PLL loop gain and stability

[qslazio]

pll loop gain

I upload a bode plot of the open loop phase transfer function of a 3rd order PLL with Charge pump. The low pass filter is a traditional 2nd order RC network.


As we know there will be 2 poles at DC, with a LHP zero at the higher frequency.
The last poles sitting in the right of the them.

From the Bode plot. We can see at frequency just around DC.The open loop gain will be very high, and the phase will be close to -180.

My question is that if i connect it in a feedback loop, and put a phase input varying slow(around DC).

Will the loop still stable?

Thanks!

 

[flatulent]

gain and stability

It all depends upon the gain of the different circuits around the loop. Plot the open loop gain. If it crosses the 1x gain (0 dB) axis with a one pole rolloff slope, it will be stable. You can adjust the gain of the circuits to make this so. The closed loop bandwidth will be at the frequency the two pole roloff slope projects to the frequency (horizontal) axis.

The above is not mathematically exact but will be within a few percent error. The two rules of thumb are handy for preliminary sketching and thinking about what to design.

 

[Btrend]

pll open loop gain

in my opinion,
1. the PLL loop is not continuous type (e.g. opamp in negative feedback), instead it is sample-data loop. that is : "the feedback is not always connected", it only connect during some period of a cycle.
2. the stability of PLL loop should be analyzed by discrete time system (Z transform).
3. in continuous type closed loop system, it should oscillate than saturate if u doing the test u stated.
4. in a stable PLL loop, ur test should not make it unstable, but phase noise will increase