In this paper, a time-mode resonator is presented that is used to realize a second-order bandpass ΔΣ time-to-digital converter (TDC). The resonator is constructed as a cascade of two lossless discrete-time integrators implemented using time-latches and some digital logic in a negative feedback configuration. This paper presents for the very first time the means in which time-mode circuits are used in a negative feedback loop. This achieves high-speed time-mode signal processing without the limitations imposed by switched-capacitor (SC) circuit techniques such as the matching of capacitors to realize precise signal gains. Instead, circuit precision is realized using an on-chip calibration circuit referenced to the main system clock to adjust for timing variations in the time-mode circuits. The operation of the timemode resonator is verified by realizing a second-order BP ΔΣ TDC. The bandpass noise-shaping is validated with transistor-level simulations.