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

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>&#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;&#1=
60;&#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 =3D
v(s)/i(s) or
> >v(f)/i(f), which makes it a strictly frequency domain parameter.
Regards,
> >Andy
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