STF optimization of 1-bit CT ΣΔ modulators based on scaled loop filter coefficients

Abstract

This paper presents how the optimization of continuous-time (CT) Σ∆ modulators by scaling the loop filter coefficients affects the signal transfer function (STF) and in which way the method can be used to reduce peaking in the STF. It is shown that, depending on the initial design, it is possible to define optimized parameter sets with increased performance and remaining flat STF or sets with constant performance and reduced STF peaking. Therefore, the system is first described as switched system to analyse its behaviour in the state space. The different effects of the optimization method on the STF are demonstrated on two example systems with differently designed noise transfer functions (NTF).

Peaking reduced STF design for CT ΣΔ modulators with selective pole compensation

“…Nevertheless another possibility is to use a system with high performance as initial system and reduce its dynamics by scaling the coefficients of the loop filter by a factor ξ < 1 [5]. The effect of the scaling method on the STF was presented in [6]. Therein, it was shown that an obvious reduction of the peaking can be achieved by scaling the dynamics of the system as shown in Fig 3. However, despite of scaling the dynamics of the system the remaining peaking of the STF can still be too high and a further scaling would reduce the performance of the system to an unacceptable level.…”

State space analysis of mixed signal systems with switched feedback and delay

“…This method can also be applied to the methods of STF optimization shown in [10]. The following example shows how the switched system model can be used to control and tune the dynamic behavior of sampled systems with continuous dynamics and discrete control.…”

State scaling of continuous-time sigma-delta modulators

“…The second example Zorn et al (2011b) shows the effect of the state scaling method on the STF of a CT sigma delta modulator and how the method can be used to reduce the peaking of the signal transfer function. The initial NTF 2 is more aggressive than the NTF in exqample 5.1 with an oversampling ratio OSR = 64 and a sampling frequency of F s = 320 kHz.…”