[SI-LIST] Re: capacitor impedance in time domain
- From: Steve Weir <weirsi@xxxxxxxxxx>
- To: group_delay@xxxxxxxxx, si-list@xxxxxxxxxxxxx
- Date: Fri, 28 Jan 2005 14:30:37 -0800
Chris,if your concern is purely theoretical, then band limit the trapezoid,
and then use Z = 1/( dv/dt * C ). You can run a series of points through
MathCad, Excel, a C program, whatever suites you.
But from a practical standpoint if you want to select a coupling capacitor,
what you will find is that you just want to make C large enough that the
capacitor impedance is much smaller than the transmission line.
Regards,
Steve.
At 09:47 PM 1/28/2005 +0000, group_delay wrote:
>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 = (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
> > the network, or more likely using a computer program we would solve the
> > difference equations over a series of discrete time steps. Now in
>either
> > case we could express impedance as dv/dt / di/dt. But I don't know how
> > useful it would be towards either visualizing behavior, or solving the
> > equations. Let's take the trapezoidal wave for instance. An effective
> > impedance is pretty easy to come by on each: the rising, and falling
> > portions of the waveform from the capacitance expression C =
>i/dv/dt, Z =
> > dv/dt / di/dt = 1/(dv/dt * C ). The flat portions are troublesome
>as are
> > the vertices, since dv/dt theoretically goes to zero and the
>impedance from
> > the formula jumps to an infinite value. Intuition should tell us
>that this
> > is wrong, as
>
> coupling capacitors routinely pass high frequency pulses.
> >
> > In the frequency domain, we have this nailed. We don't have
> > discontinuities at the vertices. The vertices and flat portions follow
> > curves formed by the frequency components, and rather than a flat
>section
> > containing DC and no HF, quite the opposite is true: the flatter we
>want
> > the pulse tops to be, the higher the frequency content required. This
> > aligns with our intuition. But when we transform the representation
>back
> > to the time domain, those piecewise linear segments are now curved
>solving
> > the discontinuities at the vertices and eliminating the flat slopes
>with
> > theoretically infinite Z between the edges.
> >
> > So if someone wanted to look only at the rising and falling edges, an
> > impedance in the time domain is reasonable, and possibly even
>useful. But
> > it really gets awkward when dealing with the whole waveform unless
>we first
> > perform frequency limiting operations, most easily performed in the
> > frequency domain.
> >
> > I am not an expert on algorithms, so I really can't say from an error
> > analysis and computational efficiency standpoint what is really the
>best
> > way to perform a transient analysis. But in my naivete, I would be
> > inclined to transform everything into the frequency domain, compute the
> > solution and transform back. In my feeble mind, this would avoid
>some of
> > the discontinuity and convergence problems in SPICE and more closely
> > follows nature. But since people a whole lot better at math than I
>have
> > worked long and hard on those algorithms, I suspect either the
> > computational overhead, or error build-up of my naive approach would be
> > unacceptably high. Maybe what this world needs is a five cent, 256 bit
> > floating point, matrix solver!
> >
> > Steve.
> >
> > 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          
> 60;
> >
> >60I           
> 0;
> > >          |
> >
> > >---------------------------------------------------------------------
> > >--  -----------------------------------------| >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 =
>v(s)/i(s) or
> > >v(f)/i(f), which makes it a strictly frequency domain parameter.
>Regards,
> > >Andy
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