Phase Frequency Research Articles

Robust Adaptive Active Islanding Detection With $\alpha$-Axis Disturbance Injection Under High Impedance Fault, Unbalanced Loading, and Phase Failure in Grid Tied PV System

Power generation with photovoltaic technology is growing expeditiously. With the high penetration of solar-based generation, a concern of islanding detection is always by the distributors due to grid side faults and abnormality. It is the demand of the situation to equip the PV-connected inverter with an islanding detection mechanism to avoid any catastrophe. In the present work, an active islanding detection technique utilizing a smaller magnitude current injection through <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -axis current controller of grid side voltage source converter (VSC) is proposed. Due to injection of current through VSC, point of common coupling (PCC) voltage is having different harmonic component in the grid connected and islanded mode. In the proposed detection method, the sensed PCC voltage is used to derive the three signals i.e. AVVM(absolute <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$v_{mag}$</tex-math></inline-formula> variation mean), AMSVV(absolute mean of square variation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$v_{mag}$</tex-math></inline-formula> ), & FAVVM(Frequency of absolute <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$v_{mag}$</tex-math></inline-formula> variation mean). These three derived signals is used to take the decision for islanding detection. Further, Complex Co-efficient Filter-Second Order Frequency Locked Loop (CCF-SOFLL) is proposed for three phase grid synchronization and frequency estimation. The proposed Strategy is tested under high impedance fault, phase failure and unbalanced loading conditions. It is found that the proposed work clearly differentiates the islanding and faults condition. The Non- detection zone (NDZ) of the proposed strategy is verified under different quality factors ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q_{f}$</tex-math></inline-formula> ) of the load. To evaluate the effectiveness of the suggested strategy, MATLAB Simulation and experimental validation is performed. The obtained islanding detection time is within the IEEE-1547 standard.

An Improved Active Damping Method for Enhancing Robustness of LCL-Type, Grid-Tied Inverters under Weak Grid Conditions.

The conventional proportional-gain-feedback link can only obtain the smallest effective damping region (EDR) due to the control delay among all the active damping methods regarding the capacitor current feedback. The digitally controlled system tends to be unstable when the system resonant frequency reaches the critical frequency caused by the grid impedance variation. To weaken the adverse effect on the system caused by the control delay, phase-lead feedback links are applied along the feedback path to provide phase compensation. By taking the simplicity and reliability of the feedback links into account, this paper proposes an alternative to an ideal differentiator, which consists of the Tustin discrete form of 's' and a digital low-pass filter. This proposed method has an identical phase frequency characteristic as an ideal differentiator but a better magnitude frequency characteristic, and its EDR can reach [0, fs/3]. The system stability analysis is conducted under different resonant frequencies, and under the condition of a weak grid, the co-design approach of the active damper and digital controller is presented. Finally, the experimental results are shown to verify the proposed method.

Robust PLL-Based Grid Synchronization and Frequency Monitoring

Nowadays, the penetration of inverter-based energy resources is continuously increasing in low-voltage distribution grids. Their applications cover traditional renewable energy production and energy storage but also new applications such as charging points for electric vehicles, heat pumps, electrolyzers, etc. The power ratings range from a couple of kW to hundreds of kW. Utilities have, in the last few years, reported more challenges regarding power quality in distribution grids, e.g., high harmonic content, high unbalances, large voltage and frequency excursions, etc. Phase-Lock-Loop (PLL) algorithms are typically used for grid synchronization and decoupled control of power converters connected to the grid. Most of the research within PLLs is mainly focusing on grid voltage angle estimation while the byproducts of the algorithms, e.g., frequency and voltage magnitude, are often overlooked. However, both frequency and voltage magnitude estimations are crucial for grid code compliance. Practical considerations for implementation on microcontroller boards of these algorithms are also missing in most of the cases. The present paper proposes a modified PLL algorithm based on a Synchronous Reference Frame that is suitable for both grid synchronization and frequency monitoring, i.e., the estimation of RMS phase voltages and frequencies in highly distorted distribution grids. It also provides the tuning methodology and practical considerations for implementation on commercial DSP boards. The performance of the proposed approach is assessed through simulation studies and laboratory tests under a wide range of operational conditions, showing that the proposed PLL can estimate the grid frequency, for all considered grid events, with an accuracy of less than ±5 mHz, which is a significant improvement on the current state-of-the-art solutions, having an accuracy of at least ±20 mHz or more.

