Laplace Domain Representation for Phase Detector
If I understand your question correctly, you have two signals having different phases, and you need them translated into Laplace domain:
$$\begin{align}
a(t)&amp;=K_a\cos(\omega_a t+\phi_a)\tag{1} \\
b(t)&amp;=K_b\cos(\omega_b t+\phi_b)\tag{2} \\
\mathcal{L}\Bigl\{a(t)\Bigr\}&amp;=K_a\dfrac{\cos\phi_a s-\omega_a\sin\phi_a}{s^2+\omega_a^2}\tag{3} \\
\mathcal{L}\Bigl\{b(t)\Bigr\}&amp;=K_b\dfrac{\cos\phi_b s-\omega_b\sin\phi_b}{s^2+\omega_b^2}\tag{4}
\end{align}$$
The signal is (3)-(4), and if the frequencies are different it will be a 3rd order transfer function, otherwise it all reduces to a simple difference.