Micro-electro-mechanical systems (MEMS) based vibratory gyroscopes (MVG) have revolutionized the field of motion sensing with their compact size and low power consumption. A single-anchor single-axis MVG of small-footprint \((4.47\,\text {mm}\times 2.94\,\text {mm})\) is modeled in MEMS \(^+\) software. In the presented design of MVG, proof mass has been supported in the middle using serpentine shaped beams which provides ease in fabrication and decreases the influence of temperature on the sensor performance. A comprehensive study and simulation of the mathematical model and a reduced-order model in MEMS \(^+\) , respectively, of this MVG is also discussed. Further, open and closed-loop configurations are implemented through an interface with MATLAB Simulink and MEMS \(^+\) . The response of MVG is analyzed for the open and the closed-loop operation. This methodology enables the demodulation of angular velocity without dependence on the correlation between the drive position and Coriolis displacement. Moreover, integrating a Phase-Locked Loop (PLL) enhances accuracy in aligning phases by utilizing the phase comparator to correct quadrature errors. For the considered model, a comprehensive drive circuit and sense circuit have been optimized. Significantly, this demodulation approach exhibits versatility beyond its specific application, suggesting its adaptability for integration into other vibratory MEMS gyroscopes. The findings presented here offer valuable guidance in optimizing the MVG.