costal loop question

Hi, I have come across a lot of literature saying that costas loop is used for phase error correction. I had few questions regarding that. After multiplying and generating a difference signal either cos(phi) or sin(phi) where phi is the phase difference between the incoming and the locally generated signals, how is this translated to an angle which can be given as an input to the VCO?? The output of the carrier discriminator which can be a multiplier is sin(2*phi). I wanted to know what the loop filter does that converts this value to an appropriate value as an input to the VCO. If we consider another discriminator such as arctan then we directly can get a phase difference angle as the input to the VCO. However what is the use of a loop filter in this case?? Are there any higher frequency terms that need to be filtered out? Could you please reply to my questions? I would greatly appreciate your response. Thanking You, Viswanath

The beauty of the Costas loop is that it is a relatively simple circuit that allows you to extract both the clock and data from a modulated data stream eg BPSK.

That's the beauty of feedback. It is not necessary to calculate an angle, just to nudge the VCO in the 'right' direction. You can use

+/- cos/sin of the phase difference, the system will settle at a 'stable equilibrium' phase, with the VCO 0/90/180/270 degrees from the incoming data.

The multiplication you've mentioned above gives will give you terms at twice the clock frequency, in addition to the low frequency term you want. On paper, the 2F terms are disposed of by averaging over a clock period, but in hardware they are eliminated by the loop filter.

What kind of Costas loop do you wish to implement ? In what kind of hardware ?

Good luck,

-rajeev-