[time-nuts] Complex PLL

[d.schuecker at avm.de]

Hi time-nuts,

a PLL takes the phase difference of the incoming signal and the 
synthesized signal and feeds that in a loop filter. The output of the loop 
filter is used to steer the local oscillator. 

In my setup I have an incoming complex signal and my local oscillator is 
generating a complex signal as well. So calculation of the phase 
difference is just the quotient of the incoming signal and the local 
oscillator, it is a sampled system. I take the quotient, calculate the 
angle using the atan function and then I feed it in the loop filter, a PI 
controller. The output of the loop filter is converted to a complex phase 
increment for the local oscillator with the sin and cos function. 

Now I have to get rid of the atan, cos and sin functions.

I am looking for a loop filter which takes the quotient of the 
incoming/synthesized signal as a complex value. The output of this loop 
filter should be the phase increment for the local oscillator. It should 
not use the angle of the complex value explicitly, as this will involve 
the atan/cos/sin functions.

Is someone aware of such a loop filter? I surfed through Gardners' 
'Phaselock Techniques' but did not find a hint.

Thank you
Detlef Schücker

DD4WV