In this paper an exact baseband equivalent model of a quadrature modulated all-digital transmitter is derived. No restrictions on the number of levels of a digital switched-mode power amplifier (SMPA) driving input, nor the pulse encoding scheme employed, are made. This implies a high level of generality of the proposed model. We show that all-digital transmitter (ADT) can be represented as a series connection of the pulse encoder, discrete-time Volterra series model of fixed degree and memory depth, and a linear timevarying system with special properties. This result suggests a new analytically motivated structure of a digital predistortion (DPD) of SMPA nonlinearities in ADT. Numerical simulations in MATLAB are used to verify proposed baseband equivalent model.