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Costas Loop - loop filter bandwidth + capture & lock ran

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Currently I am designing a BPSK demodulator uses Costas Loop. The IF signal is 10.7 MHz. So based on this, I wish calculate the loop filter bandwidth and the capture and lock range by formula. Anyone know the formulae?

Thanks!
 

Re: Costas Loop - loop filter bandwidth + capture & lock

Good question. I am curious too. Obviously, the 10.7 MHz IF frequency has nothing to do withthe loop bandwidth of the control loop. I think it must have something to do with frequency switching time (if you never switch, you can have a small loop bandwidth, but if you do switch you have to reacquire faster), and if the dynamics of your transmission path are changing (like big multipath or a mobile environment).
 

Re: Costas Loop - loop filter bandwidth + capture & lock

I think the formula will be similar to a normal PLL. Costas loop is nothing but a PLL with a non-linear operator. In fact, Costas loop is a PLL with a square operator. It exploits cyclostationary property of the signal to get a sine wave for synchornization. Once you get the sine wave, it is just a job of PLL. The formula for loop BW, etc and design trade off can be found at Ronald Best's book, for example.
 
As I know that the loop bandwidth is varied with applications. So for my case, I have to determine the loop filter bandwidth then only I can proceed to practical design of the low pass filter. For the capture & lock range, prior calculation also is essential. So I wish to know these values beforehand. Anyone who have related articles please to share out. Very appreciate for you all helps.
 

Let say, if the input is 100 kbps, how to determine the low pass filter cutoff frequency?
 

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