pole synchronous machines have been recently proposed for efficient interfacing in state-variable-based simulation programs. Therein, a constant and decoupled RL interfacing circuit is achieved using a low-pass filter (LPF) approximation that relaxes an algebraic-loop making the model explicit. However, in machine-converter systems, the ac currents and voltages contain harmonics due to switching, which necessitates the use of stiff poles in the LPF resulting in slow simulations. This letter proposes using a band-pass filter (BPF) that may be tuned depending on the switching harmonics of interest. The proposed hybrid LPF-BPF method allows the use of nonstiff poles and reduces the computational burden without compromising numerical accuracy as opposed to the conventional method.