Matrix D-Tree Method and Its Application for Symbolic Analysis of Linear Periodically Time-Variable Circuits in Frequency Domain

This paper presents a general theory of the adjoint network of multiphase periodically switched linear (PSL) circuits in frequency domain. The phasor representation of Tellegen's theorem for PSL circuits in the steady-state is introduced and the adjoint networks of elements typically encountered in PSL circuits are developed. It is shown that the transfer functions from multiple input sources to one output of a PSL circuit can be computed efficiently by solving the adjoint network of the circuit only once. More importantly, it is demonstrated that the aliasing transfer functions from the input sources in the side bands to the output in the base band can be obtained efficiently by computing the corresponding high-order frequency components of the response of the adjoint network of the circuit.

Problems of test and measurement dealing with diagnostic procedures of analog circuits in frequency domain using the multitest method are discussed. The method for measurement of real and imaginary parts of complex node potentials is described as well as its implementation based on the FPGA.

Introduction to Circuit Analysis and Design

LINEAR CIRCUIT ANALYSIS. Fundamental Circuit Concepts. Network Laws and Theorems. Terminal and Port Representation. Signal Flow Graphs in Filter Analysis and Synthesis. Analysis in the Frequency Domain. Tableau and Modified Nodal Formulations. Frequency Domain Methods. Symbolic Analysis. Analysis in the Time Domain. State-Variable Techniques. FEEDBACK CIRCUITS. Feedback Amplifier Theory. Feedback Amplifier Configurations. General Feedback Theory. The Network Functions and Feedback. Measurement of Return Difference. Multiple-Loop Feedback Amplifiers. Index.

A symbolic approach to the frequency domain characterization of dc-dc converters is presented. The symbolic analysis is based on a sampled-data technique derived from a state variable approach, exploiting the numerical values of the state variable and output samples obtained by s-domain symbolic network functions of the circuit. A symbolic program developed by the authors is presented. It is shown that the computer symbolic analysis can be easily applied also to the averaged models of DC-DC converters. Possible developments to the frequency domain analysis of the whole DC-DC converter including the control system are also proposed.

Foetal heart rate variability is considered an important parameter, capable to highlight foetal reactivity and wellbeing. Many studies focused their attention on foetal heart rate variability analysis, using different techniques both in time and frequency domain. Proposed parameters have shown some limitations, due to their inability to analyze nonlinear dynamics, involved in heart rate control and relevant for clinical aims. In the last decades, nonlinear analysis methods have gained a growing interest. Here, we described an application of a nonlinear analysis (symbolic dynamic analysis) and introduced a new index to quantify foetal heart rate variability, in a simple and concise way, in healthy foetuses near to term. The index was able to highlight differences in foetal heart rate variability, not always so evident on printed cardiotocographic signals, and resulted significantly correlated with the different kinds of delivery (spontaneous or caesarean); in particular, higher variability index values corresponded to spontaneous delivery.

SummaryKnowing the Network Function (NF) pertaining to a certain input–output couple individuated inside a linear electrical network (LEN) is crucial, as it provides a synthetic and effective description of the input–output relationship and allows one to derive several key features of the subject system as well as to devise proper strategies to modify them.From a mathematical point of view, an NF may be expressed as the product of a real number, called the gain constant (GC), by a real rational function of the complex variables, whose numerator and denominator are called the zero polynomial (ZP) and the characteristic polynomial (CP), respectively, and may be obtained by calculating the determinants of proper matrices. However, when a design‐oriented symbolic hand analysis is needed, calculating the said polynomials in this manner may turn out to be tediously cumbersome; and above all, such a route may fail to illuminate the way that their coefficients depend on the circuit elements. The same may be said of numerical computer methods, which are suited to providing a global description of the NF in the frequency domain rather than analytical expressions of its coefficients. In this paper, a method is proposed that permits one to obtain the ZP without calculating any determinants. With respect to other methods that achieve the same goal, the present one does not require prior calculation of the CP or a nullator‐norator pair (NNP) to be compulsorily inserted in the subject circuit. Instead, it is based on applying the Andreani‐Mattisson extension (AME) of the Cochrun–Grabel algorithm (CGA) for the calculation of the CP to a circuit obtained from the assigned one by inserting in the latter a proper dependent source. The nature of such new circuit allows the worker to employ the classical tools of LEN theory so as to make the analysis as simple as possible and often performable by straightforward inspection, without the need for possibly involved equilibrium equations. Moreover, it is shown how the same technique can be applied to a properly modified version of the original network in order to calculate the CP as well. In this case (not compulsorily but if judged convenient for simplifying the calculations), a NNP may be employed in conjunction with the dependent source. The proposed method once again allows one to exploit the classic tools of LEN theory so as to considerably, if not drastically, simplify the analysis associated with the direct application of the AME to the original network. Finally, the calculation of the GC (that completes the knowledge of the whole NF under study) as well as circuit degeneracy are discussed and practical examples of application of the proposed techniques are given. Copyright © 2013 John Wiley & Sons, Ltd.

