Hi, Regarding PLL loop bandwidth, is it referring to closed loop bandwidth or open loop bandwidth? As I read some references about that, the loop bandwidth should be around 1/20 of reference clock frequency. Hope that someone can enlighten me. Thank you.
if I have loop filter transfer function,F(s) VCO transfer function, Kv/s and gain of phase detector, Kpd, is it sufficient for me to find the loop bandwidth? I'm using matlab to simulate the stability of PLL.
The value of 1/20 of reference clock frequency is presumably a rule of thumb. The dominant bandwidth determinant is the loop compensator which, at its most basic, is often a simple passive low pass filter. PLL Loop transfer functions are typically modelled as ideal linear 's' domain forms. These are "useful" under steady-state conditions, but may not reflect true physical performance with large dynamic signal perturbations - such as one might observe (say) during the signal capture. The phase detector may be a contributing factor to non-linearity. Presumably you have a low pass filter component in your design. I would focus on that in the analysis. @Ramussons made an important comment in post #2.
How can I find the loop bandwidth of PLL by using the transfer function in MATLAB? by using the closed-loop transfer function of the system?
Do you want to know this so that you can design the loop compensation or simply because you want to know what the complete closed loop system bandwidth turns out to be? If the former, then you start with the open loop TF and proceed with the design "optimisation" using whatever analytical techniques you are familiar with - such as root locus. There is of course another interpretation of what you understand by "bandwidth" in the context of PLL. Perhaps you mean the bandwidth to be that reference or input frequency range over which the loop will stay in lock...???
I want to know whether the loop bandwidth of PLL is within 1/20 of reference signal frequency or not, so I would like to find out the loop bandwidth of PLL.
It might help if you post some actual equations & numbers. What's the actual expression for your open loop TF (phase out vs phase in) and the value of the reference frequency?
Fs = 50000 -------------------- s^2 + 1000 s + 50000 vco = 1 - s Gain of phase detector is 8.0112 and the value of reference frequency is 1kHz.
So using the values you posted, have you plotted the closed loop frequency response? The -3dB point will presumably give you the nominal bandwidth. Also is the transient response typically overdamped or underdamped? Is the bandwidth near the target value of your 'rule of thumb' factor of 1/20 of the reference frequency? It might be useful to do some Bode plots at various loop gains and / or a root locus plot using the open loop TF, to ascertain whether your chosen loop gain setting is giving you a satisfactory (albeit non-optimal) bandwidth with acceptable dynamic & steady-state stability. For the benefit of myself & others you might indicate whether there are other system or design constraints that you have not disclosed thus far.