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I'm doing a project involving FMCW linear chirp signals.

Given the phase

$\phi = 2\pi\frac{k}{2}t^{2} + 2\pi f_{c} t + \theta$

where $k$ is the frequency increase rate.

When transmitting frequency modulated pulses continiously will the phase increase in this manner?

enter image description here

Or simply repeat in this manner?

enter image description here

What is the advantages and disadvantages of either one?

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Remember that phase is usually only defined on the $[0;2\pi[$ interval (or on $[-\pi;+\pi[$). When you do that $\mod 2\pi$ operation on your graphs, you'll notice that there's no significant difference between your two plots.

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