An OTA-Less Second-Order VCO-Based CT $\Delta\Sigma$ Modulator Using an Inherent Passive Integrator and Capacitive Feedback

Voltage-controlled oscillator (VCO)-based continuous-time $\Delta \Sigma $ modulators (CTDSMs) are deemed attractive for deep-scaled process. However, to realize high-order noise shaping, existing works still employ operational transconductance amplifiers (OTAs), which limits the benefits brought by the VCO. This article presents an OTA-less second-order VCO-based CTDSM featuring a hybrid passive-VCO architecture. It exploits the gain-efficient and scaling-friendly nature of the VCO integrator, enabling the use of a fully passive loop filter to increase the order with minimum power. The proposed architecture is realized in a low-cost, low-noise cascaded-integrator feedback structure that makes use of the parasitic effect of the VCO as an inherent passive stage. Fabricated in 40-nm CMOS, the prototype occupies 0.028 mm2 of active area and consumes 590 $\mu \text{W}$ when sampling at 330 MHz. The CTDSM achieved peak Walden figure of merits of 22 fJ/step with 68.7-dB signal to noise and distortion ratio (SNDR) over 6-MHz bandwidth.