[SI-LIST] Re: capacitor impedance in time domain
- From: Steve Weir <weirsi@xxxxxxxxxx>
- To: steven.corey@xxxxxxxxxxxxxx, si-list@xxxxxxxxxxxxx
- Date: Sun, 30 Jan 2005 01:37:17 -0800
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>          
> >>>>>>-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
> >>>>
> >>>>
> >>>>
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> >>>>>
> >>>>
> >>>>#160;
> >>>>
> >>>>
> >>>>
> >>>>>>  http://si-list.org/wiki/wiki.pl?Si-List_FAQ List =
> >>>>>>
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> > 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
Other related posts:
