  We demonstrate the continuous broadband microwave receivers based on AC Stark
shifts and Floquet States of Rydberg levels in a cesium atomic vapor cell. The
resonant transition frequency of two adjacent Rydberg states 78$S_{1/2}$ and
78$P_{1/2}$ is tuned based on AC Stark effect of 70~MHz Radio frequency (RF)
field that is applied outside the vapor cell. Meanwhile, the Rydberg states
also exhibit Floquet even-order sidebands that are used to extend the
bandwidths further. We achieve microwave electric field measurements over
1.172~GHz of continuous frequency range. The sensitivity of the Rydberg
receiver with heterodyne technique in the absence of RF field is
280.2~nVcm$^{-1}$Hz$^{-1/2}$, while it is dramatically decreased with tuning
the resonant transition frequency in the presence of RF field. Surprisingly,
the sensitivity can be greatly improved if the microwave field couples the
Floquet sideband transition. The achieving of continuous frequency and high
sensitivity microwave detection will promote the application of Rydberg
receiver in the radar technique and wireless communication.
