Systems and methods for ring-oscillator based operational amplifiers for scaled CMOS technologies

A closed loop amplifier, comprising:

• a first oscillator having an input and a plurality of N outputs;
• a second oscillator having an input and a plurality of N outputs;
• a plurality of N phase detectors, each of the plurality of N phase detectors has a first input, a second input, a first output, and a second output, wherein each first input of each phase detector is coupled to respective one of the plurality of N outputs of the first oscillator, wherein each second input of each phase detector is coupled to respective one of the plurality of N outputs of the second oscillator;
• a first impedance element having two terminals, wherein one terminal is coupled to the input of the first oscillator;
• a second impedance element having two terminals, wherein one terminal is coupled to the input of the second oscillator;
• a plurality of N third impedance elements, each of the plurality of N third impedance elements has a first terminal and a second terminal, wherein each first terminal of each third impedance element is coupled to the input of the first oscillator, wherein each second terminal of each third impedance element is coupled to respective one first output of the plurality of N phase detectors;
• and
• a plurality of N fourth impedance elements, each of the plurality of N fourth impedance elements has a first terminal and a second terminal, wherein each first terminal of each fourth impedance element is coupled to the input of the second oscillator, wherein each second terminal of each fourth impedance element is coupled to respective one second output of the plurality of N phase detectors,
• wherein the closed loop amplifier amplifies a continuous-time continuous-amplitude signal to a continuous-time discrete-amplitude signal.