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

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

Design of a Delayless Feedback Path Free 2nd-order Two-Path Time-Interleaved Discrete-Time Delta-Sigma Modulator- a New Approach

This paper presents the design procedure for a 2nd_order two-path Discrete-Time Time-Interleaved (DTTI) ΔΣ modulator from a conventional single-loop 2nd-order Discrete-Time (DT) ΔΣ modulator through the use of time domain equations and time-interleaving concepts [1]. The resulting modulator is free from the delayless feedback path and has only one set of integrators. The delayless feedback path issue in Time-Interleaved (TI) ΔΣ modulators is a critical restriction for the implementation of TI ΔΣ modulators and is effectively eliminated through the use of the approach proposed in this paper. The DTTI ΔΣ modulator requires only three op-amps and two quantizers both of which work concurrently, in comparison to the single-loop DT counterpart that also deploys two op-amps. For an OverSampling Ratio (OSR) of 16 and a clock frequency of 640MHz, our simulation results show a maximum Signal-to-Noise Ratio (SNR) for the DTTI ΔΣ modulator to be 70.5dB with an input bandwidth of 20MHz which has 15dB improvement in comparison to its single-loop, single-path DT counterpart

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

Time Interleaved Delta Sigma Modulator

In order to overcome the so-called delayless path problem, a time interleaved delta sigma modulator includes a plurality of paths for respective time interleaved data channels, said paths comprising a feed forward path arrangment, including first, second and third filter stages (3a, 3b, 3c), a first path including a first quantizer (Q1 64) being connected to a second feedback path (8) including a DAC (92), and the output of the first DAC having a coupling (31) to the input of the second quantizer intentionally introducing errors in the analog domain, and the output of the first quantizer being coupled to the output of the second quantizer via a correction means performing a difference between the present time sample and the previous one and correcting the intentional errors introduced by said coupling (31)

NEUTRINOS FROM PRIMORDIAL BLACK HOLES

The emission of particles from black holes created in the early Universe has detectable astrophysical consequences. The most stringent bound on their abundance has been obtained from the absence of a detectable diffuse flux of 100 MeV photons. Further scrutiny of these bounds is of interest as they, for instance, rule out primordial black holes as a dark matter candidate. We here point out that these bounds can, in principle, be improved by studying the diffuse cosmic neutrino flux. Measurements of near-vertical atmospheric neutrino fluxes in a region of low geomagnetic latitude can provide a competitive bound. The most favorable energy to detect a possible diffuse flux of primordial black hole origin is found to be a few MeV. We also show that measurements of the diffuse $\nu _\tau$ flux is the most promising to improve the existing bounds deduced from gamma-ray measurements. Neutrinos from individual black hole explosions can be detected in the GeV-TeV energy region. We find that the kilometer-scale detectors, recently proposed, are able to establish competitive bounds.Comment: 19 pages plus 9 uuencoded and compressed postscript figure

Modelling of the effect of ELMs on fuel retention at the bulk W divertor of JET

Effect of ELMs on fuel retention at the bulk W target of JET ITER-Like Wall was studied with multi-scale calculations. Plasma input parameters were taken from ELMy H-mode plasma experiment. The energetic intra-ELM fuel particles get implanted and create near-surface defects up to depths of few tens of nm, which act as the main fuel trapping sites during ELMs. Clustering of implantation-induced vacancies were found to take place. The incoming flux of inter-ELM plasma particles increases the different filling levels of trapped fuel in defects. The temperature increase of the W target during the pulse increases the fuel detrapping rate. The inter-ELM fuel particle flux refills the partially emptied trapping sites and fills new sites. This leads to a competing effect on the retention and release rates of the implanted particles. At high temperatures the main retention appeared in larger vacancy clusters due to increased clustering rate

Modelling of tungsten erosion and deposition in the divertor of JET-ILW in comparison to experimental findings

The erosion, transport and deposition of tungsten in the outer divertor of JET-ILW has been studied for an HMode discharge with low frequency ELMs. For this specific case with an inter-ELM electron temperature at the strike point of about 20 eV, tungsten sputtering between ELMs is almost exclusively due to beryllium impurity and self-sputtering. However, during ELMs tungsten sputtering due to deuterium becomes important and even dominates. The amount of simulated local deposition of tungsten relative to the amount of sputtered tungsten in between ELMs is very high and reaches values of 99% for an electron density of 5E13 cm$^{-3}$ at the strike point and electron temperatures between 10 and 30 eV. Smaller deposition values are simulated with reduced electron density. The direction of the B-field significantly influences the local deposition and leads to a reduction if the E×B drift directs towards the scrape-off-layer. Also, the thermal force can reduce the tungsten deposition, however, an ion temperature gradient of about 0.1 eV/mm or larger is needed for a significant effect. The tungsten deposition simulated during ELMs reaches values of about 98% assuming ELM parameters according to free-streaming model. The measured WI emission profiles in between and within ELMs have been reproduced by the simulation. The contribution to the overall net tungsten erosion during ELMs is about 5 times larger than the one in between ELMs for the studied case. However, this is due to the rather low electron temperature in between ELMs, which leads to deuterium impact energies below the sputtering threshold for tungsten

Tritium distributions on W-coated divertor tiles used in the third JET ITER-like wall campaign

Tritium (T) distributions on tungsten (W)-coated plasma-facing tiles used in the third ITER-like wall campaign (2015–2016) of the Joint European Torus (JET) were examined by means of an imaging plate technique and β-ray induced x-ray spectrometry, and they were compared with the distributions after the second (2013–2014) campaign. Strong enrichment of T in beryllium (Be) deposition layers was observed after the second campaign. In contrast, T distributions after the third campaign was more uniform though Be deposition layers were visually recognized. The one of the possible explanations is enhanced desorption of T from Be deposition layers due to higher tile temperatures caused by higher energy input in the third campaign