Multiphase Oscillator Using Traveling Pulses Developed in a System of Transmission Lines with Regularly Spaced Resonant-tunneling Diodes

SummaryIn a system of transmission lines with regularly spaced resonant‐tunneling diodes (RTDs), where several straight RTD lines are connected halfway to a closed RTD line, a pulse‐shaped rotary traveling wave develops on the closed line by mutual synchronization of the oscillatory edge developed in each straight RTD line. The oscillating edge on each straight line is synchronized with the traveling pulse, such that the system has the potential to generate multiphase oscillatory signals in millimeter‐wave frequencies. To examine the dynamics of traveling pulses at such high frequencies, the system is modeled in the framework of the finite‐difference time‐domain method. It is found that a traveling pulse develops in the closed RTD line synchronized with the oscillatory edges moving in the straight lines, assuming a microstrip structure for each RTD line. We then compare the results of the finite‐difference time‐domain calculation with those predicted by the transmission line theory with parameter values obtained by the quasi‐transverse electromagnetic estimation. In addition, the RTD line that compactly confines the electromagnetic fields is shown to have the potential to generate multiphase oscillatory signals at submillimeter‐wave frequencies.

A scheme is proposed for generating low-phase-noise oscillatory signals in sub-millimeter-wave frequencies, which utilizes the dynamics of a traveling pulse rotating in a closed system of oscillators, which consists of transmission lines periodically loaded with resonant-tunneling diodes (RTDs) that is coupled with evenly spaced straight RTD lines. The spatial extendedness of the oscillator component results in an effective method of self-injection locking, by which the phase noise is reduced significantly. Herein, the principle of operation is described with its numerical/experimental validation, together with the potential to generate harmonic signals. To detect pulse dynamics definitely, the experiment was carried out in MHz frequencies utilizing tunnel diodes in place of RTDs.

Injection‐locking properties of a rotary travelling pulse developed in a system of tunnel‐diode (TD) transmission lines are characterised for multiphase oscillation. The system includes a unique TD line loop coupled with evenly spaced straight TD lines. The oscillating voltage edges in straight lines are synchronised to organise the rotary pulse on the closed one. Based on the phase‐reduction theory, the authors determine where to connect an external oscillator for sufficient locking frequency range. Inherently, the travelling pulse can rotate on the loop in either clockwise or anti‐clockwise fashion. The rotation frequency slightly depends on the rotation direction by the finite fluctuation of device parameter values. By matching the frequency of the external oscillator with one of such frequencies, the rotation direction is specified as required. These injection‐locking properties are validated experimentally.

Synthetic and analytical methods are usually used to investigate multidimensional spaces and sets of subspaces. Shortcomings of a synthetic method — the appeal to spatial imagination and the researcher´s intuition, impossibility of formalization, need of creation of big and complex logical constructions don´t allow to go beyond four-dimensional space, with rare exceptions. The theory of enumerative geometry submitted as geometry of conditions with a basic element – a multidimensional flags incidence condition allows solve many problems which up to now were considered as insoluble ones. The simplest of such problems is a classical problem for calculation of final number of given space’s subspaces meeting the set of given conditions (the normal problem of algebraic geometry). A more serious problem – calculation a number and values of algebraic characteristics for given variety in given space. For this problem solution it was necessary to develop a formalized method, as well as technique algorithmization. This problem has been solved by professor. V.Ya. Volkov in his doctoral dissertation by means of developed by him so-called e-calculations. For an understanding of e-calculation fundamentals or calculation of Schubert conditions a rather good mathematical background and method promotion are necessary. The last demands consideration of various approaches to conditions calculation problem. In the present paper are considered the simplest cases of a tabular method for conditions calculation, in relation to conditions of incidence which is understood in a general sense. Calculation of one-, two- and ((k + 1) (n – k) – 1)-dimensional conditions are considered. Conditions calculation formalization and incidence conditions reduction are explained. The problem about a final number of straight lines crossing the set number of k-planes in n-dimensional space is considered as an example. In particular, the problem about a number of straight lines crossing some number of the set straight lines can be correct only in three- and four-dimensional spaces. Conditions of the minimum multiplicity equal to three exist only in (3k + 1)-dimensional spaces. Conditions of the multiplicity equal to four exist only in odd dimensionality spaces. And so on. The concrete number of straight lines in all cases can be counted by reduction of the corresponding conditions.

