Reciprocal Bandwidth Research Articles

Analysis and Optimization of Thermal-Driven Global Interconnects in Nanometer Design

Global interconnects play an increasingly important role in nanometer-scale integrated technologies. The optimization of global wire size (width and/or spacing) has been well studied. However, many optimization methodologies do not consider thermal effects. As technology scales, decreasing interconnect pitch and the introduction of low-k dielectrics have made self-heating of global interconnects an important issue. In this paper, we present a temperature-aware methodology for systematically optimizing the size of global interconnects with optimal repeater for maximizing the circuit performance. We develop techniques to calculate the full-chip temperature as a function of global interconnect width and spacing and analytically analyze the impacts of wire size on the substrate and self-heating temperature. We then reinvestigate the temperature -and size-dependent interconnect delay, bandwidth, and power consumption, and define a product of the delay per unit length, power dissipation per unit length, and reciprocal bandwidth per unit chip edge as an appropriate figure of merit for optimum wire size for various International Technology Roadmap for Semiconductors technology nodes.

An Embedded All-Digital Circuit to Measure PLL Response

We present an all-digital measurement circuit that enables wafer-level test and characterization of phase-locked loop (PLL) response. Through modifications only in the PLL feedback divider state machine, this technique facilitates accurate estimation of PLL frequency-domain closed-loop bandwidth and gain peaking by respectively measuring the time-domain crossover time and maximum overshoot of phase error to a self-induced phase step in the feedback clock. These transient measurements are related back to bandwidth and peaking through the proportionality relationships of crossover time to reciprocal bandwidth and maximum overshoot to peaking. The design-for-test circuit can be used to generate a transient plot of step response, measure static phase error, and observe phase-lock status. We report silicon results from two demonstration vehicles built in a 45-nm SOI-CMOS logic technology for high-performance microprocessors.

Conditional sign flip of two photons without pulse distortion

We theoretically demonstrate a deterministic conditional sign flip of a two-photon pulse that preserves the pulse profile. The nonlinear optical system used is a $V$-type three-level atom confined in a cavity, and the input photons are down-converted twin photons having temporal entanglement. The input and the output pulse profiles are nearly perfectly preserved when the reciprocal bandwidth of the input photons is tuned to the atomic linewidth.

Modal group time spreads in weakly range-dependent deep ocean environments

The temporal spread of modal group arrivals in weakly range-dependent deep ocean environments is considered. It is assumed that the range dependence is sufficiently weak that mode coupling is predominantly local in mode number. The phrase "modal group arrival" is taken here to mean the contribution to a transient wave field corresponding to a fixed mode number. There are three contributions to modal group time spreads which combine approximately in quadrature. These are the reciprocal bandwidth (the minimal pulse width), a deterministic dispersive contribution that is proportional to bandwidth and grows like range r, and a scattering-induced contribution that grows approximately like r(32). The latter two contributions are shown to be proportional to the waveguide invariant beta, a property of the background sound speed profile. The results presented, based mostly on asymptotic theory, are shown to agree well with full-wave numerical wave field simulations and available exact mode theoretical results. Simulations are shown that correspond approximately to conditions during the LOAPEX acoustic propagation experiment.

Resolution: a survey

In applied science, resolution has always been, and still is, an important issue. Since it is not unambiguously defined, it is interpreted in many ways. In this paper, which reviews the concept of optical resolution, a number of these interpretations are discussed. A discussion of resolution has to be preceded by a discussion of what is actually understood by an ‘‘optical image.’’ In a remarkable paper, Ronchi1 distinguished ethereal images, calculated images, and detected images. The term ethereal image was introduced only to represent the physical nature of the imaging phenomenon. As is customary in science in general, attempts have been made to give a mathematical representation of this phenomenon, both geometrically and algebraically. According to Ronchi, the images that have thus been calculated are mere mathematical constructions and should therefore be called calculated images. In the past, many approaches to the concept of resolution concerned these calculated images. This resulted in the so-called classical resolution criteria, such as Rayleigh’s criterion and the associated reciprocal bandwidth of the image. These criteria provide resolution limits that are determined solely by the calculated shape of the point-spread function associated with the imaging aperture and the wavelength of the light. From now on, they will be called classical resolution limits. Calculated images are by their very nature exactly describable by a mathematical model and thus noise free. Such images do not occur in practice. Therefore Ronchi stated that the resolution of detected images is much more important than the classical resolution, since it provides practical information about the imaging system employed. Hence one should consider primarily the resolution of detected images instead of that of calculated images. This means a necessary introduction of some new quantities of interest, such as the energy of the source and the sensitivity properties of the detector. Since Ronchi’s paper, further research on resolution— concerning detected images instead of calculated ones— has shown that in the end, resolution is limited by systematic and random errors resulting in an inadequacy of the description of the observations by the mathematical model chosen. This important conclusion was independently drawn by many researchers who were approaching the concept of resolution from different points of view, which will be discussed in the subsequent sections.

