Signal Flow Graph Research Articles

Utilizing signal flow graph on multiple feedback amplifiers of NMC and DACFC with emphasis on design space exploration and conversion

SummaryOver a long time, different methods of frequency compensation of multistage amplifiers have been exploited for improvement in the behavior of stabilizing. In the present paper, the step‐by‐step conversion process of the dual active capacitive feedback compensation (DACFC) three‐stage amplifier into the nested Miller compensation (NMC) three‐stage amplifier is presented by a systematic approach and signal flow graphs (SFGs) based on the graph theory rules in graph domain. Also, according to graph rules, the conversion of the multiple feedback amplifier NMC into the multiple feedback amplifier DACFC is investigated in detail in the graph domain. During the conversion process, the difference in the gain‐bandwidth product (GBW) in the two mentioned case study's amplifiers is examined in terms of the graph at the system level. The elimination of two branches in one step of the conversion process of the SFG of the NMC into the SFG of the DACFC leads to a significant improvement in the behavior of GBW. This paper also conducts verification of the design of conventional NMC and DACFC amplifier circuits in HSPICE using 0.35‐μm CMOS technology and compares the circuit simulation results to SFG simulation results. In order to show the correctness of the idea, they are redesigned in HSPICE using 0.18‐μm CMOS technology, and appropriate results are obtained.

Hardware Implementation of FIR Filter for ECG Signal Processing: Design, Optimization, and Performance Analysis on an FPGA

Electrocardiogram (ECG) signals are commonly used to diagnose heart-related diseases. However, noise induced during the measurement process can affect the accuracy of the diagnosis. Digital filters, such as the Finite Impulse Response (FIR) filter, are widely used to filter out noise from the ECG signal. Nevertheless, the processing speed of software-based FIR filters is slow for large ECG datasets due to serial processing. This paper presents a hardware implementation of the FIR filter for ECG signal processing to overcome the processing speed issue. The filter is designed using the Kaiser Window method and implemented on the Intel Cyclone IV Field Programmable Gate Array (FPGA). The filter is first designed in MATLAB to obtain the filter coefficients where the ECG data were obtained from Physionet database. From the difference equation, we designed the signal flow graph (SDFG) and then mapped into hardware logics to enable parallel processing. Simulation results of the software (MATLAB) and hardware (FPGA) implementations are obtained and compared. The results show that the FPGA-based FIR filter can process the ECG signal up to 1,250 times faster than software implementations. To further optimize the design and reduce hardware cost, we introduce optimized designs by applying the operation scheduling and constrained resource allocation techniques. The maximum operating frequency, logic utilization, and power consumption of each design were analysed and compared. This study demonstrates that custom-designed hardware logic for digital signal processing can significantly outperform software implementations due to its parallel processing capabilities. The proposed optimization techniques reduce the hardware cost while maintaining high processing speed and accuracy. The hardware implementation of the FIR filter for ECG signal processing has numerous applications in diagnosing heart-related diseases and real-time monitoring of ECG signals in critical care settings.

Wideband 4×4 Nolen Matrix with 360° Continuously Tuned Differential Phase and Low In-Band Phase Deviation Error

In the paper, a wideband tunable 4×4 Nolen matrix is proposed. By using the presented topology of the Nolen matrix, tunable output port phase differences can be realized by inserting one type of tunable phase shifters (T-PS). Besides, the in-band phase deviation error is minimized by adding compensation phase shifters (C-PSs) to the output ports of the Nolen matrix. Analytical design methods based on signal flow graphs and complex exponential signal are given to obtain the rigorous relationships of the coupling and phase shifts in the Nolen matrix. Besides, a detailed method for output ports phase slope compensation is provided. For validation, a prototype centered at 5.8 GHz is designed and fabricated. Measurement results agree well with the simulated ones. By using only one voltage to control the phase shifts of the T-PS in a 90° range for each input excitation of the Nolen matrix, a full 360° range of the progressive phase difference is realized by switching four input ports. The measured fractional bandwidth under 10 dB return loss and isolation is larger than 24.5% with the in−band±1.5 dB amplitude imbalance and ±15° phase deviation error for ports 1-4 excitations. Besides, for a more strict criterion of ±1 dB amplitude imbalance and 10° phase deviation error, the measured bandwidths are larger than 15% for all port excitations.

