This paper explains the nonlinear dynamic memory effects observed on both AM-AM and AM-PM conversions of nonlinear microwave power amplifier, PA, circuits. The study is introduced via an analytic Volterra series analysis which is then illustrated with envelope simulations gathered from a GaN HEMT based microwave PA. This way, a theoretically supported explanation of the small- and large-signal dynamic asymptotic behavior, observed in the amplitude and phase conversions of microwave/RF PA's, could be achieved.