Optimizing and Analyzing Performance of Motor Fault Diagnosis Algorithms for Autonomous Vehicles via Cross-Domain Data Fusion

Electric motors play a pivotal role in the functioning of autonomous vehicles, necessitating accurate fault diagnosis to ensure vehicle safety and reliability. In this paper, a novel motor fault diagnosis approach grounded in vibration signals to enhance fault detection performance is presented. The method involves capturing vibration signals from the motor across various operational states and frequencies using vibration sensors. Subsequently, the signals undergo transformation into frequency domain representations through fast Fourier transform. This includes normalizing and concatenating the amplitude frequency and phase frequency signals into comprehensive frequency domain information. Leveraging Gramian image-encoding attributes, cross-domain fusion of time-domain and frequency-domain data is achieved. Finally, the fused Gram angle field map is fed into the ConvMixer deep learning model, augmented by the ECA mechanism to facilitate precise motor fault identification. Experimental outcomes underscore the efficacy of cross-domain data fusion, showcasing improved pattern recognition and recognition rates for the models compared to traditional time-domain methods. Additionally, a comparative analysis of various deep learning models highlights the superior performance of the ECA-ConvMixer model. This study makes significant contributions by introducing a cross-domain data fusion method, merging time-domain and frequency-domain information to enhance motor vibration signal analysis. Additionally, the incorporation of the ECA-ConvMixer deep learning model, equipped with attention mechanisms, effectively captures critical features, thus serving as a robust tool for motor fault diagnosis. These innovations not only enhance diagnostic accuracy but also have broad applications in areas like autonomous vehicles and industry, leading to reduced maintenance expenses and enhanced equipment reliability.

A 4–5.2 GHz PLL with 74.8 fs RMS jitter in 28 nm for RF Sampling Transceiver application

AbstractThis paper presents a novel ultra low jitter phase‐locked loop (PLL) circuit architecture for RF Sampling Transceiver. The programmable frequency divider with duty cycle expansion and the new phase frequency detector and charge pump circuit are used to solve the problem of voltage domain conversion of narrow pulses in the traditional high‐performance charge pump PLL structure. The traditional structure degrades charge pump linearity and noise, thus deteriorating overall jitter performance. Furthermore, voltage‐controlled oscillator uses the dual core structure and the second harmonic suppression technology, combined with the proposed new switching capacitor structure, and achieves −139.3 dBc/Hz phase noise at the 1 MHz frequency offset of the 5.2 GHz carrier under the open loop state. The PLL implemented in a standard Taiwan Semiconductor Manufacturing Company 28 nm process occupies a core area of 0.4 mm2 and generates a frequency ranging from 4 to 5.2 GHz using 50 MHz oscillator input, the power consumption is 40 mW. It achieves 74.8 fs root‐mean‐square jitter integrated from 10 KHz to 30 MHz. When the PLL output is divided by 2, the output phase noise at 1 MHz frequency offset is −125.75 dBc/Hz, and the PLL FoM is −246.

Light-by-light polarization control using Stimulated Brillouin Scattering with retardance spectrum shaping

The spectral broadening of a nonlinear polarization retarder based on the polarization dependent interactions of Stimulated Brillouin Scattering is proposed and demonstrated. Through phase-to-retardance conversion, it is shown that polarization can not only be controlled in a bandwidth wider than the natural Brillouin response, but it can also be tailored to provide a certain retardance profile. Broadening is achieved through the engineering of Brillouin phase frequency response via feedback pump regulation, unlike previous schemes based on amplitude and time delay control. Retardance broadening from 51 MHz (natural SBS interaction) to 0.9 GHz along with retardance flattening is demonstrated. This technique contributes to expand optical signal processing tools and opens new possibilities in all-optical switching and routing of data signals as well as in the field of microwave photonics.

Simple, low-cost, and well-performing optical phase-locked loop for frequency and phase locking of semiconductor lasers.

