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: > >>>>>>si-list-request@xxxx with 'unsubscribe' in the Subject 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