The resonant photon energy of an adjustable-phase undulator (APU) is varied with the relative motion of the magnet arrays along the longitudinal direction. There exists, however, a transverse field gradient (TFG) of order 100 T/m in an APU of small gap (∼10 mm). Whereas the TFG might affect the electron beam as it contributes to the dynamic field integral and the radiation integrals, the TFG might also degrade the performance of the synchrotron radiation due to the transverse position-dependent magnetic field. The effects of the TFG on the present Taiwan Photon Source (TPS) and future TPS-upgraded are analyzed to investigate the feasibility of an APU that operates in the soft x-ray region.