VCO based multi-stage noise shaping ADC

A way to combine several analogue-to-digital converters (ADCs) based on voltage-controlled oscillators (VCOs) to implement a multi-stage noise shaper (MASH) is proposed. By means of a simple digital circuit, the phase quantisation error in one stage is extracted as a pulsed signal. Then, this pulsed signal modulates the VCO in the next stage. First, the equations that describe the system are discussed and then a hardware implementation suitable for low power applications is proposed. The proposed implementation circuit also desensitises the ADC from the VCO nonlinearity by precoding the input signal using a pulse width modulation modulator.