rf amplifier saturation when input chirp
Are you sure you are using that SA correctly? Chirps are tricky to measure, especially as 11MHz likely exceeds the widest res bandwidth that instrument is capable of. 

What RBW have you selected?

Basically the SA is looking at a bandwidth much narrower then 11MHz at any given time and is sweeping that band to produce its plot, your chirp however is only spending a tiny amount of time in that bandwidth during each chirp... Throw in some averaging and get nonsense. 

My bet is that your generator is putting out something a good 30dB higher then you think it is, and that you are massively saturating the SA input stage, it is for this kind of thing that owning a RF power meter as well as a SA is so very useful (They however have their own issues).