>>>>>>>>>
>>60;htt
>>
>>
>>>>>>p:/=
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>>/www.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>>qsl.net/wb6tpu
>>>>>>>>>>>>--------------------------------------------------------------
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Other related posts:[SI-LIST] capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain [SI-LIST] Re: capacitor impedance in time domain
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