Series Parallel Resonance.

Cuthbert Nyack

The circuit shown below has both series and parallel resonance.

Applet below show the behaviour of the Impedance with frequency.
eg parameters:-
(100.0, 102.0, 2.5, 1.0, 99.999, 1.0, na, 375, na, 10.0)
This shows that the reactance(Cyan) has 2 zeros at the series and parallel resonant frequencies. The lower resonant frequency is series resonant(minimum resistance and maximum admittance). The higher frequency is parallel resonant with maximum impedance and minimum admittance. The resonant frequencies are shown on the applet. Setting parameters to (100.0, 102.0, 2.5, 1.0, 99.999, 1.0, na, 375, na, 1.5) and changing Cp shows that the upper frequency can be changed by Cp.

This is the equivalent circuit of a quartz crystal, although the parameters may be very different, the behaviour is the same. The crystal can be "tuned" by varying a small capacitor in parallel with it.

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