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1) Costas Phase Lock Loop + 2) MSK first nulls bandwidth

Hello,

Hopefully this is appropriate place to ask.

1) I'm studying Costas Phase Lock Loop (e.g.
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And I'm trying to analyse it, and I'm a bit stuck.

Consider that the baseband signal (carrier / y(t) ) is = m(t) \cos {\omega_c t}

The output produced by the VCO is 2\cos{\omega_c t + \theta}

Then after the in-phase LPF the signal is m(t)\cos\theta and the quadrature signal is m(t)\sin\theta

This leads to the output from the third mixer to be 0.5m^2(t) \sin{2\theta}

Now I cannot work out that the signal will be supplied to the VCO and how does that produce Phase Lock Loop on the carrier. Can you help me please?

2) How to calculate the location of first-null bandwidth for the Minimum Shift Keying algorithm (considering a random input stream). It is suppose to be larger than of the QPSK coding, but I can't work it out either. For QPSK it is 1/T_s, where T_s is the symbol period.

Thanks, and hopefully someone will read this =) exam on tuesday....... =(

Reply to
Dima
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So here you have a DC 'error' term that depends on the phase difference theta. This is applied to the VCO (which changes frequency with the applied DC voltage)

You just have to make sure that the error voltage is applied in the right direction. This will then shift the frequency to make the phase difference smaller.

(I have no practical knowledge of PLL's I've never gotten to build one... maybe my next project?)

Sorry can't help you with the above... There is a time constant determined by the last low pass that sets how fast the VCO can swing it's frequency. Perhaps that's the answer?

George H.

Reply to
George Herold

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