The problem with this explanation of the (undoubted) observation is that it doesn't tally with the 'expected' properties of a small signal diode or a diode substitute. One would expect to see only the diode junction capacitance linking the coil and the variable capacitor. The diode junction capacitance is presumably an order of magnitude or more less than the variable capacitor.I suppose the variable, located after the diode, performs the resonance function while effectively bypassing the carrier and allowing only the envelope into the phones.
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