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This single layer PCB (solder side shown here) is from an old fan remote: front pcb

The inductor in the plastic tube is not connected physically to any components; however, the two loops of wire surrounding it are soldered to the board. This raises some questions into the transmitter's operation:

The frequency of the OOK transmission was determined to be approximately 305 MHz.

transmission frequency.

The data output from the HT12E encoder is a kHz-frequency signal as defined by its internal oscillator. At the two wire loops surrounding the coil, the data output from the encoder is observed (my scope cannot do >20 MHz), which is identical minus some voltage drop.

data

It seems that an inductor should be required for operation of what would appear to be a high frequency oscillator circuit (MPSH10 RF NPN), which would modulate the encoder output to 305 MHz. In the above diagram, "Loop 1" and "Loop 2" represent physical connections to the wire loops, where #1 is closest to the BJT.

Is it correct that the wire loops should also act as antennas?

Since the inductor is not connected physically to anything in the circuit, what is the theory behind its operation here? Why use such an inductor instead of a standard piece?

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The inductor in the plastic tube is not an inductor. It's the inductor core. The loops of wire are the coil around that core. It's an adjustable inductor. Fixed to its given value with hot glue.

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The plastic sleeve is not active, it just holds the core and allows it to be adjusted by screwing in or out, to tune the transmitter.

The two loops of wire are the antenna windings. Most likely the one surrounding the core is the tuned circuit, while the other provides positive feedback to sustain the RF oscillation.

And the whole assembly can indeed act as an antenna - in fact you may recognise this as just a miniaturised ferrite rod antenna as seen in AM transistor radios. enter image description here

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