A comprehensive analysis of the effect of finite amplifier bandwidth and excess loop delay in continuous-time sigma–delta modulators

Study of non-ideal effects in a CT ΣΔ modulator with decaying exponential feedback waveforms

“…When the notch is located at the origin (ω z = 0, g = 0), the coefficient values are: a 1 = -16, and a 2 = -10, in agreement with the values found in a previous paper (Quintanilla et al, 2009a). The absolute values of a 1 and a 2 for a modulator with exponential pulses is significantly higher than those of a modulator with rectangular ones (Quintanilla et al, 2009b). In consequence, integrators must be able to operate with signals having high initial values.…”

“…Some of these effects are: finite gainbandwidth product (GBW) and non-linear transfer function in amplifiers, thermal and flicker noise, clock jitter, digital-to-analog converter (DAC) digital-to-analog converter pulse delays, along with non-idealities in the embedded ADC (hysteresis, metastability, and non-linearity). We carried out a detailed analysis of the impact of some of these effects on CT AEΔ modulators with rectangular feedback pulses in previous papers (Arias et al, 2008;Quintanilla et al, 2009bQuintanilla et al, , 2011.…”

“…A modulator with decaying exponential signals has been implemented by van Veldhoven (2003), and Ortmanns, Gerfers, and Manoli (2003). We designed a current-mode CT AEΔ modulator with exponential feedback in a previous paper (Quintanilla et al, 2009a(Quintanilla et al, , 2009b. Very recently, a multi-step current waveform has been proposed (Chang, Chiu, Liu, & Lin, 2011).…”

“…In most of these papers, rectangular DACs pulses were used and their study was based on simulation results. When non-rectangular pulses are taken into account, the study is usually focused on jitter (see, for instance, Quintanilla et al, 2009aQuintanilla et al, , 2009b. To the best of our knowledge, a detailed analytical study focused on the impact of the combination of the three non-ideal effects -finite gainbandwidth product, excess loop delay, and hysteresis -on the performance of a CT AEΔ modulator with exponential feedback pulses has not been accomplished yet.…”

“…In particular, an active-RC integrator implementation is considered. In a previous paper (Quintanilla et al, 2009b), assuming that amplifiers are described by a single-pole transfer function, we proposed the following non ideal transfer function for integrators:…”