In this paper, a new methodology to improve the performance of continuous-time sigma-delta modulators is presented. The proposed structure notated as the time-based continuous-time sigma-delta modulator (TCSDM) utilizes the time encoding approach. Time-based encoding is known as a promising alternative to overcome the resolution problems of analog-to-digital converters (ADCs) in low-voltage circuits. The proposed TCSDM incorporates a novel time-based noise-shaped quantizer (NSQ) to significantly enhance its performance at a very low cost. Using the proposed NSQ, the modulator's noise-shaping order is improved by two without increasing the loop filter order. Furthermore, the implementation of the proposed TCSDM is alleviated using a new single-opamp resonator (SOR) to realize the loop filter. This significantly reduces the power consumption and saves more area. The concept is elaborated for a second-order TCSDM. The analytical calculations and the system-level simulation results are presented to verify the performance. To further confirm the effectiveness of the presented structure, the circuit-level implementation of the modulator is provided in TSMC 90nm CMOS technology. The results show that the proposed modulator achieves a dynamic range of 82dB over a 30MHz bandwidth while consuming less than 18.2mW power from a single 1V power supply. With the proposed NSQ and SOR, both the order and bandwidth requirements of the loop filter are relaxed, and as a result, the analog complexity of the modulator is significantly reduced.