4. Linear domain operation
– It is assumed that the signal :
• At t = 0, the loop is therefore hooked with ϕe = ϕs = ϕ = 0, u1 = u2 = 0.
• For t > 0, we apply ϕe (t ) and propose to determine the response ϕs under the assumption that the phase error ϕ is limited to the linearity zone of the phase comparator (linear zone around 0).
We can then make the approximation :
4.1 Equations
Since the system is linear, we use the Laplace transform :
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Linear domain operation
Operation in the presence of noise
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