Design and Analysis of a New Three-Stage Feedback Amplifier Utilizing Signal Flow Graph Domain Inspection Approach

Design and Analysis of a New Three-Stage Feedback Amplifier Utilizing Signal Flow Graph Domain Inspection Approach

Signal-Flow-Graph Analysis of Weakly Nonlinear Microwave Circuits Around a Large-Signal Operating Point

A signal flow graph (SFG) representation of small-signal responses of nonlinear microwave circuits around a large-signal operating point is developed using the X-parameters. It is shown that, unlike the SFGs for linear circuits, negative-frequency nodes need to be included explicitly. The development elucidates the circuit-operational meaning of the elusive T-type small-signal X-parameters, which represent the interaction between positive-and negative-frequency components. As an example, such an SFG is used to derive a closed-form expression of the output power of an amplifier as a function of the load reflection coefficient. It is then used to plot approximate load-pull power contours. The result is consistent with the expressions of the optimum load reflection coefficient derived by Root et al. (EuMIC 2017) and power contours derived by Peláez-Pérez et al. (TMTT 2013). SFGs provide an alternative systematic means to derive closed-form expressions in terms of X-parameters and gain illuminating insights into the workings of weakly nonlinear circuits.

Stability Analysis of Phase Locked Loops for AC Microgrids With Hybrid Power Sources

Synchronous instability of the multiple distributed generations has been an important issue for microgrids. Therein, the phase locked loop (PLL) instability is one of the significant reason for synchronous instability of multi-inverter microgrids. Although this instability issue has been widely studied, it is ignored for microgrids with numerous inverters controlled through different controllers. To full this gap, this paper proposes a multi-inverter parallel microgrid stability analysis method based on PLL. Firstly, this paper establishes a PLL small signal model based on the droop control strategy and the P&Q control strategy. Furthermore, the whole PLL small signal analysis model of multi-inverter parallel microgrid is proposed by signal flow graph and Mason Gain Theorem, which is more convenient for power engineers. Eventually, the closed-loop transfer function of PLL is obtained. The proposed integrated small signal model can predict the synchronous stability regarding the PLL of the multi-inverter under grid-connected mode and the island mode. Finally, the simulation and experimental results can well validate the feasibility and effectiveness of the proposed stability analysis strategy based on PLL in the multi-inverter parallel microgrid. Therein, the simulation and experimental results illustrate that the proposed stability identification approach can provide an effective stability control parameter selection method.

Control and Synchronization of a Novel Realizable Nonlinear Chaotic System

The study proposes a novel chaotic system with a cubic non-linear term. Different system characteristics are investigated including equilibria, stability, invariance, dissipation, Lyapunov dimension, and Lyapunov exponents. Also, the electronic circuit and Signal flow graph of the system are carried out to show the applicability of the chaotic system. Lyapunov stability theorem converts the system’s chaotic behavior to unstable trivial fixed point. The study also focuses on demonstrating complete synchronization between two similar novel chaotic systems. According to Lyapunov stability theorem, simple application in secure communication was developed by employing the chaos synchronization results. Numerical simulations for the systems are performed for establishing the synchronization strategy effectiveness and proposed control.

Graphical evaluation of evidence structure within a component network meta-analysis.

Component network meta-analysis (CNMA) compares treatments comprising multiple components and estimates the effects of individual components. For network meta-analysis, a standard network plot with nodes for treatments and edges for direct comparisons between treatments is drawn to visualize the evidence structure and the connections between treatments. However, the standard network plot does not effectively illustrate the connections between components for a CNMA. For example, the comparison between linear combinations of components within a trial is not shown directly in a standard network plot, and whether all components are identifiable cannot be deduced directly from the plot. Therefore, we need a new approach to visualizing the evidence structure of a CNMA. In this article, we proposed a new graph, a modified signal-flow graph representing a system of equations, to evaluate the evidence structure for CNMA. In our new graph, each node represents a component, and arrows are used to show linear relationships between components. We used two examples to demonstrate how to draw and interpret the graph and how to use it to identify components that require more evidence.

Stability, existence, and uniqueness for solving fractional glioblastoma multiforme using a Caputo–Fabrizio derivative

In this study, fractional order is applied to the glioblastoma multiforme (GBM) and IS interaction models. The monoclonal brain tumor GBM gives rise to other tumors with varying growth rates and treatment susceptibilities once it reaches a certain density. The two populations of macrophages and activated macrophages make up the IS cells as well. Because of this, this model depicts two conversions: the transformation of a sensitive tumor cell into a resistant tumor cell and the transformation of passive macrophages into active macrophages, as well as an interaction among the tumor cell and the macrophages. The memory and nonlocalization properties of fractional derivatives make them an excellent tool for simulating the spread of epidemics. Numerous characteristics exist in the Caputo–Fabrizio fractional derivative kernel, including nonsingularity, nonlocality, and an exponential establish. For simulating disease spreading systems, it is preferred. We suggest defining the Caputo–Fabrizio fractional derivation procedure as the paradigm for the GBM disease in this work. The hypothesized fractional‐order GBM disease paradigm's stability is investigated. The hypothesized fractional‐order GBM disease paradigm's existence and originality are established. A suggested novel signal flow graph introduces the system. We have established the existence of GBM and its uniqueness. Additionally, the numerical integrations necessary for the fractional‐order glioma immune model are carried out using the predictor–corrector Adams–Bashforth–Moulton (ABM) approach for fractional‐order differential equations. These simulations demonstrate that the behavior of the model can be affected by changing the parameters for the fractional order, contact evaluation, or quarantine evaluation. The findings demonstrate how epidemiologically sound the proposed fractional model is.

