Recovering Signal and Σ-Δ Modulator Parameters
In the paper models of one bit cascaded sigmadelta modulator (SDM) of analog-to-digital converter (ADC) is presented. By discussing models of ADC, we have developed a technique of definition of inner modulator parameters, which are based on linear model. For ADC model applied a slightly random exciting deviation to modulator parameters has been successfully recovered from output samples. The linear ADC model contains the following parameters: inner scale coefficients, open-loop gain of operational amplifier, integrator’s leakage. A stability criterion in non-chaotic mode of SDM has been applied to one-bit architecture. The criterion can be extended to n-th SDM order. The technique of recovering parameters includes the stability criteria, extremum problem in 3n-1 dimensional space. Parameters are taken from output sampling by applying Monte Carlo (MC) algorithm to extremum-solving problem. An essential part of Monte Carlo algorithm is annealing. Other problem is signal recovering. For simulation purposes, we rather suggest retarded-advanced filter than a well-known finite impulse response filter. That technique better improves performance of signal recovering than applying the low pass finite impulse response filter to the modulator output. Offered filter provides to get a component, which is phase-correlated with modulator output and is not phase-correlated with input signal. The component can efficiently substrate modulator noise. It is important that extracted component correlates with nonlinear noise components. Comparing recovered and input signal we have defined an expression on parameters. Other expressions and MC algorithm define the rest parameters. By discussing unipolar and difference amplifier connection, it has been shown that there is no parasitic common-mode output component for the unipolar architecture. For testing ADC devices, recovering parameters and common-mode observation can be applied independently.