Key the PTT line of your UHF FM transmitter for a CW uplink. Turn the mic gain down or remove the mike all together.
It will chirp a bit, but it can be copied.
If your HT does odd splits and has wide coverage, you might be able to reduce or eliminate this. Generally, the VFO has to switch from receive to transmit by the amount of the IF. That's probably where the chirp comes from. I have not done this experiment with a service monitor to see exactly what happens, but you might try an odd split such that the RX frequency has been shifted by the IF frequency (you might have to try both +/- to see which works for your rig). Then when you key the rig, the VFO doesn't have shift very far (if at all) and that might make the chirp go away. If you try the experiment, please let me know. -- KD6PAG (Networking Old-Timer, Satellite QRPer)
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