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This e-book presents, details and exemplifies famous symbolic analysis techniques. Industrial R&D topics, recent developments and future trends in the field of symbolic analysis are also highlighted. This makes the e-book a good resource for circuit analysis. Thus, it is intended for students and researchers as well as for industry designers.

This e-book provides several state-of-the-art analog circuit design techniques. It presents both empirical and theoretical materials for system-on-a-chip (SOC) circuit design. Fundamental communication concepts are used to explain a variety of topics including data conversion (ADC, DAC, S-? oversampling data converters), clock data recovery, phase-locked loops for system timing synthesis, supply voltage regulation, power amplifier design, and mixer design. This is an excellent reference book for both circuit designers and researchers who are interested in the field of design of analog communication circuits for SOC applications.

The model presented by Gabriel Kron in 1945 is an example of an analog computer simulating quantum phenomena on a hardware level. It uses passive RLC elements to construct a hardware solver for the problem of quantum particles confined by rectangular or other classes of potential. The analytical and numerical validation of Kron’s second model is conducted for different shapes of particle-confining potentials in the one-dimensional case using an LTspice simulator. Thus, there remains potential for obtaining solutions in two- and three-dimensional cases. Here, a circuit model representing a linearized Ginzburg–Landau equation is given. Kron’s second model is generalized by the introduction of linear and non-linear resistive elements. This transforms the deformed Schrödinger equation into a linear dissipative Schrödinger equation and its non-linear form. The quantum mechanical roton problem is the main result of this work and is formulated by means of classical physical states naturally present in the LC classical circular electrical transmission line. The experimental verification of Kron’s model is confirmed.

Metastructures hold the potential to bring a new twist to the field of spatial-domain optical analog computing: migrating from free-space and bulky systems into conceptually wavelength-sized elements. We introduce a metamaterial platform capable of solving integral equations using monochromatic electromagnetic fields. For an arbitrary wave as the input function to an equation associated with a prescribed integral operator, the solution of such an equation is generated as a complex-valued output electromagnetic field. Our approach is experimentally demonstrated at microwave frequencies through solving a generic integral equation and using a set of waveguides as the input and output to the designed metastructures. By exploiting subwavelength-scale light-matter interactions in a metamaterial platform, our wave-based, material-based analog computer may provide a route to achieve chip-scale, fast, and integrable computing elements.

The extension of many-body quantum dynamics to the nonunitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time, on one hand, and unitarity and nonunitarity, on the other, can be used to realize steady-state phases of nonunitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size—from logarithmic to extensive to fractal. We show how these outcomes in nonunitary circuits (that are “spacetime dual” to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets “radiated away” from one edge of the system. In spacetime duals of chaotic unitary circuits, this mapping allows us to analytically derive a nonthermal volume-law entangled phase with a universal logarithmic correction to the entropy, previously observed in unitary-measurement dynamics. Notably, we also find robust steady-state phases with fractal entanglement scaling,S(ℓ)∼ℓαwith tunable0<α<1for subsystems of sizeℓin one dimension. We present an experimental protocol for preparing these novel steady states with only a vanishing density of postselected measurements via a type of “teleportation” between spacelike and timelike slices of quantum circuits.

Dissipative Kerr soliton (DKS) frequency combs—also known as microcombs—have arguably created a new field in cavity nonlinear photonics, with a strong cross-fertilization between theoretical, experimental, and technological research. Spatiotemporal mode-locking (STML) not only adds new degrees of freedom to ultrafast laser technology, but also provides new insights for implementing analogue computers and heuristic optimizers with photonics. Here, we combine the principles of DKS and STML to demonstrate the STML DKS by developing an unexplored ultrahigh-quality-factor Fabry–Pérot (FP) mesoresonator based on graded index multimode fiber (GRIN-MMF). Complementing the two-step pumping scheme with a cavity stress tuning method, we can selectively excite either the eigenmode DKS or the STML DKS. Furthermore, we demonstrate an ultralow noise microcomb that enhances the photonic flywheel performance in both the fundamental comb linewidth and DKS timing jitter. The demonstrated fundamental comb linewidth of 400 mHz and DKS timing jitter of 500 attosecond (averaging times up to 25 μs) represent improvements of 25× and 2.5×, respectively, from the state-of-the-art. Our results show the potential of GRIN-MMF FP mesoresonators as an ideal testbed for high-dimensional nonlinear cavity dynamics and photonic flywheel with ultrahigh coherence and ultralow timing jitter. Here the authors demonstrate spatiotemporal mode-locked dissipative Kerr soliton and enhanced photonic flywheel performances in both the fundamental comb linewidth and DKS timing jitter.

