The ac-ac dual active bridge (DAB) converter is an advanced bidirectional two-port grid interface converter that facilitates active and reactive power flow control between two grids without a dc-link capacitor. This article presents a novel modeling approach for the ac-ac DAB converter using the extended generalized average modeling (EGAM) technique. Unlike the conventional generalized average modeling (GAM) framework, the ac-ac DAB converter's dynamic state variables, including the leakage inductor current and ac grid side LC filters, exhibit grid and switching frequency components, making the standard GAM framework unsuitable for dynamic modeling involving two distinct excitation frequencies. Furthermore, the 2-D GAM (2D-GAM) framework, although capable of capturing the dynamics of two frequencies and their cross interactions, fails to handle product terms involving double fourier series (DFS) states resulting from the switching terms in the ac-ac DAB converter. To address these challenges, the EGAM technique is proposed, which involves transforming the DFS product terms in the time domain into the 2D-convolution of their discrete fourier images (DFI) in the frequency domain. As a consequence of this analysis, it is shown that in an ac-ac DAB converter, the power is transferred in the grid-switching sideband frequency components at the bridge level. The effectiveness of the EGAM modeling framework is demonstrated through extensive simulation and hardware experiments, and the results are compared with PLECS results, validating the accuracy and efficacy of the proposed approach.