In the FDTD simulation of microwave circuits, a device in very small size compared with the wavelength is often handled as a lumped element, but it may still occupy more than one cell instead of a wire structure without volume routinely employed in classical extended FDTD algorithms. In this paper, two modified extended FDTD algorithms incorporating a lumped element occupying more than one cell are developed directly from the integral form of Maxwell's equations based on the assumption whether displacement current exists inside the region where a device is present. If the displacement current exists, the modified extended FDTD algorithm can be represented as a Norton equivalent current-source circuit, or otherwise as a Thevenin equivalent voltage-source circuit. These algorithms are applied in the microwave line loaded by a lumped resistor and an active antenna to illustrated the efficiency and difference of the two algorithms.