"Tim Williams" wrote:
"Ralph Barone" wrote in message
news:338871053453128354.323302address_is-invalid.invalid@shawnews...
Perhaps not the right place in the thread to say this, but what problems
would come up if you modelled a varistor as a behavioural current source
with I = k* V^alpha in series with a bulk resistance? I've had pretty
good
luck with that model (just not in SPICE).

I've seen that advertised before in appnotes, but it doesn't make sense.
There's no physical reason to have a power law in a semiconducting device,
and it suggests way more leakage current than there should be (the
breakdown region might be softer than an exponential, but there still has
to be an exponential leakage tail in there). Perhaps it's just a crude
fit to the random breakdown-ESR pattern. In much the same way as 1/f
noise (another odd order power law) can be modeled as a stacked chain of
noise sources of random bandwidth.

I can't say whether it makes physical sense, but in the limited research
I've done into the characteristics of metal oxide varistors, the I = k*
V^alpha equation keeps popping up. In the curve matching that I have done
(in Excel, mind you), a bit of series resistance kept the curve from
flattening out too much at high applied voltages, and also made sense in
terms of the bulk resistance of the material (disregarding the grain
boundaries where all the non-linear magic occurs).

SPICE won't appreciate it, because a negative number to a random power is
likely to result in some random complex number. You'd at least need
abs(V) to start, then put the sign back on the current later. Most of the
derivatives all disappear at V=0, which doesn't help.

Definitely, it would need a bit of a wrapper around it (sign() and abs()
functions) to make it symmetrical. I tend to post from my phone, so
tenseness is rewarded (at least while I'm typing).

A symmetrical exponential function, like tanh, would probably do a good
job, though being a bit too sharp. As John says, connecting some
resistors in series with that, then cleaning it up with a few more of
different threshold voltages and ESRs, would do; but some may balk at this
solution using "too many lines".

A single-line rendering of that isn't actually possible, because a
"resistor in series with an exponential" is a transcendental equation, and
has to be solved iteratively by the SPICE engine. Your alternative would
be to build a "dulled" tanh function (say, toning down the exponential
asymptotes by taking the sqrt or something), but that is also impossible,
because the only thing that's "dull" enough to tame an exponential is a
log (any polynomial or power law just becomes a constant factor to the
exponent). But that simply undoes the exponent entirely, giving flat
asymptotes; and doesn't work for negative values (see
http://www.wolframalpha.com/input/?i...tanh%28x%29%29 ).

Probably, best would be to sit down with a spreadsheet and plug in curves
until it works. There's always boring old polynomials, which are probably
quite a good idea in this case -- with the right combination of (complex)
poles and zeroes, the function can be odd (= gives opposite current for
negative argument) and the asymptotes can be linear or quadratic (linear
would make sense in that it's the minimum ESR when all semiconducting
grains are conducting). With some tweaking, perhaps a non-geometric
polynomial could be built that exhibits realistic leakage current, and
approximates the V^alpha asymptote.

One can also make polynomials from other polynomials (Chebyshev and other
named orthogonal polynomial series are typically better for building
curve-fits than just throwing coefficients at a geometric series), or from
other functions (e.g., the periodic polynomials in cos^n(phi) and such,
useful for harmonic analysis).

Tim