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: >>>>>> >>>>> >>>>>            &= >>>>> >>>> >>>>#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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