Design of State-Space Controllers with the Help of Signal Flow Graphs Shown for a Buck Converter

When consulting the text books on control engineering, state space controllers are described and designed with the help of matrix calculus. This implies good knowledge of linear algebra. Especially in Europe many Universities of Applied Sciences have extremely reduced mathematics in their curricula. Here a teaching concept with the help of signal flow graphs can help to explain and design the controller without solving matrix equations. As example, the bidirectional Buck converter is used. The model of the plant is derived and a simple state space controller is designed. The plant model is linearized around a working point. Therefore, the simple state space controller leads to correct results only at this point. Combination with an additional controller or using the error between the desired value and the actual value as a third state variable improves the quality of the control. The signal flow graphs for these concepts are given and the controllers designed. With the help of LTSpice the designs are checked.

A Signal Flow Graph Approach to the Resolution of Spherical Triangles Using CORDIC

Jack Volder’s original motivation for the COordinate DIgital Computer (CORDIC) was the real-time digital solution of spherical triangle equations employed in airborne navigation, for which he presented a solution flow diagram without detailing its construction. In fact, without a strong guidance, it is not easy to express the solutions of linear algebraic problems such as those involved when solving spherical triangles as cascades of CORDIC operations—called by Volder CORDIC solution-flow diagrams—and thus to devise a system solution on CORDIC processing units. As it gives a bird’s eye view of the system design problem, a signal flow graph representation of the underlying system of linear equations provides such guidance; the operations leading to the problem solution are uncovered by performing a sequence of partial flow reversals on the graph. The approach is illustrated by the problem where two sides and the included angle of a spherical triangle are given, called SAS problem, that is encountered in applications as diverse as air navigation, lattice filters for adaptive processing, and dexterous robotic hands. The solutions thus obtained are at least as efficient as existing ones, whenever available.

Enhancing Attainment of Learning Outcomes Through Active Learning

This paper presents an experimental study conducted on employing Active Learning strategies towards enhancing the attainment of learning outcomes of a course "Linear Control Systems" in the undergraduate (UG) Electrical and Electronics Engineering (EEE) programme. The existing UG programme curriculum is retrofitted into outcome-based curriculum. The Programme Outcomes (POs) for this programme are derived from the Graduate Attributes of Washington Accord (WA). In order to meet the POs, Course Learning Outcomes (CLOs) are written predominantly in the Cognitive (Revised Bloom's taxonomy) and Psychomotor (Dave's taxonomy) domains for lecture-based courses and laboratory courses, respectively and very few are written in Affective (Bloom's taxonomy) domain. In this paper, four CLOs (i) Discuss the various classification of control systems (K2), (ii) Define the time and frequency response of the system (K2), (iii) Derive the overall transfer function of the given Block diagram of a system (K3) and (iv) Derive the overall transfer function of a Signal Flow Graph (SFG) of a system (K3) are considered to measure the effectiveness of active learning methods in attaining the outcome. Active learning methods such as Jigsaw, Think-pair-share and Peer instruction, and traditional lecture-based methods were employed. In addition, ClassComm software with student interactive devices was used to measure the students' learning in the classroom and subsequently the attainment of CLOs. This study compares the effectiveness of active learning methods with the traditional lecture-based instruction method in relation to the attainment of CLOs. The overall analysis results reveal that both instructors and students received the active learning methods very well, and they are very effective in enhancing the attainment of learning outcomes. However, instructors are of the view that the duration of the contact period should be at least two hours. Keywords— active learning, Bloom's taxonomy, concept map, control systems, learning outcomes

Instruction mapping techniques for processors with very long instruction word architectures

Abstract This paper presents an instruction mapping technique for generating a low-level assembly code for digital signal processing algorithms. This technique helps developers to implement retargetable kernel functions with the performance benefits of the low-level assembly languages. The approach is aimed at exceptionally long instruction word (VLIW) architectures, which benefits the most from the proposed method. Mapped algorithms are described by the signal-flow graphs, which are used to find possible parallel operations. The algorithm is converted into low-level code and mapped to the target architecture. This process also introduces the optimization of instruction mapping priority, which leads to the more effective code. The technique was verified on selected kernels, compared to the common programming methods, and proved that it is suitable for VLIW architectures and for portability to other systems.