We demonstrate a simple, low-cost, and well-performing optical phase-locked loop (OPLL) circuit with ADF4007 as the phase frequency detector chip to achieve frequency and phase locking of two semiconductor lasers in both short and long terms. The measured short term performances, determined by fast feedback, show that the spectral width of the beat signal is low, around 1Hz, and the residual phasing error is 0.04r a d 2. The measured long term performances, determined by slow feedback, show that the drift of the central frequency of the beat signal is within 1.1(1)Hz in 2h, and the derived Allan deviation is less than 0.4Hz within all integration times of up to 1000s. The phase noise measurement shows a suppression of phase noise of the beat signal from free running to closed-loop OPLLs in a Fourier frequency of 10Hz-20kHz. These measurements show that the OPLL circuit we modified can fit most scientific experiments requiring a fixed frequency difference and phase coherence.

PDM-SHD NFDM transmission with envelope-detection feedback polarization tracking and optical injection locking.

Nonlinear frequency division multiplexing (NFDM) systems, especially the eigenvalue communications have the potential to overcome the nonlinear Shannon capacity limit. However, the baud rate of eigenvalue communications is typically restricted to a few GBaud, making it challenging to mitigate laser frequency impairments such as the phase noise and frequency offset (FO) using digital signal processing (DSP) algorithms in intradyne detections (IDs). Therefore, we introduce the polarization division multiplexing-self-homodyne detection (PDM-SHD) into the NFDM link, which could overcome the impact of phase noise and FO by transmitting a pilot carrier originating from the transmitter laser to the receiver through the orthogonal polarization state of signal. To separate the signal from the carrier at the receiver, a carrier to signal power ratio (CSPR) unrestricted adaptive polarization controlling strategy is proposed and implemented by exploiting the optical intensity fluctuation of the light in a particular polarization rather than its direct optical power as the feedback. Optical injection locking (OIL) is used subsequently to amplify optical power of pilot carrier and mitigate the impact of signal-signal beat interference (SSBI). Additionally, the effects of cross-polarization modulation (XPolM) and modulation instability (MI) in long haul transmission are explored and inhibited. The results show that the tolerable FO range is about 3.5 GHz, which is 17 times larger than the ID one. When 16-amplitude phase shift keying (APSK) or 64-APSK constellations are used, identical Q-factor performance can be obtained by using distributed feedback (DFB, ∼10 MHz) laser, external cavity laser (ECL, ∼100kHz), or fiber laser (FL, ∼100 Hz), respectively, which demonstrates that our proposed PDM-SHD eigenvalue communication structure is insensitive to the laser linewidth. Under the impact of cycle slip, the Q-factor difference of 16-APSK signal between the ECL-ID system and ECL-SHD system can be up to 8.73 dB after 1500 km transmission.

A Three-Phase Synchronization Algorithm Based on a Modified DSOGI with Adjustable Re-Filtering

The precise calculation of phase angle, voltage magnitude and frequency is crucial for the effective control of power electronic inverters connected to an electrical power system. The phase-locked loop (PLL) is a commonly employed method for measuring these variables. Nevertheless, the reliability of this measurement is influenced by transient events in the electrical power system and varies depending on the nature of the event and the specific design of the PLL. Notably, PLLs utilizing the double second-order generalized integrator are widely adopted for power converter synchronization purposes. This article proposes a three-phase PLL, which is based on the single-phase version previously reported by the authors. The proposed PLL, based on an alternative integrator approach, allows a fine adjustment of the tolerance to disturbances in the input voltage thanks to a second feedback gain in its pre-filter. It is reasonable to anticipate that the three-phase PLL will exhibit similar strengths to the single-phase version; however, in the three-phase case, an additional integrator is involved in pre-filtering the quadrature signals, and the double integrator is not employed as the quadrature signal generator. The performance of the proposed PLL is assessed by comparing it to other PLLs based on the second-order integrator, using a processor-in-the-loop approach.

Fractal Characterization of Particle Size and Coordinate Distribution of Dispersed Phase in the Steelmaking Process of Combined Blowing Conversion

A two-dimensional water model was used to simulate the process of combined blowing. The effect of boundary conditions on the size and coordinate distribution of the dispersed phase was investigated. The results showed that the frequency of the dispersed phase at a certain size level is proportional to its size; the coordinates of the dispersed phase can be expressed in a dimensionless form that shows its uniformity of distribution. An empirical equation for the influence of the boundary conditions on the size and coordinate distribution of the dispersed phase in combined blowing process is also presented.