In high-speed digital signal transmission, VPX connectors play a crucial role as an important link for blind plug interconnection, ensuring the quality of high signal transmission. For high-speed circuit signal transmission, in order to ensure the absolute equal length of high-speed signals and avoid crosstalk caused by high-speed signals, this paper proposes a testing method that establishes a high-speed signal transmission link by designing equal-length sector modules and backplane blind plug interconnection through VPX; By using a vector network analyzer to test relevant parameters, we will analyze the differential characteristic impedance of VPX connectors after engagement under different structural tolerances, and obtain the quality of high-speed signal transmission. This testing research method can effectively analyze the main influencing factors of high-speed signal transmission in VPX connectors, and the research results provide effective support for engineering applications.

Synthetic analog gene circuits can be engineered to execute logarithmically linear sensing, addition, ratiometric and power-law computations in living cells using just three transcription factors. Living-cell computation simplified The design of novel genetic control systems for synthetic biology is dominated by digital logic. This is necessarily a complex arrangement. Now Timothy Lu and colleagues have harnessed analog building-blocks found in natural cells to perform arithmetic operations in the logarithmic domain. Such analog circuits — which could be integrated with digital — should make it possible to use fewer components to implement complex computations that require wide dynamic range in biosensing. A central goal of synthetic biology is to achieve multi-signal integration and processing in living cells for diagnostic, therapeutic and biotechnology applications 1 . Digital logic has been used to build small-scale circuits, but other frameworks may be needed for efficient computation in the resource-limited environments of cells 2 , 3 . Here we demonstrate that synthetic analog gene circuits can be engineered to execute sophisticated computational functions in living cells using just three transcription factors. Such synthetic analog gene circuits exploit feedback to implement logarithmically linear sensing, addition, ratiometric and power-law computations. The circuits exhibit Weber’s law behaviour as in natural biological systems 4 , operate over a wide dynamic range of up to four orders of magnitude and can be designed to have tunable transfer functions. Our circuits can be composed to implement higher-order functions that are well described by both intricate biochemical models and simple mathematical functions. By exploiting analog building-block functions that are already naturally present in cells 3 , 5 , this approach efficiently implements arithmetic operations and complex functions in the logarithmic domain. Such circuits may lead to new applications for synthetic biology and biotechnology that require complex computations with limited parts, need wide-dynamic-range biosensing or would benefit from the fine control of gene expression.

Digital differential analyzer(DDA) can be used to generate circles and can be treated as a one-step or two-step numerical scheme. DDA algorithms have been classified by the order of some polynomials. We present and discuss a novel fifth-order DDA circle generating algorithms based on the one-step numerical scheme. Numerical experiments show that they are more accurate than the third-order one-step DDA algorithm.

Chaotic analog circuits are commonly used to demonstrate the physical existence of chaotic systems and investigate the variety of possible applications. A notable disparity between the analog circuit and the computer model of a chaotic system is usually observed, caused by circuit element imperfectness and numerical errors in discrete simulation. In order to show that the major component of observable error originates from the circuit and to obtain its accurate white-box model, we propose a novel technique for reconstructing ordinary differential equations (ODEs) describing the circuit from data. To perform this task, a special system reconstruction algorithm based on iteratively reweighted least squares and a special synchronization-based technique for comparing model accuracy are developed. We investigate an example of a well-studied Rössler chaotic system. We implement the circuit using two types of operational amplifiers. Then, we reconstruct their ODEs from the recorded data. Finally, we compare original ODEs, SPICE models, and reconstructed equations showing that the reconstructed ODEs have approximately 100 times lower mean synchronization error than the original equations. The proposed identification technique can be applied to an arbitrary nonlinear circuit in order to obtain its accurate empirical model.