[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 = (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>&#160;&#160;&#160;&#160;&#160;&#160;&#160&#160;&#160;&#160
> >-LIST] Re: capacitor impedance in time
>
>domain&#160;&#160;&#160;&#160;&#160;&#16&#160;&#160;&#160;&#160;&#160;&#160;&#1
>
>60I&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#16
> >&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;|
>
>&#160;>---------------------------------------------------------------------
> >-- &#160;-----------------------------------------| >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.&#160; 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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