Geoff/W5OMR writes:
Because When Inductive Reactance (X(l)) equals Capacitive Reactance (X(c)) you get Resonance! At least in triodes. Pentodes need some extra work, due to screen voltages/current.

As far as I know, the condition of resonance: XsubL = XsubC ; holds for the LC resonant circuit, regardless of the active element it may be connected to, be it a pentode, tride, bipolar transistor, FET, tunnel diode, or whatever. Of course when the LC is connected to other "stuff," the parasitic reactances of the whole mess need to be considered and will contribute to the "total" XsubL and XsubC which determines the resonant point.
That brings up a question... (and I'm asking because I just don't know pentodes/tetrodes) should the screen circuit be resonant at the operating frequency, as well?

If we are considering a pentode/tetrode amplifier, the screen should be grounded for RF (i.e., well-bypassed at the operating frequency). Exceptions are certain oscillator circuits (modified Pierce, for example) where the screen is actually used as the plate of the triode formed by the cathode - control grid - screen grid, or when the screen may be used for signal injection in a mixer circuit.
73,
-Larry/NE1S
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