The Modular Multilevel Converter (MMC) topology has been suggested to transmit the dc bulk power as oppose to other similar multilevel topologies, due to its multiple advantages. An stability analysis is fundamental to evaluate the operation of the MMC during normal operating conditions, and small and large disturbances The understanding of the MMC's performance along with the knowledge of the state-space representation are fundamental to describe the system at any operating condition and to evaluate new control schemes. In this paper, an equivalent linear model of an MMC terminal in the dq synchronous reference frame is presented. This model is obtained as a result of a feedback linearization technique and considers the circulating currents and the internal energy dynamics of the MMC terminal, allowing for a complete small-signal stability analysis. As a result of applying a feedback linearization technique on the nonlinear system, a set of linear equations are obtained, facilitating the design of a control strategy In order to verify the effectiveness of the proposed model, extensive time-domain simulations are carried out on an MMC terminal under different operating conditions. Results show that when an small perturbation is applied, the control system has fast response to stabilize the system proving the efficacy of the resulting linear model.