Parasitic Oscillation Analysis of Trench IGBT During Short-Circuit Type II Using TCAD-Based Signal Flow Graph Model

The oscillation phenomenon of trench-type insulated gate bipolar transistors during short-circuit (SC) type II was investigated experimentally and theoretically. The gate resistance required to suppress oscillations decreased with an increasing collector voltage. The oscillation conditions were calculated from the signal flow graph model using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${S}$ </tex-math></inline-formula> -parameter based on a technology computer-aided design simulation. The calculation results reproduced the locus of the collector voltage dependence of the experimentally measured gate resistance. The oscillation mechanism was investigated using the device simulation. The response of carrier density modulation at the base-drift layer boundary was found to transmit to the collector side through the electron–hole plasma region during the oscillation, indicating that the transfer characteristics of the carrier density modulation in the drift region at the specific collector voltage influence the collector voltage dependence of the SC oscillation. The influence of circuit parameters on the oscillation was also investigated. An increase in the emitter inductance suppressed the oscillations, whereas an increase in gate inductance increases oscillations.

Software Defined Radio-Based Wireless Sensing System.

In this paper, we investigate the application of using software-defined radio (SDR) and surface acoustic wave (SAW) device for wireless measurement of the response of in situ sensors. SDR uses software to realize different communication functions. After collecting the magnitude and phase of the response at discrete frequencies, we apply inverse Fourier transform to analyze the time domain responses which, in turn, allows for monitoring the changes of the response of the in situ sensor. We employ microwave signal flow graph concepts to improve the quality of the received signals. Comparing the normalized results obtained by SDR with those obtained from a commercial vector network analyzer (VNA), we demonstrate that the results are sufficiently close, and the SDR-based experiments can provide satisfactory measurement of the in-situ sensors. The objective is to eventually employ this wireless measurement system for soil nutrient sensing.

Widely Wavelength-Swept Single-Longitudinal-Mode Fiber Laser With Ultra-Narrow Linewidth in C+L-Band

This study proposes and demonstrates a widely wavelength-swept single-longitudinal-mode (SLM) erbium-doped fiber laser (EDFL) enabled by a dual-coupler-ring based compound-cavity (DCR-CC) filter, a fiber Fabry-Pérot tunable filter (FFP-TF) and a C+L-band erbium-doped fiber amplifier (EDFA). Moreover, it develops a novel methodology utilizing the signal-flow graph combined with the matrix algebra to analyze the DCR-CC filter and obtain its essential design parameters for SLM selection of the EDFL. The C+L-band EDFA is constructed to provide a gain range >90 nm. On the other hand, it demonstrates that, under a sweep-rate ≤100 Hz, a lasing wavelength-swept range >87 nm is obtained, the SLM operation is permanently guaranteed for every instantaneous lasing wavelength. Furthermore, the instantaneous lasing parameters of an optical signal-to-noise ratio ≥66 dB, a relative intensity noise ≤−153.33 dB/Hz@≥3 MHz, a linewidth ≤625 Hz and a power fluctuation ≤0.704 dB are achieved. The distinguished performance of the proposed fiber laser enables it to have a significant potential for application in optical frequency domain reflectometry, spectroscopy and Lidar system.

Equivalence Checking of System-Level and SPICE-Level Models of Linear Circuits

Due to the increasing complexity of analog circuits and their integration into System-on-Chips (SoC), the analog design and verification industry would greatly benefit from an expansion of system-level methodologies using SystemC AMS. These can provide a speed increase of over 100,000× in comparison to SPICE-level simulations and allow interoperability with digital tools at the system-level. However, a key barrier to the expansion of system-level tools for analog circuits is the lack of confidence in system-level models implemented in SystemC AMS. Functional equivalence of single Laplace Transfer Function (LTF) system-level models to respective SPICE-level models was successfully demonstrated recently. However, this is clearly not sufficient, as the complex systems comprise multiple LTF modules. In this article, we go beyond single LTF models, i.e., we develop a novel graph-based methodology to formally check equivalence between complex system-level and SPICE-level representations of Single-Input Single-Output (SISO) linear analog circuits, such as High-Pass Filters (HPF). To achieve this, first, we introduce a canonical representation in the form of a Signal-Flow Graph (SFG), which is used to functionally map the two representations from separate modeling levels. This canonical representation consists of the input and output nodes and a single edge between them with an LTF as its weight. Second, we create an SFG representation with linear graph modeling for SPICE-level models, whereas for system-level models we extract an SFG from the behavioral description. We then transform the SFG representations into the canonical representation by utilizing three graph manipulation techniques, namely node removal, parallel edge unification, and reflexive edge elimination. This allows us to establish functional equivalence between complex system-level models and SPICE-level models. We demonstrate the applicability of the proposed methodology by successfully applying it to complex circuits.

