An amplifier-less continuous-time analog-to-digital converter consisting of only passives, comparators, and inverters is presented. Beyond simplicity, the architecture displays significant robustness properties with respect to component variations and comparator input offsets. We give an analytical design procedure demonstrating how to parameterize the architecture to a range of signal-to-noise and bandwidth requirements and validate the procedure’s accuracy with behavioral transient simulations.

In this paper, the design flexibility of the control-bounded analog-to-digital converter principle is demonstrated. A band-pass analog-to-digital converter is considered as an application and case study. We show how a low-pass control-bounded analog-to-digital converter can be translated into a band-pass version where the guaranteed stability, converter bandwidth, and signal-to-noise ratio are preserved while the center frequency for conversion can be positioned freely. The proposed converter is validated with behavioral simulations on several filter orders, center frequencies, and oversampling ratios. Additionally, we consider an op-amp circuit realization where the effects of first-order op-amp non-idealities are shown. Finally, robustness against component variations is demonstrated by Monte Carlo simulations.

This article presents analytical tools for high-level design of the leapfrog (LF) control-bounded analog-to-digital converter (CBADC). We derive closed-form design equations for parameterizing the analog system for a target signal-to-noise ratio (SNR) and bandwidth. Furthermore, we show how the parameterization can be modified to compensate for finite amplifier gain-bandwidth product (GBWP) and to control the signal swing at different nodes of the system. Behavioral circuit simulations are used to compare the LF CBADC to relevant continuous-time sigma–delta modulators (CT-$\Sigma \Delta $Ms) in terms of nominal performance and sensitivity to component variations, clock jitter, and finite GBWP. Simulations show that the nominal performance of the LF is similar to that of a CT-$\Sigma \Delta \text{M}$of the same loop-filter order and with the same number of quantization levels. The simple, modular structure, analytical stability guarantee, and single-bit quantizers make the LF an interesting alternative to conventional CT-$\Sigma \Delta $Ms.

The paper proposes a new method to determine a binary control signal for an analog linear system such that the state, or some output, of the system follows a given target trajectory. The method can also be used for digital-to-analog conversion.The heart of the proposed method is a new binary-enforcing NUV prior (normal with unknown variance). The resulting computations, for each planning period, amount to iterating forward-backward Gaussian message passing recursions (similar to Kalman smoothing), with a complexity (per iteration) that is linear in the planning horizon. In consequence, the proposed method is not limited to a short planning horizon.

Control-bounded analog-to-digital conversion as described in the work of Loeliger et al. opens opportunities for entirely new analog circuit topologies. The structure of such a converter is shown in Fig. 1. In this paper, we propose such a converter where the analog linear system is a network of N fully connected identical integrators, with uniform sensitivity to noise and mismatch across the network. Nonetheless, the converter achieves a nominal conversion error similar to that of a ΔΣ converter with a N-th order loop filter.

The paper considers the problem of joint system identification and input signal estimation of an unknown linear system from noisy observations of the output signal. The input signal is assumed to be sparse, and each individual input pulse may affect the system in its own (and unknown) way. Based on ideas from sparse Bayesian learning, we derive an efficient expectation maximization (EM) algorithm for jointly estimating all unknown quantities. Unlike related prior work, the proposed algorithm does not alternate between estimating the input signal and estimating the system parameters; instead, all unknown quantities are jointly updated in each EM step. We give closed-form expressions for these EM updates, which can be efficiently computed by Gaussian message passing.

We use ideas from sparse Bayesian learning for estimating the (weakly) sparse input signal of a linear state space model. Variational representations of the sparsifying prior lead to algorithms that essentially amount to Gaussian message passing. The approach is extended to the case where the state space model is not known and must be estimated. Experimental results with a real-world application substantiate the applicability of the proposed method.