PLL

BigBoss said:

Use Mason's Rule. Convert your block diagram to Mason's Diagram with their individual transfer functions in s-domain then compute whole Transfer Function by applying Mason's Rule.
After obtaining the transfer function in s-domain, you can convert it into frequency domain.
After all these manipulations, you have to verify the system in a system simulator or matlab.

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czjpassby said:

Hi,all, plese guide me how to derive the transfer function of the PLL as shown in the figure, the signal from the PFD can control the resistance of the resistor

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LvW said:

* The transfer function of a PLL can be defined under lock-in condition only (only in this case, the PLL can be considered as a linear system)
* In this case. the input and output variables are phase signals !

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FvM said:

Term (R+1/sC2) can't be right for RC parallel circuit.
Where's I2 in the schematic?

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LvW said:

Here are some background informations about the classical (linearized) PLL model (s-domain)

* Summing junction compares PHI_in(s) (input) with PHI_out(s)
* Kd is the PD constant and is given in V/rad
* Loop filter function Fr(s) is given in V/V
* The VCO function (phase output PHI_out) is Fo=Ko/s with the VCO constant Ko in rad/Vs
* The phase input PHI_in is derived from the frequency input via the function 1/s (not part of the loop).

From this, the closed-loop transfer function is:

PHI_out(s)/(PHI_in(s)=H(s)=Kd*Fr(s)*Ko/(s+Kd*Fr(s)*Ko)

Question to you:
* What are the input and output variables in the function Hopen(s) as given by you?
* In your diagram, the transconductance gm creates a voltage across R||C which controls the oscillator.
But why do you consider this oscillator as a CCO (and not as a VCO)?

Comment: It is rather uncommon (and can lead to interpretation errors) when the closed -loop is a mixture between a block diagram and a circuit diagram (as in your case),
Examples:
1) Will the current out of the block gm distributed between the two connected blocks (RC combination resp. CCO-input) - yes or no?
2) Is the output signal of the block "CP" a voltage - and what is function of C1 in this case?

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output signal of the block "CP" is current. Current is converted into voltage by C1

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