# 2,3,4 Capacitor coupled Resonant Circuits, Phasors.

Cuthbert Nyack
The circuits used for the coupled oscillators are shown below.

Applet below show the behaviour of the loop currents shown as phasors with frequency. The function of the applet can be changed by changing Fn as shown on the applet.

Fn = 0 shows the phasors for 2 coupled oscillators.
eg parameters(0.5, 1.0, 0.02, 0.055, na, na, 0, 420, 10.0, 1.4142)
and(0.5, 1.0, 0.01, 0.055, na, na, 0, ~450, 10.0, 8.6445) show the resonant frequencies for 2 oscillators

Fn = 1 shows the phasors for 3 coupled oscillators.
eg parameters(0.5, 1.0, 0.01, 0.055, 0.075, na, 1, 420, 10.0, 1.4142)
(0.5, 1.0, 0.01, 0.055, 0.075, na, 1, 347, 10.0, 5.69347)
and (0.5, 1.0, 0.01, 0.055, 0.075, na, 1, 155, 10.0, 9.88155)
show the resonant frequencies for 3 oscillators

Fn = 2 shows the phasors for 4 coupled oscillators.
eg parameters(0.5, 1.0, 0.01, 0.055, 0.075, 0.15, 2, ~421, 10.0, 1.41421)
(0.5, 1.0, 0.01, 0.055, 0.075, 0.15, 2, ~200, 10.0, 3.792)
(0.5, 1.0, 0.01, 0.055, 0.075, 0.15, 2, ~699, 10.0, 6.69699)
and (0.5, 1.0, 0.01, 0.055, 0.075, 0.15, 2, ~490, 10.0, 9.9749)
show the resonant frequencies for 4 oscillators

For reference Fn = 3 shows the i phasor for a single oscillator.
eg parameters(0.5, 1.0, 0.01, na, na, na, 3, ~421, 10.0, 1.41421) show resonance for a single oscillator
In all cases, the lowest frequency is 1/(ÖLC)