By introducing normalized mode excitation coefficient and total mode excitation coefficient, we improve the 3-D mode propagation analysis (MPA) method for convenient design and analysis of multimode interference (MMI) coupler. With the improved 3-D MPA method and point-matching method, we present a novel formulation technique to analyze the low-and high-frequency characteristics for the impedance-matched polymer Mach-Zehnder interferometer electro-optic (EO) switch based on MMI couplers. As an application, under 1550 nm, optimization and simulation performed for the designed device reveal low driving voltage of 1.375 V with short EO region length of 5 mm. The insertion loss and extinction ratio are less than 3.75 dB and more than 42 dB, respectively. The microwave characteristic impedance is about 49.6 , and due to the less mismatch between lightwave velocity and microwave velocity, the estimated cutoff switching frequency is up to 263 GHz with the 10-90% rise time and fall time about 1.90 ps under the operation of step-style square-wave switching signal. This theoretical cutoff switching frequency is almost 1.53 times of that of our previous reported shielded EO switch with similar design technique.