In many PLL phase loop theory discussions, it's often said that the VCO acts as an integrator and therefore has a 90 degree phase shift. I've seen derivations of the VCO transfer function and this image (taken from here) is particularly enlightening:
Here we see the integrating behaviour of the VCO where Vcontrol is integrated to produce a phase that rotates forever around the time axis.
So, $$\theta(s)=K_{vco}\cdot \frac{V_{control(s)}}{s}$$
What I'm having problems with is the "90 degree phase shift" part. I understand that integrators have a 90 degree phase shift and the classic example is the RC low-pass filter. Here the phase shift between input and output voltage can be understood by the voltage/current phase relationship of the capacitor.
But, I'm struggling to understand the 90 degree phase difference of the VCO in a similar intuitive way (especially since the product of the integration is phase). I assume it's between the phase output and some reference. But, I'm struggling to see what that reference is. Is it the control voltage? But, then that's a DC voltage, right? Can anyone help me out?