In the magnetic impedance approach for damage detection, there is no direct contact between the sensor and the host structure, and the impedance sensor can be moveable above the structure surface. This has promising aspects, especially for online health monitoring of structures with complicated geometries and boundaries. In an earlier study, we have demonstrated that integrating a synthetic, tunable negative resistance and a tunable capacitor with the magnetic transducer can amplify both the measurement magnitude and the damage-induced impedance anomaly and yield much higher signal-to-noise ratio and detection sensitivity. In this research, we formulate detailed modeling and carry out comprehensive analysis to investigate the enhanced magnetic impedance sensing with circuitry integration. Specifically, aiming at providing design and implementation guidelines, we investigate systematically the magnetomechanical coupling effect in such a sensing scheme, which focuses on elucidating quantitatively the influence of various sensor parameters to the impedance measurements. The modeling and analysis are validated by experimental studies.