An analog multiplier based on asynchronous sigma-delta pulse amplitude modulation

Asynchronous sigma-delta modulation (ASDM) has been proposed as a possible solution for the amplitude to duty-cycle conversion. The information conveyed by voltage level of the ASDM input signal is converted into the duty cycle of the ASDM output signal period. Applying pulse amplitude modulation (PAM) to ASDM output pulse stream, 2-input analog multiplier can be obtained. The mean value of the output pulse stream period corresponds to the product of the ASDM input and PAM input signals. This paper gives the mathematical analysis of the ASDM-PAM analog multiplier output signal spectrum for the DC and sinusoidal input signals. It has been shown that combination of ASDM and PAM modulation generates a product of the two input signals in the baseband and around multiples of the central frequency, which can be later on efficiently filtered out. The ASDM-PAM multiplier Simulink model has been used for confirmation of the mathematical analysis.