Confusion with power amplification concept in common base topology
When Zbe(f) =0 It forces a lower input Ze(f) so there is no power gain, just level shift on Vc.

But if you add Rb such that Ic/Ib&lt; Hfe you will have high Ze and thus lower input power, thus power gain.  Power gain depends on Vcc, Ic, Rb,Rc , f and GBW of Q.