A class of analog CMOS circuits based on the square-law characteristic of an MOS transistor in saturation

The examined class of circuits includes voltage multipliers, current multipliers, linear V-I convertors, linear I-V convertors, current squaring circuits, and current divider circuits. Typical for these circuits is an independent control of the sum as well as the difference between two gate-source voltages. As direct use is made of the basic device characteristics, only a small number of transistors is required in the presented circuits

A CMOS analog continuous-time delay line with adaptive delay-time control

A CMOS analog continuous-time delay line composed of cascaded first-order current-domain all-pass sections is discussed. Each all-pass section consists of CMOS transistors and a single capacitor. The operation is based on the square-law characteristic of an MOS transistor in saturation. The delay time per section can either be controlled by an external voltage or locked to an external reference frequency by means of a control system which features a large capture range. Experimental verification has been performed on two setups: an integrated cascade of 26 identical all-pass sections and a frequency-locking system breadboard built around two identical on-chip all-pass section

A CMOS four-quadrant analog multiplier

A new circuit configuration for an MOS four-quadrant analog multiplier circuit is presented. It is based on the square-law characteristics of the MOS transistor. Two versions have been realized. The first has a linearity better than 0.14 percent for an output current swing of 36 percent of the supply current and a bandwidth from dc to 1 MHz. The second version has floating inputs, a linearity of 0.4 percent at an output current swing of 40 percent of the supply current and a bandwidth from dc to above 4.5 MHz

Ruijsenaars' hypergeometric function and the modular double of U_q(sl(2,C))

Simultaneous eigenfunctions of two Askey-Wilson second order difference operators are constructed as formal matrix coefficients of the principal series representation of the modular double of the quantized universal enveloping algebra U_q(sl(2,C)). These eigenfunctions are shown to be equal to Ruijsenaars' hypergeometric function under a proper parameter correspondence.Comment: Replaced to synchronize formula numbers with the published version. 25 page

The aperiodic X-ray variability of the accreting millisecond pulsar SAX J1808.4-3658

We have studied the aperiodic variability of the 401 Hz accreting millisecond X-ray pulsar SAX J1808.4-3658 using the complete data set collected with the Rossi X-ray Timing Explorer over 14 years of observation. The source shows a number of exceptional aperiodic timing phenomena that are observed against a backdrop of timing properties that show consistent trends in all five observed outbursts and closely resemble those of other atoll sources. We performed a detailed study of the enigmatic ~410 Hz QPO, which has only been observed in SAX J1808.4-3658. We find that it appears only when the upper kHz QPO frequency is less than the 401 Hz spin frequency. The difference between the ~410 Hz QPO frequency and the spin frequency follows a similar frequency correlation as the low frequency power spectral components, suggesting that the ~410 Hz QPO is a retrograde beat against the spin frequency of a rotational phenomenon in the 9 Hz range. Comparing this 9 Hz beat feature with the Low-Frequency QPO in SAX J1808.4-3658 and other neutron star sources, we conclude that these two might be part of the same basic phenomenon. We suggest that they might be caused by retrograde precession due to a combination of relativistic, classical and magnetic torques. Additionally we present two new measurements of the lower kHz QPO, allowing us, for the first time, to measure the frequency evolution of the twin kHz QPOs in this source. The twin kHz QPOs are seen to move together over 150 Hz, maintaining a centroid frequency separation of $(0.446 \pm 0.009) \nu_{spin}$.Comment: 18 pages, 9 figures, 7 tables. Accepted for publication in Ap

Pulse amplitude depends on kHz QPO frequency in the accreting millisecond pulsar SAX J1808.4-3658

We study the relation between the 300-700 Hz upper kHz quasi-periodic oscillation (QPO) and the 401 Hz coherent pulsations across all outbursts of the accreting millisecond X-ray pulsar SAX J1808.4-3658 observed with the Rossi X-ray Timing Explorer. We find that the pulse amplitude systematically changes by a factor of ~2 when the upper kHz QPO frequency passes through 401 Hz: it halves when the QPO moves to above the spin frequency and doubles again on the way back. This establishes for the first time the existence of a direct effect of kHz QPOs on the millisecond pulsations and provides a new clue to the origin of the upper kHz QPO. We discuss several scenarios and conclude that while more complex explanations can not formally be excluded, our result strongly suggests that the QPO is produced by azimuthal motion at the inner edge of the accretion disk, most likely orbital motion. Depending on whether this azimuthal motion is faster or slower than the spin, the plasma then interacts differently with the neutron-star magnetic field. The most straightforward interpretation involves magnetospheric centrifugal inhibition of the accretion flow that sets in when the upper kHz QPO becomes slower than the spin.Comment: 5 pages, 4 figures, Accepted for publication in ApJ

Fourier spectra from exoplanets with polar caps and ocean glint

The weak orbital-phase dependent reflection signal of an exoplanet contains information on the planet surface, such as the distribution of continents and oceans on terrestrial planets. This light curve is usually studied in the time domain, but because the signal from a stationary surface is (quasi)periodic, analysis of the Fourier series may provide an alternative, complementary approach. We study Fourier spectra from reflected light curves for geometrically simple configurations. Depending on its atmospheric properties, a rotating planet in the habitable zone could have circular polar ice caps. Tidally locked planets, on the other hand, may have symmetric circular oceans facing the star. These cases are interesting because the high-albedo contrast at the sharp edges of the ice-sheets and the glint from the host star in the ocean may produce recognizable light curves with orbital periodicity, which could also be interpreted in the Fourier domain. We derive a simple general expression for the Fourier coefficients of a quasiperiodic light curve in terms of the albedo map of a Lambertian planet surface. Analytic expressions for light curves and their spectra are calculated for idealized situations, and dependence of spectral peaks on the key parameters inclination, obliquity, and cap size is studied.Comment: 15 pages, 2 tables, 13 figure

Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions

We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relations, such as transformations and three-term relations, of these functions by considering geometrical properties of this polytope. The most general functions we describe in this way are sums of two very-well-poised _10φ_9's and their Nassrallah-Rahman type integral representation