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

[Dima]

Hello,

Hopefully this is appropriate place to ask.

1) I'm studying Costas Phase Lock Loop (e.g.
http://zone.ni.com/cms/images/devzone/tut/a/620a9f541484.gif)

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.......
=(

 

[George Herold]

On Aug 27, 1:08 pm, Dima <dmitrij.led...@gmail.com> wrote:

Hello,

Hopefully this is appropriate place to ask.

1) I'm studying Costas Phase Lock Loop (e.g.http://zone.ni.com/cms/images/devzone/tut/a/620a9f541484.gif)

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}

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?)

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.

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.

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