Given a sinusoid input of frequency f, an RLC network, no matter how complex, should produce a sinusoidal output of frequency f, with possible attenuation and phase shift. At least that's my understanding of AC circuit theory, and confirmed here. It follows from the fact that, at a given frequency, any R, L, or C can be viewed as a complex impedance following the complex version of Ohm's law, E=IZ.
Yet, even these simple LC circuits change frequency, or produce beat frequencies:
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Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Even if we assume that the components have parasitic resistance, capacitance, or inductance, they still should form a passive linear RLC network.
How is it possible to explain the behavior shown? And, more importantly, if I can't use the classic AC circuit theory of complex impedances to analyze them, how do I analyze them? And how do I know that the classic AC circuit analysis will not apply here?
