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We propose an analytical device model for a graphene nanoribbon field-effect transistor (GNR-FET) under the dc and ac operating conditions. The GNR-FET under consideration is based on a heterostructure, which consists of an array of nanoribbons clad between the highly conducting substrate (the back gate) and the top gate controlling the dc and ac source-drain currents. Using the model developed, we derive explicit analytical formulas for the GNR-FET transconductance as a function of the signal frequency, collision frequency of electrons, and the top gate length. The transition from the ballistic to strongly collisional electron transport is considered.