How does a CM choke reject common-mode noise while allowing the signal of interest?
How does it block common-mode noise and pass the signal of interest?


Let's say you have an unspecified 1:1 transformer and wire the primary to a 1 V 1 kHz AC source. The output from the transformer will be a 1 V, 1 kHz voltage as expected. Now if you were to apply a separate 1 V, 1 kHz to the secondary no current will flow in the secondary because it's like putting two identical batteries in parallel.

Let's also say that the transformer is ideal in that each winding has infinite inductance. In the scenario painted above there will be zero current taken from the primary and secondary sources. This, in effect is the device blocking common-mode voltages i.e. two identical AC sources are applied to both input and output and no current flows.

If you applied different AC sources there could of course be significant current flow. So this tells us how re-wiring a 1:1 transformer as a common mode choke works.

But, the primary and secondary inductances are nowhere near infinity so there will be current flow but, that current flow reduces as frequency increases so, a common mode choke performs better as frequency rises but, up to a point and that point is determined by the winding capacitances and the core losses.


  Should we think of it as an LR filter?


Thinking of it like a transformer is just fine but remember the limits mentioned above as frequency gets too high.


  If I use a CM choke I cannot use it for conveying DC signals ?


Transformers don't work at DC so, DC passes unhindered.