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So,

I need to design a PLL that needs to track carrier frequencies used in WLAN 802.11b (2.412 GHz to 2.484 GHz with 20 MHz of bandwidth for each carrier). Below the schema.

schematic

simulate this circuit – Schematic created using CircuitLab

Where

K_PD
and
K_VCO
are the constants of the phase detector and the VCO. N divider is the divider for the referance frequency that, in my case is 1 MHz (N divider varies between 2412 and 2484 according to which frequency I’m tracking).

To design the PLL I have a VCO with bandwith from 2.3 GHz to 2.5 GHz and 𝛿 = 1. The LPF must ahve bandwith 50 kHz.

With these informations I need to find R1, C1 of the LPF and

K_PD
and
K_VCO
of the PLL but I have no idea where to start.

I know the transfer function of the PLL in my scheme is:

    \[T_N(s) = frac{1}{1+sR_1C_1}frac{K_{PD}K_{VCO}}{s}frac{1}{N}\]

and I know the equation 𝛿 and 𝜔_n but still I can’t understand how to proceed.

I have calculated R1 and C1 given the bandwitch of my filter but, there are multiple solutions because of the position of where I want o put my pole in the transfer function