RLC Capacitively Coupled Resonance
Two capacitively coupled RLC circuits are shown in the circuit
below. Having 2 circuits gives 2 resonant frequencies whose
separation depends on the value of the coupling capacitor C1.
The Equation for the currents i1(first loop) and i2(
second loop) is given below:-
Where a and b are:-
The solution, from which the frequency response can be
Resonance occurs at the 2 frequencies:-
Applet below illustrates the dependence of the frequency response
on the parameters C1, C and R. L is assumed to be 1/C to keep the
LC product equal to 1. The vertical scale for phase is from +pi at the top to
-pi at the bottom. With HGain = 1 the horizontal frequency scale
goes from 0 to 2rad/s.
Current i1 magnitude response is in green, phase is in red,
real part is in orange and imaginary part in yellow.
Because of the small values of L and frequency used here, then
R must be small to give a "sharp" peak. The sharpness of the peak
changes with C because L also changes. Note that the oscillators are
in phase at the lower frequency and out of phase at the higher
The applet below is similar to the one above but shows the solution for i2
in the second loop. For this applet the vertical scale for phase goes
from +0.5pi at the top to -1.5pi at the bottom.
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COPYRIGHT © 1996 Cuthbert A. Nyack.