Time-delay interferometry is put forward to improve the signal-to-noise ratio of space-borne gravitational wave detectors by canceling the large laser phase noise with different combinations of measured data. Based on the Michelson data combination, the sensitivity function of the detector can be obtained by averaging the all-sky wave source positions. At present, there are two main methods to encode gravitational wave signal into detector. One is to adapt gravitational wave polarization angle depending on the arm orientation in the gravitational wave frame, and the other is to divide the gravitational wave signal into plus and cross polarizations in the detector frame. Although there are some attempts using the first method to provide the analytical expression of sensitivity function, only a semianalytical one could be obtained. Here, starting with the second method, we demonstrate the equivalence of both methods. First time to obtain the full analytical expression of sensitivity function, which provides a fast and accurate mean to evaluate and compare the performance of different space-borne detectors, such as LISA and TianQin.
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