Research on the noise characteristics of a closed-loop 87Rb atom comagnetometer

Spin-based comagnetometers have essential applications in studying new physical effects such as the fifth force, Lorentz violations, and spin-gravity interactions. In this paper, a transfer function model of the spin precession phase (frequency) is derived to analyze the comagnetometer's noise mechanism. The theory combined with experiments reveals that the output frequency noise of the spin oscillator above 5 Hz is mainly phase noise from the phase-locked loop. The noise below 5 Hz is mainly from the biased magnetic field noise. When building a comagnetometer using two spin oscillators, the symmetry of the spin oscillator is significant. When the intrinsic physical parameters cannot be symmetrical, the comagnetometer's common-mode suppression capability to magnetic field fluctuations can be enhanced by optimizing the control parameters. In addition, the closed-loop control of Bz can significantly weaken the effect of system asymmetry in the low-frequency band. Finally, when considering the comagnetometer system in nuclear magnetic resonance gyroscopes, a trade-off between the bandwidth and sensitivity can be achieved using theory. This paper is an excellent reference for both the research and application of comagnetometers.

Brief Submotor-Threshold Electrical Stimulation Applied Synchronously Over Wrist Flexor and Extensor Muscles does Not Suppress Essential Tremor, Independent of Stimulation Frequency.

Electrical stimulation of muscles below motoneuron threshold has shown potential as a low-cost and minimally invasive treatment for Essential Tremor (ET). Prior studies have stimulated wrist flexor and extensor muscles synchronously with diverging results, calling for further investigation. Also, prior studies have only used a narrow range of stimulation parameters, so stimulation parameters have not been optimized. Our purpose was to further investigate synchronous submotor stimulation and identify the effect of stimulation frequency on tremor suppression. We quantified the effect of brief, synchronous stimulation at 15 different frequencies from 10-150 Hz applied over wrist flexors and extensors on both tremor power and frequency in 20 ET patients. We compared tremor power and frequency from hand acceleration and sEMG between pre-, per-, and post-stimulation phases. Our stimulation paradigm did not result in significant tremor suppression or tremor frequency changes at any tested stimulation frequency, showing no significant interaction between phase and stimulation frequency for tremor power measured by either hand acceleration (p = 0.69) or sEMG (p = 0.07). Additionally, the effect of phase interacting with stimulation frequency on tremor frequency was statistically insignificant for acceleration (p = 0.64) and sEMG (p = 0.37). We conclude that brief synchronous submotor-threshold stimulation does not reduce tremor in ET patients, independent of stimulation frequency (from 10 to 150 Hz). Our results are consistent with the hypothesis that brief submotor-threshold stimulation suppresses tremor via reciprocal inhibition, which requires asynchronous stimulation. In contrast, it is hypothesized that synchronous stimulation might require longer stimulation durations to affect supraspinal tremor networks. We studied the effects of synchronous submotor electrical stimulation over wrist flexor and extensor muscles on Essential Tremor. Our results indicate that suppressing tremor with brief synchronous stimulation is ineffective. Based on recently hypothesized mechanisms of peripheral tremor suppression, we hypothesize that asynchronous stimulation or long-duration synchronous stimulation are more effective approaches to peripheral tremor suppression.

On measurements of spurious components of heterodyne signal in radiometric receivers

With a heterodyne frequency conversion, a significant contribution to the intrinsic noise of the radiometric receiver is made by a heterodyne. The spectral components generated by the heterodyne will be present in the processed signal at the output of the radiometric receiver and may manifest themselves when analyzing the received signal in spectral lines when high frequency resolution is required for processing. The purpose of the work is to analyze various types of modulation of the heterodyne signal, including modulation with an arbitrary phase shift between the components in the lower and upper side bands of the heterodyne signal. In this article, the methods of frequency transfer used in determining the spectral composition of the signal received by a radiometric receiver are considered. For heterodyne frequency conversion, in addition to the classical types of parasitic modulation of the heterodyne signal described in the literature – amplitude, phase (frequency) and single-band modulation, modulation with an arbitrary phase shift between the components in the lower and upper side bands of the heterodyne signal is considered. It is shown that with a small deviation of the frequencies of the modulating signal, ambiguity is possible in determining the level of components when using signal analyzers to measure the characteristics of heterodynes of radiometric receivers. The results of the analysis performed in the article can be used in the design of heterodynes with multiple output frequencies, taking into account the spectral comtent of the synthesized signal. The study was carried out at the expense of the grant of the Russian Science Foundation No. 22-19-00063 dated 13.05.2022. https://rscf.ru/project/22-19-00063.

