Kirchhoff's voltage law (KVL) and band-pass filter theory (BPFT) have been utilised for estimating the power transfer efficiency (PTE) and power delivered to the load (PDL) of magnetically-coupled resonant wireless power transfer (WPT). By using the two approaches, three aspects for in-depth understanding of power transfer characteristics and designing a high-efficiency WPT system are illuminated in this research. First, by introducing generalised mistuning factor and using diagram discriminance method in KVL, the effect conditions of source- and load-loaded quality factors on PTE and PDL are analysed. Then, by applying frequency and element transformations in BPFT, the restraints of Butterworth and Chebyshev type filter for WPT application are revealed. Third, it is verified that BPFT is a special case of KVL, and the former simplifies the design and analysis under the derived restraints than the latter. The maximal PDL at original frequency and the transfer characteristics in frequency splitting region can be easily achieved by Butterworth and Chebyshev type, respectively. The PTE and PDL versus frequency and coupling coefficient can be analysed in detail by KVL. Finally, the calculated results of the design examples are verified through experimental measurements.