On the measurement of modal group time delays in the deep ocean

The modal description of sound propagation in deep ocean environments is considered. Recently published inversion algorithms have assumed that modal group time delays can be measured. Such a measurement is straightforward to make if either: (1) the modal group arrival of interest is resolved in time; or (2) the wave field is sampled on a dense vertical array which spans much of the water column, thereby enabling the orthogonality of the modes to be exploited. In order to temporally resolve modal group arrivals using measurements made on a single hydrophone, the frequency bandwidth must: (a) be sufficiently broad that the temporal separation between successive modal arrivals exceeds the reciprocal bandwidth; and (b) be sufficiently narrow that, across the band, the group slownesses of neighboring mode numbers do not overlap. To satisfy both conditions [(a) and (b)] the ratio of the range to the center frequency must be large. Unlike ray arrivals, modal group arrivals broaden as range increases due to dispersive spreading. To minimize dispersive spreading so that accurate group delay time estimates can be obtained, the ratio of range to center frequency should be kept small. Thus the requirements for temporally resolving modal group arrivals conflict with the conditions that minimize dispersive spreading. Numerical results are presented which give quantitative estimates of which combinations of range, center frequency, bandwidth, and mode number produce conditions which are favorable for temporally resolving modal group arrivals in six regions of the deep ocean at mid and low latitudes. These results suggest that it is extremely difficult to find conditions which allow modal group arrivals to be temporally resolved and simultaneously allow group delay times to be measured with sufficient accuracy to be useful for tomography. The situation is further complicated by internal waves which appear to cause mode coupling and significant broadening of modal group arrivals at frequencies above approximately 50 Hz. The combined effects of dispersive spreading and internal wave-induced mode coupling suggest that, without employing mode filtering techniques, modal group time delay-based inversion schemes in the deep ocean do not appear to be promising.

Observation of nonlocal interference in separated photon channels.

