Relative Advantages of Series and Parallel Resonance
(Reproduced from "Zero to Eighty" pp.321-322 by EF Northrup)
Since capacitors are necessary to satisfactory operation of
the electric gun, the next problem is to determine in what
manner the capacitors are to be connected. There are two
general methods of connecting capacitors to produce
resonance: series and parallel. Using simplified circuits consisting
of an inductance, a capacitor, and a source of electromotive force,
we find that in the series resonated circuit the inductor, the
capacitor, and the source of e.m.f. all carry the same current. An
ammeter inserted in any part of this circuit will indicate the current
for all parts of it. In the parallel resonated circuit, the capacitor is
connected in parallel, or shunt, across the terminals of the inductor.
For convenience, the source of e.m.f. is also considered to be
connected across the terminals of the capacitor and inductor. In
the parallel resonated circuit, each element of the circuit will
generally carry more or less widely differing amounts of the current,
which must be separately measured or calculated for each element.
In many circuits, parallel resonance is the accepted method. By
means of parallel resonance, enormous currents can be built up
between the inductor and capacitor without carrying them through
the source of e.m.f. Moreover, in this circuit, resonance does not
need to be perfect to maintain reasonably stable conditions of
current. In the series resonated circuit, resonance must be very
close, or else the current drops off rapidly. As pointed out above,
the source of e.m.f. must carry whatever current exists in the circuit.
In general, parallel resonance is best adapted to circuits employing
high currents at comparatively low voltages, whereas series resonance
is suitable where high voltages and small currents are desirable.
At first thought it might seem that parallel resonance is the better
method for the electric gun. However, although it appears simple
in application, there are serious difficulties which greatly hinder
the best operation of the electric gun when the parallel method is
used. For instance, if each unit phase coil of the gun is separately
resonated either with or without the projectile being in the coil,
we have a large number of places where currents due to magnetic
induction can flow. Since the coils are coaxial and quite close
together, the coupling factor or coefficient of magnetic induction
between coils is very high. From experience, it has been found
that these induced currents and magnetic induction effects interfere
with the action of the polyphase currents in the coils, and tend to
diminish the thrust on the projectile.
To minimize these harmful induction effects, series resonance
may be used. Although the generator must carry a high value of
current, the voltage of the machine need only be high enough to
overcome the equivalent resistance of the connected circuit. This
is possible, since in series resonance the e.m-f.’s necessary to
overcome the reactance of the capacitor and inductor are one hundred and eighty electrical degrees
out of phase, and hence neutralize each other.
If the capacity is so adjusted as to cause resonance to occur only while the projectile is in the
coils, then the switching devices will have less current to make and break as the power is shifted along
with the projectile.
To decrease further any possibility of undesirable current surges
between coils and capacitors, the three-phase currents are generated
in single-phase machines which are mechanically locked together so that the one hundred and twenty
degree phase relation is maintained.
As explained under the subject “The Use of Electric Condensers
or Capacitors,” the number of capacitors used depends only on
the requirement that the electrostatic energy be kept equal to the
electromagnetic energy. Hence, series resonance is as economical as parallel resonance.