Transverse Mode Instability (TMI) and Nonlinear Optical Effects (NLE) prevent high-power all-fiber lasers from further power scaling. Low Numerical Aperture (NA) Large Mode Area (LMA) active fibers can maintain large effective areas while suppressing the Higher-Order Modes (HOMs) and increasing the thresholds of NLE and TMI. Additionally, it is easier to match the passive component for low NA LMA fiber because its structure is simpler and consistent with the step-index fiber structure. Mode Field Adapters (MFAs) match the mode field between LMA fibers and Single-Mode Fibers (SMFs) and are crucial passive components in fiber laser systems. The insertion loss and beam quality of MFAs significantly affect the power scaling and beam quality of laser systems. This paper made MFA based on tapered low NA LMA fiber with NA=0.05 and Thermally Expanded Core (TEC) fibers, maintaining high coupling efficiency and improving the output beam quality. The impact of mode field mismatch, core offset, and angular misalignment between LMA fibers with different NAs and SMF on coupling efficiency and beam quality of MFA was studied theoretically and experimentally. First, theoretical models for TEC and tapered LMA fibers were built based on diffusion and adiabatic criterion equations. The mode field distribution and propagation characteristics of TEC and tapered LMA fibers were simulated based on the beam propagation method to optimize the device structure and preparation parameters. Second, a simulation model was created to analyze the insertion loss and beam quality degradation caused by mode field mismatch, core offset, and angular misalignment between LMA fibers with different NAs and SMFs. The simulation results show that reducing the NA of LMA fibers helps suppress HOMs and reduces the insertion loss and beam quality degradation of MFAs caused by core offset and angular misalignment. During the experimental process, the SMF was heated with an H₂-O₂ flame to expand the Mode Field Diameter (MFD) of SMF without causing transmission loss. The MFD of the TEC SMF under different heating times was measured using the far-field method. Two MFAs were prepared by LMA fibers (25/400 μm) with NAs of 0.06 and 0.05, respectively, to TEC SMF (5.3/125 μm, NA=0.14). The insertion loss and beam quality factor (M²) of the devices were measured. The forward insertion loss decreased from 4.50 dB to 0.29 dB, and the difference in bi-directional insertion loss decreased from 2.50 dB to 0.19 dB when the LMA fiber (NA=0.06) for MFD matched with the SMF. The experimental results show that matching the MFD of SMF and LMA fibers effectively reduces the insertion loss and the difference in bi-directional insertion loss. The taper ratios of the LMA fibers are both 2, and the heating times for the SMF are 25 min and 20 min, respectively, when the MFD is matched between the LMA fibers with NAs of 0.05 and 0.06 and SMF. Due to the MFD matching between the LMA fibers and SMFs, only the unavoidable core offset and angular misalignment during the fusion process, which affect the coupling efficiency and beam quality, are considered, and these misalignments are random variables. The impact of misalignment on beam quality and coupling efficiency in LMA fibers with different NAs was indirectly reflected by performing multiple measurements and calculating the mean and standard deviation. The forward insertion loss decreases to 0.29 dB with a standard deviation of 0.085, and the bi-directional insertion loss difference is 0.19 dB with a standard deviation of 0.077 when the MFD is matched between the LMA (NA=0.06) fiber and the SMF. The forward insertion loss decreases to 0.23 dB with a standard deviation of 0.024, and the bi-directional insertion loss difference is 0.06 dB with a standard deviation of 0.011 when the MFD is matched between the LMA (NA=0.05) fiber and SMF. Cladding modes caused the difference in bi-directional insertion loss, and HOMs were not stripped by the cladding light strippers as they do not propagate in SMF. Therefore, this difference is positively correlated with the beam quality of the MFA. The difference in bi-directional insertion loss for the MFAs based on LMA fibers with NAs of 0.05 and 0.06 are 1.76 dB and 2.50 dB, and the M² are 1.88 and 2.15, respectively, when the MFD of the SMF and the LMA fiber are not matched. This difference for the MFAs based on LMA fibers with NAs of 0.05 and 0.06 is 0.06 dB and 0.19 dB, and the M² value is 1.15 with a standard deviation of 0.017 and 1.26 with a standard deviation of 0.092, respectively, and when the MFD of the SMF and the LMA fiber are matched. The experimental results show that the LMA fiber with NA=0.05 contains fewer HOMs and reduces beam quality degradation and insertion loss caused by core offset and angular misalignment during the splicing process, resulting in higher beam quality and lower insertion loss of the MFA. These conclusions are consistent with the theoretical analysis and simulation results. The MFA based on LMA fiber with NA=0.05 has promising application prospects in single-mode output high-power fiber lasers due to its low insertion loss and high beam quality advantages.