What i want to know is the meaning of this two LPF's bandwidth, w_lpf.
I think that this bandwidth is about input frequency before. But considering that LPF's input is PD's output, it is wrong.
So i think that this bandwidth is about the frequency of input-output varying amounts, is it all right?
1.) Speaking about filtering and transfer functions, we must assume a LINEAR system.
That means: We consider the PLL under
locked conditions only.
2.) Because the locked PLL reacts upon
phase changes, the input and output quantities for the corresponding PLL transfer function are signal phase relations (and its variations).
For a first-order loop filter, the loop transfer function is of 2nd-order because the VCO acts as an integrator as far as the phase is concerned.
3.) As a result, the PLL`s phase-transfer function can be seen as a second-oder lowpass. The frequency variable is
w=d(phi/dt).
The pole frequency wp of this 2nd-oder lowpass is
mainly determined by the pole frequency wp of the loop filter (you call it w_lpf).
4.) This lowpass function (and the corresponding cut-off frequency wc~wp) determines the slope of the
maximum phase deviations d(phi)dt which can be tolerated by the PLL without loosing lock.
Hence, wp it is called "loop bandwidth".