A General Formula for Impulse-Invariant Transformation for Continuous-Time Delta-Sigma Modulators

this paper presents a generalised new formula for impulse-invariant transformation which can be used to convert an nth-order Discrete-Time (DT) ΔΣ modulator to an nth-order equivalent Continuous-Time (CT) ΔΣ modulator. Impulse-invariant transformation formulas have been published in many open literature articles for s-domain to z-domain conversion and vice-versa. However, some of the published works contain omissions and oversights. To verify the newly derived formulas, very many designs of varying orders have been tested and a representative 4th-order single-loop DT ΔΣ modulator converted to an equivalent CT ΔΣ modulator through the new formulas are presented in this paper. The simulation results confirm that the CT ΔΣ modulator which has been derived by these formulas works in accordance with the initial DT specifications without any noticeable degradation in performance in comparison to its original DT ΔΣ modulator prototype

A 28mW 320MHz 3rd–Order Continuous-Time Time-Interleaved Delta-Sigma Modulator with 10MHz Bandwidth and 12 Bits of Resolution

this paper presents a 3rd-order two-path Continuous-Time Time-Interleaved (CTTI) delta-sigma modulator which is implemented in standard 90nm CMOS technology. The architecture uses a novel method to solve the delayless feedback path issue arising from the sharing of integrators between paths. The clock frequency of the modulator is 320MHz but integrators, quantizers and DACs operate at 160MHz. The modulator achieves a dynamic range of 12 bits over a bandwidth of 10MHz and dissipates only 28mW of power from a 1.8-V supply

Design and Simulation of a 3rd-order Discrete-Time Time-Interleaved Delta-Sigma Modulator with Shared Integrators between Two Paths

This paper presents the design and simulation of a 3rd-order two-path Discrete-Time Time-Interleaved (DTTI) ΔΣ modulator. By exploiting the concept of the time-interleaving techniques and time domain equations, a conventional 3rd-order Discrete-Time (DT) ΔΣ modulator is converted to a corresponding 3rd-order two-path DTTI counterpart. For the sake of saving power and silicon area, the integrators between the two paths of the DTTI ΔΣ modulator are shared. Using one set of integrators makes the DTTI ΔΣ modulator robust to path mismatch effects compared to the typical DTTI ΔΣ modulator which has individual integrators in all paths. A problem arises out of sharing integrators between paths which we call the delayless feedback problem. A solution for this problem is proposed in this paper and for an OverSampling Ratio (OSR) of 16 and a clock frequency of 320MHz, a maximum SNR of 76.5dB is obtained

Escaping Saddle Points with Adaptive Gradient Methods

Adaptive methods such as Adam and RMSProp are widely used in deep learning but are not well understood. In this paper, we seek a crisp, clean and precise characterization of their behavior in nonconvex settings. To this end, we first provide a novel view of adaptive methods as preconditioned SGD, where the preconditioner is estimated in an online manner. By studying the preconditioner on its own, we elucidate its purpose: it rescales the stochastic gradient noise to be isotropic near stationary points, which helps escape saddle points. Furthermore, we show that adaptive methods can efficiently estimate the aforementioned preconditioner. By gluing together these two components, we provide the first (to our knowledge) second-order convergence result for any adaptive method. The key insight from our analysis is that, compared to SGD, adaptive methods escape saddle points faster, and can converge faster overall to second-order stationary points.Comment: Update Theorem 4.1 and proof to use martingale concentration bounds, i.e. matrix Freedma

Stability analysis of higher-order delta-sigma modulators for sinusoidal inputs

The aim of this paper is to determine the stability of higher-order Δ-Σ modulators for sinusoidal inputs. The nonlinear gains for the single bit quantizer for a dual sinusoidal input have been derived and the maximum stable input limits for a fifth-order Chebyshev Type II based Δ-Σ modulators are established. These results are useful for optimising the design of higher-order Δ-Σ modulators

Advancing family science through public scholarship: fostering community relationships and engaging in broader impacts

This is the peer reviewed version of the following article: Monk, J.K., Bordere, T.C. and Benson, J.J. (2021), Emerging Ideas. Advancing Family Science Through Public Scholarship: Fostering Community Relationships and Engaging in Broader Impacts. Fam Relat, 70: 1612-1625. https://doi.org/10.1111/fare.12545, which has been published in final form at https://doi.org/10.1111/fare.12545. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley's version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.Objective: To increase the awareness and support for family scientists' engagement in public scholarship. Background: Without appropriate dissemination efforts, important research findings may remain solely in academic journals and never reach the public. Grounded in a social justice perspective, we argue that family scientists are and should be on the frontlines of direct social change and activities related to broader impacts. Method: In this call-to-action, we articulate the utility and praxis of public scholarship, or the production and dissemination of scientific knowledge for and with communities to create social change for the public good. Results: When engaging in public scholarship, we can build community trust, increase our impact and demonstrate the relevance of family science. Therefore, we offer practical suggestions like collaborating with individuals who serve in complementary roles, hosting a research press conference to disseminate key findings, and writing for local outlets like community newspapers. We also provide insights to help implement (e.g., resources for developing press releases, infographics or visual abstracts) and document (e.g., in promotion and tenure materials) these activities. Conclusion: We encourage scholars to keep these suggestions in mind when trying to think of creative broader impacts activities that illustrate the relevance of research in people's lives. Implications: By shifting academic cultures and engaging in public scholarship, family scholars can increase their reach and contribute to the enfranchisement of marginalized populations, while also enhancing the visibility of findings, building their scholarly networks, and growing public support for family science