How to add a low frequency dither signal in a bias-tee?
You could try applying the 1 kHz signal to the DC port of the bias tee and see if it passes through to the RF+DC port. Unfortunately the s-parameters provided by Mini-Circuits only cover down to 100 kHz, so it's hard to tell in advance how well this will work.

If that doesn't work, you could look for a different bias tee with more bandwidth in the path from DC to RF+DC.

You could design your own bias tee specifically to allow ~1 kHz signals through from the DC port to the output port. Or you could design a network with 3 input ports (RF, 1 kHz, and DC) and one output port combining these signals.


For the record, here is the insertion loss for your chosen bias tee, from RF to RF+DC (S21), and from DC to RF+DC (S23) according to the s-parameters provided by Mini-Circuits: