Continue to Site

# PLL

#### czjpassby

##### Newbie level 5
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

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.

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.
Thank you for your reply, I tried to derive the transfer function as follows. But this result is based on current I2 equals to 0, so is it right? please

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
* 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 !

* 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 !
Thank you for your reply, I tried to derive the transfer function as follows. But this result is based on current I2 equals to 0, so is it right? please

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

Term (R+1/sC2) can't be right for RC parallel circuit.
Where's I2 in the schematic?
Thank You . I1 represents Ir+Ic2, and I2 represents the current follwing into CCO, change term (R+1/sC2) to (R//1/sC2)

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?

Last edited:
czjpassby

### czjpassby

Points: 2
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?
So kind of you. I am sorry for my unspecific picture, circuit diagram represents block diafram of filter, the redrawn picture is as follow:

Answer to first question is phase ;

The answer to the second question is the same as the answer to Example 1，yes, there will be current flow into oscillator.

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