Can Varactor Diodes Cause Frequency Modulation in LC Oscillators?

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Okay, simple question. Why doesn't the AC voltages and currents present in an LC oscillator tank arrangement that uses a varactor diode as the C cause the frequency to be modulated at 1/2 the freq?
 
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I wondered the same thing and why the varactor diodes don't just work as rectifiers in oscillator circuits.

The reason is that varactor diodes are diodes that are not normally capable of operating at the frequency in use.

Even power diodes can be used at high frequencies as varactor diodes because they have large capacitances and other characteristics which make them poor rectifiers at high frequencies.
 
Many thanks! One of my friends thought it was a time constant deal but same end effect.
 
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So, I'm told you can't use varactors in an RF circuit that has a bunch of voltage running around. Some say you can put two back to back and that averts the phase modulation that would happen otherwise.
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Varactor or Varicap diodes just behave like normal capacitors except that their capacitance changes with the DC voltage across them.

I have viewed the output of oscillators using these diodes and the waveform was just a sine wave. If the diodes were causing modulation as you describe, this should be visible as distortion on the waveform.