Effect of phase noise on Loop BW

I noticed that when the Loop BW of the loop filter increases, the phase noise of PLL degrades a lot.
What is the relationship between these two?

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the only relationship that shows is that the phase noise of your reference clock, or the phase noise floor of your PLL chip's digital electronics, are very poor.

close loop response in PLL is low pass filter with 3db cuttoff frequency, let BW be loop bandwidth so for the frequecy offsets at the output less than BW, the dominent phase noise here are beacuse of refrence noise, N counter noise, and charge pump noise, keeping large Kd phase detector gain and N small will minimize phase noise inside the loop BW.

For the frequency offset much greater than BW the dominent noise here is because of the VCO and This is due to high pass filtering of the VCO phase noise by the loop.

so small BW will improve your integrated phase noise of PLL chip and increase contribution of phase noise due to VCO.

so finally i can say that your VCO phase noise is good but as you increase your loop bandwidth your integrated phase noise comes into play and degrade your overall phase noise.

If you are interested in proof just apply the classical control theory to the attached block diagram of phase look loop with phase noise contributors.