A two-photon coincidence experiment of the kind recently proposed by J. D. Franson [phys. Rev. Lett. 62, 2205 (1989)] has been carried out with signal and idler photons produced in the process of parametric down-conversion. The coincidence rate registered by the two detectors is found to exhibit a cosine variation with the optical path difference, with periodicity equal to the wavelength. A number of fourth-order optical interference experiments have been carried out in recent years. [1-8] Unlike conventional second-order interference experiments, these depend on the detection of photon pairs and the interference of two two-photon probability amplitudes.[9] It The two-photon probability amplitude for the shorter is an interesting feature of those experiments that quantum mechanics allows the visibility of the interference to be larger for a two-photon state than is allowed by classical electromagnetic theory. A new and particularly simple form of fourth-order interference experiment with two photons has recently been proposed by Franson [10] as a test for locality violations. The outline of the experiment is shown in Fig. 1. Figure 1: Outline of the experiment proposed by Franson. Two photons emitted together by some common source travel along arms A and B to two detectors DA and DB, either directly along the shortest path or via a longer path involving reflections from two beam splitters and two mirrors, as shown. Franson supposed that the two photons might be produced by the cascade decay of an atom in which the initial excited state is very long lived. But we may also suppose that the two photons could arise from the down-conversion of a highly monochromatic laser beam, of long coherence time, in a nonlinear crystal.[11] In both cases the two photons are highly correlated in time and their state is an entangled quantum state. Let us suppose that the difference in propagation time between the longer and the shorter paths is the same in both channels and is much greater than the coherence time (reciprocal bandwidth 1/∆ω) of the light, or the length of each photon wave packet. Then one might naively suppose that there would be no interference. Indeed the mean detection rate registered by DA or DB would not show any dependence on path difference. However, we arrive at a different conclusion if we look for simultaneous detections by both DA and DB. The two-photon probability amplitude for the shorter paths, A to DA and B to DB, then interferes with the two-photon probability amplitude for the longer paths involving the two mirrors. After forming the sum of the two probability amplitudes and squaring we find that the coincidence rate exhibits a cosine variation with a path difference. This is so despite the fact that the two detectors are widely separated and the trajectories of the two photons never mix. We wish to report the results of an experiment in which this nonlocal interference effect, which has no direct classical counterpart, has been observed. The experiment is shown in Fig. 2. The source of the two photons is the process of spontaneous parametric down-conversion[11] in a crystal of LiIO3 that is optically pumped by the 351.1-nm line of an argon-ion laser. The signal (s) and idler (i) photons produced have wavelengths close to 700 nm but substantial bandwidth, which is restricted by interference filters to about 1012Hz. The main difference between the optical arrangement in our experiment and that proposed by Franson is that the variable delay is introduced via an unbalanced Michelson-type interferometer, rather than with the MachZehnder interferometer arrangement shown in Fig. 1. This requires only one beam splitter in each arm instead of two. One of the mirrors M1, of the Michelson interferometer is mounted on a motor-driven micrometer and can also be moved piezoelectrically, and this allows the optical path difference 2(BS−M1)k−2(BS−M2)k ≡ cTk (where k = s, i) to be nearly equalized in the two arms, and for Ti to be varied in submicron steps in a controlled manner about the fixed value cTi ≈ cTs ≈ 3 cm. The time difference Ts, Ti ∼ 10−10sec therefore greatly exceeds the coherence time 1/∆ω ∼ 10−12sec of the light. In order to make Ts and Ti equal to within 10−12sec in the signal and idler

Quantum theory of fourth-order interference.

The quantum theory of fourth-order interference of light is presented in a general format and compared with classical wave theory. The conditions under which nonclassical phenomena occur are discussed. In particular, the interference between the quantum field and classical field may give rise to a nonclassical effect. For some special states of light, the interference pattern does not disappear even though one field is much stronger than the other, for which no classical analog exists. Fourth-order effects in the interference between two independent fields are analyzed in detail. It is pointed out that the fourth-order interference between independent fields will not disappear when the integration time of detection is of the order of the reciprocal bandwidth of the two light fields as long as the spectra of the two fields are symmetric around the same center frequency, and for some correlated fields, the interference does not vanish even if the detection time is much larger than the reciprocal bandwidth of the fields. A new type of fourth-order interference experiment involving a beam splitter is proposed in which local realism of the Einstein-Podolsky-Rosen form is violated for quantum mechanics. This general argument is then applied to the interference between two photons generated in the parametric down-conversion process. The possibility of violations of Bell's inequalities in interference experiments is investigated.

Interference of two photons in parametric down conversion.

A theoretical treatment is given of the process in which the two photons produced simultaneously in the parametric frequency splitting of light are allowed to interfere. It is shown that, while there is no interference in the usual sense involving quantities that are of the second order in the field, fourth-order interference effects are present. These may be revealed by measuring the joint probability of detecting two photons at two points x,x' in the interference plane with photoelectric detectors as a function of the separation x-x'. The probability exhibits a cosine modulation with x-x', with visibility that can approach 100%, even though the integration time in the experiment may greatly exceed the reciprocal bandwidth of the photons. The interference effect has a nonclassical origin and implies a violation of local realism in the highly correlated two-photon state.

Microsecond Intensity Variations in the Radio Emissions from CP 0950

view Abstract Citations (143) References (10) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Microsecond Intensity Variations in the Radio Emissions from CP 0950 Hankins, T. H. Abstract A technique for the removal of the effect of dispersion by the interstellar medium from the radio emission from pulsars has been developed. Observations of the pulsar CP 0950 over a bandwidth of 125 kHz at 111.5 MHz have revealed time structure as short as the reciprocal bandwidth limit of 8 microseconds. Occasional isolated subpulses of 40000 flux units have been observed. Publication: The Astrophysical Journal Pub Date: November 1971 DOI: 10.1086/151164 Bibcode: 1971ApJ...169..487H full text sources ADS |