# [SI-LIST] Re: capacitor impedance in time domain

*From*: Alan Hilton-Nickel <alan@xxxxxxxxxxxxxxxxx>*To*: weirsi@xxxxxxxxxx*Date*: Fri, 28 Jan 2005 15:04:22 -0800

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: >> >> >>>>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: >>>> >>>> >>>            &= >>> >>> >>#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: >>>> >>>> >>>            = >>> >>> >>  >> >> >>>           http:/= >>> >>> >>/www. >> >> >>>>freelists.org/archives/si-list or at our remote archives: >>>> >>>> >>>           = >>> >>> >>60; >> >> >>>          http://group= >>> >>> >>s.yah >> >> >>>>oo.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@xxxx with 'unsubscribe' in the Subject field >>>> >>>>or to administer your membership from a web page, go to: >>>>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: >>>> 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: >>>> http://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 >>>> >>>> >>>> >>>=20 >>>=20 >>>------------------------------------------------------------------ >>>To unsubscribe from si-list: >>>si-list-request@xxxx with 'unsubscribe' in the Subject field >>>=20 >>>or to administer your membership from a web page, go to: >>>http://www.freelists.org/webpage/si-list >>>=20 >>>For help: >>>si-list-request@xxxx with 'help' in the Subject field >>>=20 >>>List FAQ wiki page is located at: >>> http://si-list.org/wiki/wiki.pl?Si-List_FAQ >>>=20 >>>List technical documents are available at: >>> http://www.si-list.org >>>=20 >>>List archives are viewable at: =20 >>> http://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 >>> >>> >> >>------------------------------------------------------------------ >>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: >>http://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: =20 >> http://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 >> =20 >> >>------------------------------------------------------------------ >>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: >>http://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: >> http://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: >http://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: > http://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 > > > > > ------------------------------------------------------------------ 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: http://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: 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**Follow-Ups**:**[SI-LIST] Re: capacitor impedance in time domain***From:*Steve Weir

**References**:**[SI-LIST] Re: capacitor impedance in time domain***From:*Steve Weir

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- » [SI-LIST] Re: capacitor impedance in time domain
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