# circuit Q

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Hello all,

I was recently discussing Q or quality factor with Malcolm Watts, and I
want to make a few general comments.

Quality factor is a dimensionless measure of how well a circuit or
component performs and it is expressed as

energy per cycle/energy lost

i.e. infinite Q means that no power is dissipated in a circuit. This
would be, for example, an inductor which has no resistance and does not
couple to anything.
Another way of looking at Q is to realise that Q is inversely
proportional to dissipation factor. Dissipation factor is also
dimensionless and is given by

1/(root(q^2+1))

for values of Q>5, DF is taken as 1/Q.

This means that any part of, for example, a primary circuit that is
resistive is capable of dissipating power: this is one reason why  the
spark gap is such a determining element.

It is the case that the voltage developed across a purely reactive
component in a resonant circuit is Q times the input to the circuit.
This means that in TC primaries the V across a cap will be say 10 times
the V applied to the circuit, albeit for a short duration. This aspect
makes us realise why some caps fail when the cct doesn't at first sight
appear to be that stressful.

I thought it might be interesting to look at a couple of design aspects
for HV pulse caps, and I refer to "High Speed Pulse Technology" by
Frungel, AP 1976 (ISBN 0-12-269003-6). It is a very good book, I think.

>From a section that discusses spark discharge caps, we see that the
biggest determining factor for quantifying the life expectancy of a cap
is the percentage voltage reversal. High Q systems imply a very
underdamped response (R<<4LC).
The lifetime of a cap in a high Q cct is a function of Q^-2.2. The %
voltage reversal is found from

%rev =100 * e^(-pi/2Q) = 100 * (1-(pi/2Q))

If you have a shot of the primary ringing (like Malcolm does on his
storage scope) then Q is approx pi * N whereby N is the no. of cycles
for the envelope to fall to an amplitude of 1/e of the maximum (this is
the 1/e folding time referred to in Sarjeant and Dollinger). 1/e works
out to approx a third.

We can see that a good TC primary will achieve voltage reversals of 80-
90 % and thus the life expectancy can be short: looking at a so-called
DC cap, you can expect it to survive 20 per cent reversals without
detriment, but an 80% reversal shortens its life by this amount:

80 per cent reversal implies a Q of approx. 7

7^-2.2 = 72 times shorter life expectancy.

As an example only, if the life expectancy was originally a million
shots, the life in a ringing cct would be something like 14000 pulses.
At 100PPS this is only a couple of minutes whereas the original million
shots would have been 2 3/4 hours. This is why we want to use caps that
are designed for the purpose.

I hope there was something useful in that lot!

Richard Craven, England
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CMPQwk #1.42 UNREGISTERED EVALUATION COPY
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