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This paper presents two simple SPICE circuit models of the memristor using two different kinds of integrators. These models expand and simplify the previous methods of solving the memristor's modeling equations presented by Hewlett-Packard Lab. The behaviors of the two memristor models are investigated when they are excited by a sinusoidal voltage source. Both models satisfy the general features of memristive systems such as having a zero-crossing property in the form of an i-v Lissajous figure. In order to explore the unique characteristics and applications of the memristor in microwave devices, first we incorporate the memristor in a microstrip transmission line as a load. We do the analysis using a finite-difference time-domain simulator integrated with a nonlinear SPICE circuit solver. Furthermore, we design a reconfigurable microstrip bandpass filter based on a memristor-loaded resonator, and utilize a memristor as a carrier-wave modulator connecting the microstrip patch antenna to the ground.