MMC Admittance Model Simplification Based on Signal-Flow Graph

Although the impedance/admittance model of modular multilevel converter (MMC) considering internal harmonic is discussed extensively in the literature, few attentions have been focused on how to determine the number of harmonics to be included in the model. This article fills this gap by developing the MMC signal-flow graph (SFG), providing the analytical transfer function to quantitatively estimate the attenuation degree of MMC harmonics, so as to guide the model truncation. Besides, SFG offers an intuitive understanding on the mathematical characteristic of MMC, including the conjugate symmetry and the effect of phase reference on admittance, which helps to reduce the modeling calculation. Moreover, conversion formula of MMC multiple input multiple output and single input single output admittance is derived based on the truncated model to further simplify the stability analysis. The correctness of this article has been verified by simulation and experiment.

String Diagram Rewrite Theory I: Rewriting with Frobenius Structure

String diagrams are a powerful and intuitive graphical syntax, originating in theoretical physics and later formalised in the context of symmetric monoidal categories. In recent years, they have found application in the modelling of various computational structures, in fields as diverse as Computer Science, Physics, Control Theory, Linguistics, and Biology. In several of these proposals, transformations of systems are modelled as rewrite rules of diagrams. These developments require a mathematical foundation for string diagram rewriting: whereas rewrite theory for terms is well-understood, the two-dimensional nature of string diagrams poses quite a few additional challenges. This work systematises and expands a series of recent conference papers, laying down such a foundation. As a first step, we focus on the case of rewrite systems for string diagrammatic theories that feature a Frobenius algebra. This common structure provides a more permissive notion of composition than the usual one available in monoidal categories, and has found many applications in areas such as concurrency, quantum theory, and electrical circuits. Notably, this structure provides an exact correspondence between the syntactic notion of string diagrams modulo Frobenius structure and the combinatorial structure of hypergraphs. Our work introduces a combinatorial interpretation of string diagram rewriting modulo Frobenius structures in terms of double-pushout hypergraph rewriting. We prove this interpretation to be sound and complete and we also show that the approach can be generalised to rewriting modulo multiple Frobenius structures. As a proof of concept, we show how to derive from these results a termination strategy for Interacting Bialgebras, an important rewrite theory in the study of quantum circuits and signal flow graphs.

Low-Loss Single-Band, Dual-Band, and Broadband mm-Wave and (Sub-)THz Interconnects for THz SoP Heterogeneous System Integration

Low-loss single-band, dual-band, and broadband terahertz (THz) interconnects for THz system-on-package heterogeneous system integration are proposed in this article. Transmission lines deployed on a 0.18- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m Complementary Metal-Oxide-Semiconductor (CMOS) chip and an integrated-passive-devices carrier, respectively, are coupled electromagnetically as the chip is flip-chip packaged onto the carrier using low-cost gold stud bumps. By doing this, two pairs of quarter-wave coupled lines can be formed to realize a low-loss THz interconnect for transiting a signal from the chip to the carrier. Moreover, single-band and dual-band operations can be acquired by designing the coupled lines to have a length of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\lambda}$</tex-math></inline-formula> /4 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\lambda}$</tex-math></inline-formula> /4 and 3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\lambda}$</tex-math></inline-formula> /4 at the frequencies of interest, respectively. The gold stud bumps are also employed to realize a broadband directly-connected THz interconnect which transfers a signal from an on-chip microstrip line to an on-carrier microstrip line in a low-loss and broadband manner. A theoretical analysis using signal flow graphs and Mason's rule is conducted to provide design guidelines. Experimental results show that the proposed single-band, dual-band, and broadband THz interconnects can provide the insertion losses of 1.7, 2.7 and 2.9 dB, and lower than 3.3 dB at 306.5, 140 and 324.5 GHz, and from 140 to 330 GHz, with the return loss better than 10 dB from 256.5 to 330, 140 to 182 and 280 to 330, and 140 to 330 GHz, respectively. To the best of the authors’ knowledge, the proposed THz interconnect demonstrates the first dual-band operation reported thus far.