A plane surface enclosed or bounded by straight lines or a curved line is called a plane figure. The least number of straight lines which can enclose a space is three. When three straight lines intersect, the plane surface enclosed is a triangle. With four straight lines, the figure obtained is a quadrilateral. The most common plane figures are set squares (30°–60° and 45°). Other common plane figures include square, rectangle, pentagon, hexagon, octagon, circle, ellipse, etc.

This paper proposes a traveling wave amplifier based on composite right/left handed (CRLH) transmission lines (TLs) periodically loaded with resonant tunneling diode (RTD) pairs. This TL can be regarded as a “lossy” TL with a negative loss because of the negative differential resistance of the RTD. This means that the TL can amplify signals while the signal travels along the line. One of the most important points to be investigated to realize this amplifier is the stability of the circuit. We discuss stability of the TLs periodically loaded with RTDs, and show that they can be stabilized by using CRLH TL configuration. It is demonstrated that this amplifier can have a gain for wide frequency range.

Summary form only given. Excitability is a well-established nonlinear dynamical concept in biological (neurons), and chemical (Belousov-Zhabotinsky reaction) systems [1]. The all-or-none response of an excitable system is a key effect of information processing in excitable oscillators. Excitability has been reported in lasers with promising applications in photonics such as clock recovery and pulse reshaping [2]. However, slow speed operation and bulky schemes make most of them too complex and slow for current and future information processing needs.In this work, we present a novel, compact, and simple excitable optoelectronic oscillator consisting of a AlAs/InGaAs double barrier quantum well (DBQW) resonant tunneling diode (RTD) driving a 1550 nm communications laser diode (LD) [3], Figs. 1(a) and (b). RTD-LD excitable optoelectronic systems exhibit a current-voltage (I-V) curve with a pronounced negative differential resistance (NDR), Fig. 1(c), and can operate at greater than GHz speeds [3] (RTDs can work up to THz). Here we present noise activated induced excitable and pulsed dynamics in both electrical and optical domains using RTD-LDs operating at room temperature. The RTD-LD is first DC biased, VDC, slightly below the peak, Fig. 1(c), i.e., in a non-oscillating equilibrium situation. For purposes of demonstration and experimental convenience, the driving signal consists of a stochastic voltage signal generated by a Gaussian white noise source, Vnoise, with a cut-off frequency of 80 MHz. The driving signal can be also injected optically, taking advantage of the optical input port of the RTD ridge waveguide [3], Fig. 1(a). The RTD-LD can emit excitable pulses in both electrical and optical outputs when the amplitude of the stochastic perturbation exceeds a given threshold, as presented in Fig. 1(d), showing upward and downward electrical pulses due to noise-induced RTD-LD switching from the peak-to-valley regions. The LD intensity output follows the switching current modulation induced by the RTD with a sequence of downward pulses of decreasing intensity with a FWHM around 200 ns. The FWHM of the pulses can go below 1 ns if an appropriate RTD-LD refractory time is chosen, determined by the circuit's resonant tank. For a given range of noise input the pulsed behavior is more regular, Fig. 2(a), with a time repetition determined by the RTD-LD refractory time. Interestingly, Fig. 2(b) shows multi-pulsing “bursting” behavior as a result of the asymmetric IV curve when the RTD-LD is DC biased closed to the valley region, which can be explored in novel applications such as signal pattern generation. We also present the numerical simulations of a system of differential equations comprising a nonlinear Liénard's oscillator that models the electrical circuit [3], stochastically driven by means of white Gaussian noise, Dξ(t) (D is the noise dimensionless amplitude, and ξ(t) the Gaussian function), and LD single mode laser rate equations [3]. As seen in Figs. 2(c) and (d), the Liénard oscillator-laser diode model subjected to stochastic fluctuations is in a very good agreement with the experimental results.We have shown excitability in a simple and compact RTD-LD optoelectronic circuit configuration. Since RTDs and LDs can be monolithic integrated, and the I-V N-shape of the optoelectronic system extends over a wide bandwidth, this approach can provide compact designs at GHz high-speed with improved performance for emerging applications in neural emulation, signal processing, and switching in optical networks.

In the article Llibre and Vulpe (Rocky Mt J Math 38:1301–1373, 2006) the family of cubic polynomial differential systems possessing invariant straight lines of total multiplicity 9 was considered and 23 such classes of systems were detected. We recall that 9 invariant straight lines taking into account their multiplicities is the maximum number of straight lines that a cubic polynomial differential systems can have if this number is finite. Here we complete the classification given in Llibre and Vulpe (Rocky Mt J Math 38:1301–1373, 2006) by adding a new class of such cubic systems and for each one of these 24 such classes we perform the corresponding first integral as well as its phase portrait. Moreover we present necessary and sufficient affine invariant conditions for the realization of each one of the detected classes of cubic systems with maximum number of invariant straight lines when this number is finite.