Sleep apnea (SA) as abreathing disorder during sleep, has an increasing incidence in recent years. As a non-invasive method, heart rate variability (HRV) analysis can be effectively used in sleep apnea research. The information-based similarity of binary symbol sequence (BS_IBS) is a symbolic dynamics analysis method, which can be employed to perform nonlinear HRV analysis of sleep apnea patients. In the study, 60 electrocardiogram recordings were used for analysis, and multiple indices in time domain, frequency domain, and nonlinearity were calculated at the same. The similarity between adjacent RR segments was evaluated by calculating the BS_IBS value of them. Our research shows that BS_IBS is a useful sleep apnea screening method and can improve the effect of sleep apnea screening with traditional time-frequency domain indices (the accuracy is increased from 81.7% to 86.7%). This study proves that nonlinear information-based similarity assessment can be used in sleep apnea research and further expands the nonlinear HRV analysis method of sleep apnea.

A procedure for the derivation of a black-box model of electromagnetic interference (EMI) filters is proposed and discussed. The modeling approach is assessed by resorting to a real EMI filter. The equivalent circuit of the filter is directly obtained from a rational approximation of the scattering-parameter matrix measured at the filter ports. Therefore, the modeling procedure does not require any information on the internal structure of the filter (e.g., components, electrical/magnetic properties of the involved materials, connections leads, etc.). The circuit model is compatible with SPICE solvers and can be used for the prediction of conducted emissions in both the frequency and time domain. Specifically, the proposed modeling approach allows time-domain simulation and performance analysis of EMI filters in combination with power-electronic equipment (i.e., nonlinear, time-variant circuits).

We build Floquet-driven capacitive circuit networks to realize topological states of matter in the frequency domain. As visible through our Floquet Laplacian formalism, the intertwining of static circuit components and parametric Floquet driving effectively creates a barrier in the frequency dimension, allowing to resolve the bulk-boundary correspondence of Floquet topological matter. By implementing a Su-Schrieffer-Heeger Floquet lattice model and measuring the associated circuit Laplacian and characteristic resonances, we demonstrate Floquet topological edge modes emerging at this frequency space barrier. Floquet circuits allow for the creation of topological phenomena in synthetic frequency dimensions with just a single unit cell of time-variable circuit components.

In this paper, we propose a new time-domain performance bound analysis method for analog circuits considering process variations. The proposed method, called TIDBA, consists of several steps to compute the bound performances in time domain. First the performance bound in frequency domain is computed for a linearized analog circuits by an variational symbolic analysis method and the Kharitonov's functions. Then the time domain performance bound is computed via a new general-signal transient bound analysis method. The new algorithm can give transient lower bound and upper bound of the performance variations affected analog circuits accurately and reliably. Experimental results from two industry benchmark circuits show that TIDBA gives the correct bounds for the Monte Carlo analysis while it delivers one order of magnitude speedup over the Monte Carlo method.

