Tutorial Review of N-Path Filters and Their Time-Domain Interpretation

Area of Science:

• Electrical Engineering
• Signal Processing
• Integrated Circuit Design

Background:

• N-path filters are crucial for reconfigurable radio-frequency (RF) front ends, offering tunable frequency selectivity, high linearity, and low static power.
• The linear periodically time-varying (LPTV) nature of N-path filters complicates analysis due to input tone harmonic translation.

Purpose of the Study:

• To synthesize and compare principal analysis methods for N-path filters.
• To provide an educational time-domain interpretation for intuitive understanding of harmonic transfer functions (HTFs).
• To guide the selection of appropriate analytical methods for specific applications.

Main Methods:

• Comparison of continuous-time window function analysis, discrete-time ordinary differential equation (ODE) modeling, and adjoint network methods.
• Development of an orthogonal sine/cosine excitation time-domain interpretation.
• Numerical integration of switched-RC equations for consistency checks.

Main Results:

• Evaluation of analytical methods based on assumptions, outputs, and computational burden.
• An intuitive explanation connecting capacitor averaging and phase cancellation to HTFs, clarifying the fundamental coefficient H0(f) and gain-null condition.
• Numerical validation showing minimal deviation (<0.001 dB) from intuitive limits for a four-path filter example, with residual responses below -49 dB at higher harmonics.

Conclusions:

• Established analytical methods for N-path filters are clarified and related.
• The orthogonal-excitation viewpoint offers physical intuition for HTFs without replacing rigorous formulations.
• Guidance is provided for selecting the most suitable analysis technique based on application requirements.