Experimental characterization of hybrid temperature and frequency effects on the performance of transformers on silicon substrate

We have performed an experimental characterization of hybrid temperature and frequency effects on the performance of on-chip square transformers. Using measured two-port S-parameters at different temperatures, we extracted and compared the maximum available gain G_{max and fractional power loss Ploss in each of three transformers (with turn numbers of = 2 3, and 4 of the primary and secondary spirals, respectively).We found that, as temperature increases, the transformer performance degrades significantly. This is caused by the increase in the conductive loss of metal tracks and the dielectric loss of silicon substrate. However, beyond a certain temperature, such as at 418 K in the case of = 4, further increase in temperature has little effect on performance, mainly because of the constitutive characteristics of silicon substrate. In addition, the decrease in Gmax and increase in Ploss with temperature depend on the number of turns.}