We report the simulation of the large-signal performance of mm-wave FET power amplifiers obtained for the first time through Full Band Monte Carlo particle-based device simulation self-consistently coupled with a Harmonic Balance (HB) frequency domain circuit solver. Due to the iterative nature of the HB algorithm, this FET simulation approach is possible only due to the computational efficiency of our Cellular Monte Carlo (CMC), which uses pre-computed scattering tables. On the other hand, a frequency domain circuit solver such as HB allows the simulation of the steady-state behavior of an external passive reactive network without the need for simulating long transient time (i.e. RC, L/C time constants) typical of time domain solutions. By exploiting this newly developed self-consistent CMC/HB code, we were able to time-efficiently characterize the mm-wave power performance of a state-of-the-art 30-nm gate-length InAlN/GaN HEMT.

In this paper a new numerical technique is proposed for the solution of nonlinear systems of equations. The techniques presented here are based on a Modification algorithm, and it has been employed to improve the numerical efficiency of a harmonic balance-based frequency domain circuit simulator (Spectre). This technique exhibits high computational efficiency and rate of convergence, presenting its best performance in case of strong nonlinearities and high integration level. To validate the convergence properties of this technique, some simulations were performed and the results were compared with those obtained using Newton and Newton-Samanskii methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper proposes a new hierarchical circuit modeling and simulation technique in s-domain for linear analog circuits. The new algorithm can perform circuit complexity reduction by deriving the exact or approximate admittances in rational form in the reduced circuit matrix and deriving the circuit characteristics for very large linear analog and interconnect circuits. We characterize some theoretical results regarding the conditions on the generations of canceling terms during the general hierarchical circuit analysis and propose an explicit de-cancellation scheme to remove canceling terms based on a new hierarchical symbolic analysis framework. The resulting algorithm can be used for modeling and simulation of linear analog and interconnect circuits in both frequency and time domain.

Introduction: Lifetime stressful conditions have been related to a higher risk of coronary heart diseases events. One recognized way is related to the disbalance of a parasympathetic and sympathetic system that can be mediated by several humoral factors, including thyroid hormones. Although the role of thyroid hormones on cardiovascular system regulation on the autonomous nervous system was very well-defined decades ago for normal conditions and there is scarce information concern to the association between subclinical thyroid disorders and the autonomous nervous system. Hypothesis: Subclinical thyroid dysfunctions are associated with autonomic disturbances assessed by the heart rate variability evaluated by linear and nonlinear variables following postural changes. Methods: At baseline of the ELSA-Brasil study (15105 adults aged 35-74 years old), we evaluated the heart variability rate at the supine position for everyone, and sampled 855 participants to repeat a standing measure of the heart rate variability. Subclinical hypothyroidism was defined as thyroid-stimulating hormone &gt;4 IU/ml for people with normal free-thyroxine levels. The cardiac autonomic nervous function was evaluated by linear time and frequency domain analyses (standard deviation of consecutive RRi - SDNN; root mean square of successive differences between adjacent regular R-R intervals - RMSSD; low frequency - LF; high frequency - HF; LF/HF ratio) as well as by nonlinear symbolic dynamics (patterns with no variation - “0V”; patterns with one variation - “1V”; patterns with two variations - 2V). Results: After exclusions, 666 (93.8%) euthyroid and 44 (6.2%) participants with subclinical hypothyroidism were eligible for analyses. At the baseline, supine rest measurement, the “0V” symbolic pattern, which reflects sympathetic modulation, was higher (31.8 vs. 24.2; P= .01) and “2V”, representing parasympathetic activity, was lower than in the euthyroid group (18.0 vs. 25.3; P= .02). Comparing the variation between positions, the “0V” pattern showed a lower delta in subclinical hypothyroidism than in euthyroid subjects (6.8 vs. 14.2%; P= .04). Additionally, it is suggested that a symbolic analysis of heart rate dynamics is an alternative and, possibly, a more sensitive method for cardiac autonomic assessment following standing position in this population. Conclusion: Subclinical hypothyroidism presented lower sympathetic and parasympathetic tonus at rest and a blunted sympathetic response to active postural change, marked by reduced variation in the “0V” of symbolic analysis.