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I am trying to design a PLL and want to test it first in Matlab.

I have seen that the phase of the input and output are linearized, but I don't understand what is defined by the input/output phase.

Usually, a transfer function is the ratio of the input's voltage/current to the output voltage/current. However, this Wikipedia article gives the transfer function of a PLL as the ratio of two phases:

#\$ \frac{\theta_O}{\theta_I} = \frac{K_P K_v F(s) } { s + K_P K_v F(s)} \$

where

• \$\theta_O\$ is the output phase in radians

• \$\theta_I\$ is the input phase in radians

• \$K_P\$ is the phase detector gain in volts per radian

• \$K_V\$ is the VCO gain in radians per volt-second

• \$F(s)\$ is the loop filter transfer function (dimensionless)

How do I interpret this transfer function ?

I am trying to design a PLL and want to test it first in Matlab.

I have seen that the phase of the input and output are linearized, but I don't understand what is defined by the input/output phase.

Usually, a transfer function is the ratio of the input's voltage/current to the output voltage/current. However, this Wikipedia article gives the transfer function of a PLL as the ratio of two phases:

#\$ \frac{\theta_O}{\theta_I} = \frac{K_P K_v F(s) } { s + K_P K_v F(s)} \$

where

• \$\theta_O\$ is the output phase in radians

• \$\theta_I\$ is the input phase in radians

• \$K_P\$ is the phase detector gain in volts per radian

• \$K_V\$ is the VCO gain in radians per volt-second

• \$F(s)\$ is the loop filter transfer function (dimensionless)

*** How do I interpret this transfer function ? ***

I am trying to design a PLL and want to test it first in Matlab.

I have seen that the phase of the input and output are linearized, but I don't understand what is defined by the input/output phase.

Usually, a transfer function is the ratio of the input's voltage/current to the output voltage/current. However, this Wikipedia article gives the transfer function of a PLL as the ratio of two phases:

#\$ \frac{\theta_O}{\theta_I} = \frac{K_P K_v F(s) } { s + K_P K_v F(s)} \$

where

• \$\theta_O\$ is the output phase in radians

• \$\theta_I\$ is the input phase in radians

• \$K_P\$ is the phase detector gain in volts per radian

• \$K_V\$ is the VCO gain in radians per volt-second

• \$F(s)\$ is the loop filter transfer function (dimensionless)

How do I interpret this transfer function ?

I am trying to design a PLL and want to test it first in Matlab.

I have seen that the phase of the input and output are linearized, but I don't understand what is defined by the input/output phase.

Usually, a transfer function is the ratio of the input's voltage/current to the output voltage/current. However, this Wikipedia article gives the transfer function of a PLL as the ratio of two phases:

#\$ \frac{\theta_O}{\theta_I} = \frac{K_P K_v F(s) } { s + K_P K_v F(s)} \$

where

• \$\theta_O\$ is the output phase in radians

• \$\theta_I\$ is the input phase in radians

• \$K_P\$ is the phase detector gain in volts per radian

• \$K_V\$ is the VCO gain in radians per volt-second

• \$F(s)\$ is the loop filter transfer function (dimensionless)

How do I interpret this transfer function ?

I am trying to design a PLL and want to test it first in Matlab.

I have seen that the phase of the input and output are linearized, but I don't understand what is defined by the input/output phase.

Usually, a transfer function is the ratio of the input's voltage/current to the output voltage/current. However, this Wikipedia article gives the transfer function of a PLL as the ratio of two phases:

#\$ \frac{\theta_O}{\theta_I} = \frac{K_P K_v F(s) } { s + K_P K_v F(s)} \$

where

• \$\theta_O\$ is the output phase in radians

• \$\theta_I\$ is the input phase in radians

• \$K_P\$ is the phase detector gain in volts per radian

• \$K_V\$ is the VCO gain in radians per volt-second

• \$F(s)\$ is the loop filter transfer function (dimensionless)

How do I interpret this transfer function?

I am trying to design a PLL and want to test it first in Matlab.

I have seen that the phase of the input and output are linearized, but I don't understand what is defined by the input/output phase.

Usually, a transfer function is the ratio of the input's voltage/current to the output voltage/current. However, this Wikipedia article gives the transfer function of a PLL as the ratio of two phases:

#\$ \frac{\theta_O}{\theta_I} = \frac{K_P K_v F(s) } { s + K_P K_v F(s)} \$

where

• \$\theta_O\$ is the output phase in radians

• \$\theta_I\$ is the input phase in radians

• \$K_P\$ is the phase detector gain in volts per radian

• \$K_V\$ is the VCO gain in radians per volt-second

• \$F(s)\$ is the loop filter transfer function (dimensionless)

How do I interpret this transfer function  ?