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A sensor typically used in electrical capacitance tomography (ECT) was generalized to reconstruct the conductivity distribution in this paper. Analytical model was established for the sensor. As a result, the sensitivity matrix and the electric field lines can be obtained directly by using the formulae, which are fast and simple. Two reconstruction methods are proposed based on the model, i.e. iterative Lavrentiev regularization and back projection based on equ-electric field lines. Both simulated and experimental validated the feasibility of the reconstruction methods.