Space-borne gravitational-wave detectors suppress overwhelming laser phase noise by recombining time-delayed heterodyne beatnote phases via time-delay interferometry (TDI). Simultaneously, TDI reshapes secondary noises in the phase, quantified through frequency-domain transfer functions. The dynamic orbits of the detectors modulate secondary noise by affecting arm-length variations, which couples into these transfer functions. We propose using a Fourier series to parameterize arm lengths. This yields an analytical method for calculating noise-transfer functions applicable to dynamic configurations for arbitrary TDI combinations. Using this method, we analyze three kinds of TDI combinations. For some TDI combinations, the secondary noise-transfer functions remain identical under both static equal-arm and dynamic triangular configuration assumptions. However, for zero-response combinations, the static equal-arm configuration assumption renders their secondary noise-transfer functions to zero. Thus, the transfer functions must be defined under dynamic triangular configuration conditions. For the $T[X,Y,Z]$ channel, the secondary noise-transfer function under the static equal-arm triangular configuration assumption is about 2 orders of magnitude lower than under dynamic triangular configuration assumptions. The proposed calculation method, being better aligned with realistic detector constellations, enables precise analytical expressions of secondary noise-transfer functions to be delivered for space-borne gravitational-wave detection data processing.

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• Astrophysical studies of gravity
• Classical mechanics
• Gravitational wave detection
• Metrology
• Noise
• Gravitational wave detectors
• Homodyne & heterodyne detection
• Optical interferometry