  Microwave electric (MW) field measurements utilizing Rydberg atoms have
witnessed significant advancements, achieving remarkable sensitivity, albeit
limited to discrete MW frequencies resonant with Rydberg states. Recently,
various continuous-frequency measurement schemes have emerged. However, when
the MW detuning surpasses 1 GHz, the sensitivity degrades by over an order of
magnitude compared to resonant measurements. In this paper, we successfully
extend the response frequency range by harnessing a controlled driving field in
conjunction with a quantum mixer and heterodyne technology, theoretically
enabling infinite scalability. Notably, second-order effects stemming from
quantum mixing necessitate careful consideration to ensure accurate electric
field measurements. In addition, compared to resonant measurements, the
sensitivity decline for far-detuned MW fields exceeding 1 GHz is less than
twice, representing a significant improvement of several orders of magnitude
over alternative schemes. Furthermore, the sensitivity of far-detuned MW fields
can be efficiently enhanced by augmenting the intensity and frequency of the
controlled field. For detunings ranging from 100 MHz to 2 GHz, we present
optimal sensitivity values and the corresponding methods to achieve them. Our
findings pave the way for Rydberg atom-based MW receivers characterized by both
high sensitivity and an exceptionally broad bandwidth.
