3,4 Capacitor coupled Resonant Circuits.

Cuthbert Nyack

The circuits used for the 3 and 4 capacitively coupled oscillators are shown below.

Applet below show the behaviour of the loop currents with frequency. The function of the applet can be changed by changing Fn as shown on the applet.
The 3 oscillators have 3 resonant frequencies. For the parameters:-
(0.5, 1.0, 0.25, 0.055, 0.075, 0.15, 0, 216, na, 1.0), the resonant frequencies can be located by varying wL. Setting wL = 288, 439 and 499 show the resonant frequencies are ~ 0.2259, 0.9081 and 1.578Hz. At wL = 288, the real parts of the 3 currents are +ve ie the 3 oscillators are in phase. At wL = 439, the real parts of the 3 currents are +ve, +ve and -ve ie the first 2 oscillators are in phase and both are out of phase with the third. At 1.578Hz adjacent osciillators are out of phase.

Fn = 3, 4, 5 and 6 show the case of 4 oscillators. For Fn = 3 the resonant frequencies are approximately 0.2259, 0.6054, 1.062 and 1.592Hz. At the lowest frequency all oscillators are in phase and adjacent ones are out of phase at the highest frequency. At 0.6054Hz the first 2 oscillators are in phase and are out of phase with the last 2. At 1.062Hz the first and last oscillators are in phase and they are out of phase with the inner 2.

When applet is enabled its appearance is illustrated by the gif image below.

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