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Depending on I.F. freq. there may be low frequency components of the mixing product fed back to input. The resistor dampens the possibility of low freq bias shift oscillations that will effect the mixer. The low frequency bias shift may gate the mixer on and off at the low freq oscillation.
I don't like this mixer much. I would prefer to inject a lower level L.O. into the gate.
yes what terminator said. these rf transistors often have GOBS of gain at low frequencies, so you need to dampen out that gain in things like bias circuits, which really do not reject 1 MHz signals very well.