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 |---------+----------------------------------> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>>-list@xxxx>           >>>>>>>>-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;&= >> >>>>>>#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;= >> >>>>>>  >>>>>> >>>>>> >>>>>> >>>>>> >>>>>>>           htt >>>>>> >>p:/= >> >>>>>>/www. >>>>>> >>>>>> >>>>>> >>>>>> >>>>>>>>freelists.org/archives/si-list or at our remote archives: >>>>>>>> >>>>>>> >>>>>>>            >>>>>> >>= >> >>>>>>60; >>>>>> >>>>>> >>>>>> >>>>>> >>>>>>>          http://gr >>>>>> >>oup= >> >>>>>>s.yah >>>>>> >>>>>> >>>>>> >>>>>> >>>>>>>>oo.com/group/si-list/messages Old (prior to June 6, 2001) list >>>>>>>> >>>>>>> >>>>>>archives are >>>>>> >>>>>> >>>>>> >>>>>> >>>>>>>>viewable at: >>>>>>>> >>>>>>> >>>>>>>            >>>>>> >>60;= >> >>>>>>  >>>>>> >>>>>> >>>>>> >>>>>> >>>>>>>           htt >>>>>> >>p:/= >> >>>>>>/www. >>>>>> >>>>>> >>>>>> >>>>>> >>>>>>>>qsl.net/wb6tpu >>>>>>>>------------------------------------------------------------------ >>>>>>>>To unsubscribe from si-list: 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