Stability Analysis of Bandpass Sigma–Delta Modulators for Single and Dual Tone Sinusoidal Inputs

Nonlinear Stability Prediction of Multibit Delta–Sigma Modulators for Sinusoidal Inputs

“…An in-depth analysis of the approach in [11], [12] with detailed simulation results is given in [13]. As the approaches in [11]- [13] are applied to quantify the stability limits of low-pass ∆-Σ modulators, the analysis and results for predicting stability in band-pass ∆-Σ modulators are detailed in [14]. A novel method based on this approach is given in [15].…”

Nonlinear Model-Based Approach for Accurate Stability Prediction of One-Bit Higher-Order Delta–Sigma Modulators

“…An in-depth analysis of the approach in [13], [14] with detailed simulation results are given in [15]. The approach in [12]- [15] is applied to quantify stability of low-pass ∆-Σ modulators and the analysis and results for predicting stability in band-pass ∆-Σ modulators are detailed in [16]. Although the analysis in [13]- [16] is similar, it is based on separate gains for each of the signal inputs and that of the quantization noise, which are derived from the concept of modified non-linearity.…”

“…The approach in [12]- [15] is applied to quantify stability of low-pass ∆-Σ modulators and the analysis and results for predicting stability in band-pass ∆-Σ modulators are detailed in [16]. Although the analysis in [13]- [16] is similar, it is based on separate gains for each of the signal inputs and that of the quantization noise, which are derived from the concept of modified non-linearity. These result in different quantizer gains for different types of input signals such as DC, single-sinusoid or dual-sinusoid.…”

“…In [15], the approach for dual-sinusoidal inputs results in three separate gains, one for each of the sinusoidal inputs and one for the quantization noise. As practical applications often utilize multiple-sinusoidal inputs such as speech signals, it is not possible to continue with the approach given in [13]- [16] for quantifying stability. In [17] a single quantizer gain for the signal and quantization noise has been used to quantify stability of a composite signal of five sinusoids.…”

“…In [17] a single quantizer gain for the signal and quantization noise has been used to quantify stability of a composite signal of five sinusoids. As the approach is simpler to the ones developed in [13]- [16] (by employing separate signal and quantization noise gains), this novel concept has been investigated and developed for a variety of signals that may be useful for other applications viz., single-, dual and Gaussian signal inputs in this paper. Detailed simulation results are undertaken for 3 rd , 4 th -, 5 th -and 6 th -order Δ-Σ modulators for these signals (including for the five-sinusoidal case as [17] only details the results for the 4 th -order Δ-Σ modulator) to validate the proposed method which is then supported by detailed simulations.…”