Resonant tunneling diodes (RTDs) have been successfully used for high speed trigger sources and millimeter wave oscillators. Here, two new circuits combining RTDs and transmission lines (TL) are proposed for square wave clock generation in multigigahertz high speed digital circuits and for sampling analog signals at multigigahertz clock frequency data rates as is required in analog-to-digital converters. Both circuits require picosecond slew rates. The designs presented here are free of transistors and are limited in performance only by the switching speed of the RTD and the bandwidth of the transmission line. SPICE simulations incorporating a physics-based RTD model demonstrate the potential of these circuits for track-and-hold applications.

Active transmission lines loaded with resonant tunneling diode (RTD) pairs were investigated as possible THz amplifiers. The RTD pair consists of two RTDs connected serially and is biased by voltages of the same absolute value with opposite signs. The RTD pair has unique current–voltage characteristics at the intermediate node; the true negative resistance appears in the low-voltage region. The linearity of this region is good owing to the symmetry of the circuit. Moreover, the RTD pair circuit can be stabilized more easily than that of a single RTD. On the basis of these advantages, the RTD pair transmission lines are a promising candidate for THz amplifiers. RF signal amplification was demonstrated by circuit simulation. The cutoff frequency was also demonstrated to increase with decreasing unit cell size, and it exceeds 1 THz with RTDs of 1 µm2 emitter area.

The aim of this paper is to present an experimental assessment of two models that use “control lines” for the indirect orientation of pushbroom imagery. Since pushbroom image acquisition is not instantaneous, six exterior orientation parameters (EOPs) must be estimated for each scanned line. The sensor position and attitude parameters are modelled with a time‐dependent polynomial. The relationship between a straight line in the image space and its homologous form in the object space is established in the first model, based on the principle that the position vector containing an image point (projection ray) and the vector normal to the projection plane in the object space are orthogonal. The second model is based on the equivalence between the vector normal to the projection plane in the image space and the vector normal to the rotated projection plane in the object space. The equivalence property between planes was adapted to consider the pushbroom geometry. A model based on collinearity equations using points adapted to the pushbroom geometry was also implemented, aiming at a comparison of the methodologies. Six experiments using different sets of observations for indirect estimation of EOPs of images from the China–Brazil Earth Resources Satellite (CBERS) were carried out, by varying the geometric distribution and the number of straight lines. Also, experiments combining points and straight lines were accomplished. The results showed that an accuracy of around twice the ground sample distance (GSD) in the check points can be achieved with the models studied, which can then be used to estimate the EOPs of pushbroom images. Several other factors affecting the accuracy, such as the distribution and number of control features, were also assessed.

In the artificial world, whether it is the city's traffic roads or engineering buildings contain a lot of linear features. Therefore, the research on the image complexity of linear information has become an important research direction in digital image processing field. This paper, by detecting the straight line information in the image and using the straight line as the parameter index, establishing the quantitative and accurate mathematics relationship. In this paper, we use LSD line detection algorithm which has good straight-line detection effect to detect the straight line, and divide the detected line by the expert consultation strategy. Then we use the neural network to carry on the weight training and get the weight coefficient of the index. The image complexity is calculated by the complexity calculation model. The experimental results show that the proposed method is effective. The number of straight lines in the image, the degree of dispersion, uniformity and so on will affect the complexity of the image.

Discussed in this paper is a two-dimensional autocorrelation function as a means of treating tow-dimensional signals. Autocorrelation functions of various patterns are measured and their interesting properties are pointed out. One of them is the following: when a pattern has straight lines in it and none of them are parallel with each other, the same number of straight lines as the original ones appear in the correlation plane parallel to the original straight lines and passing through the origin of the plane. By using this property, it is possible to detect the presence of straight lines and their relative orientation in the pattern by means of a photoelectric device. An analogue correlation method is also proposed to classify these detected signals.

Anthropology at the Ends of the Lines

Double-barrier GaAs/AlAs resonant tunneling diodes (RTDs) have become the promising elements for the development of sub-mm and THz emitters. We report on the fabrication of the RTD samples that were characterized via RF-reflectometry to determine the parameters of its equivalent circuit. By using numerical simulation we show that the coplanar transmission line with the RTD under study provides an amplification up to 8 GHz. Keywords: Resonant tunneling diodes, active microstrip transmission lines, distributed emitters, diodes with double metal contacts.