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

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 |---------+---------------------------------->
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>-list@xxxxxxxxxxxxx>      &#160  &#160
>-LIST] Re: capacitor impedance in time
>domain     &#16      &#1
>60I            &#16
>          |
> >---------------------------------------------------------------------
>--  -----------------------------------------| >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 ------------------------------------------------------------------ To
>unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx 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@xxxxxxxxxxxxx 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:
>        &#1    &#16
> http://www.si-list.org List archives are viewable at:
>             
>           http://www.
>freelists.org/archives/si-list or at our remote archives:
>   &#1         &#16
>          http://groups.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@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:     
                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

Other related posts: