Time-Based High-Pass, Low-Pass, Shelf, and Notch Filters

This paper presents formulations for time-based first-order and second-order high-pass, shelf, and notch filters. These formulations are an extension to the existing literature where low-pass filters are already developed using a multiphase controlled oscillator in conjunction with a phase detector and charge pump. The presented high-pass filter expands the circuit by introducing a current-controlled delay line (CCDL) that provides a direct path from input to output. By combining the high-pass filter with the low-pass filter, we show that shelf and notch filters can be obtained without an increase in circuit complexity compared to the high-pass filter. The results show good matching between the ideal small signal and the simulated time-based large signal frequency response. The simulated of total harmonic distortion for the filters shows an increase in distortion due to the nonlinearities introduced by the CCDL for the high-pass, notch, and shelf filter compared to the existing low-pass filter. The derivation of the new filter types allows the creation of complex high-order time-based filters by combining multiple first- or second-order filters.