European Green Deal: Study of the Combined Agricultural Aggregate

The modern world industry involves the use of innovative approaches and optimisations of the existing agricultural management methods, which contribute to the implementation of the sustainable development of related industries and economies of different countries. The use of mobile agricultural units with extended functional properties can have a steady demand in the agricultural machinery market and contribute to the practical implementation of the philosophy of the “European Green Deal”. The research results show that when assembling a unit for mowing agricultural crops with simultaneous grinding and placing their stubble in the soil, preference should be given to a self-propelled machine with rear swivel wheels. When using a wheeled tractor, it must have a reversible control post and a reversible transmission. A mathematical model of the collecting unit was developed, which allows for obtaining the corresponding amplitude and phase frequency characteristics and, with their help, the stability of the horizontal movement was evaluated. According to the results of field studies, the dispersion of the angle of directional oscillation of the tractor with front-steered wheels was 4.48 grad2. For the tractor with rear-steered wheels, the value of this statistical parameter was 2.90 grad2, which, according to the F-test at the level of statistical significance of 0.05, is naturally lower.

Early Postoperative Aqueous Suppression Therapy and Surgical Outcomes of Ahmed Tube Shunts in Refractory Glaucoma

To compare early vs. delayed use of aqueous suppressants on Ahmed glaucoma valve (AGV) outcomes. Single-center retrospective comparative case series. Patients who underwent AGV surgery at Wills Eye Hospital in the period between 2016 and2021. Retrospective review of AGV surgery at Wills Eye Hospital 2016 to 2021 for refractory glaucoma. Two groups were created: group 1 or those who received early aqueous suppressant therapy in the first 2 weeks postoperatively whenever the intraocular pressure (IOP) was> 10 mmHg, and group 2 or those who received delayed treatment after 2weeks whenever the IOP exceeded the target pressure. Aqueous suppressant therapy included topical beta blockers, carbonic anhydrase inhibitors, and/or alpha agonists. The primary outcome measures were the frequency of hypertensive phase (HP) defined as IOP> 21 mmHg in first 3 months after an initial reduction to 21 mmHg or less in the first postoperative week not caused by tube obstruction or retraction, and month-12 surgical failure defined as 5 ≥ IOP > 21 mmHg on 2 consecutive visits, vision decline to no light perception (NLP), or glaucoma reoperation. Secondary outcome measures included changes in visual acuity (VA), IOP, and glaucoma medications at 12 months. Predictive factors for surgical failure were also identified. A total of 407 eyes of 391 patients (260 in group 1, 147 in group 2) with similar baseline characteristics were included. Hypertensive phase was more common in group 2 than 1 (41.5% vs. 18.5%; P<0.001). At month 12 (N=303 eyes), group 1 was less likely to fail than group 2 (21.2% vs. 36.8%, P=0.003). Multivariate regression analysis showed that HP (odds ratio [OR]=10.47, P<0.001), delayed aqueous suppression use (OR=2.17, P=0.003), and lower baseline VA (OR=1.56, P=0.015) were the strongest predictors of month-12 failure. Early use of aqueous suppressants may lower the risk of HP and improve AGV outcomes. Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Ensuring the performance of modified microstrip loops in the frequency band

Problem statement. Microstrip loop structures of various configurations are widely used to form topologies of multi-pole microwave devices. In this regard, there is a need to study the frequency properties and topological features of the construction of loop structures that determine the amplitude and phase frequency characteristics, as well as the overall parameters of a microstrip radio engineering device. Objective. Studying of frequency characteristics of T- and U-shaped loop configurations implemented on the basis of high-resistance and low-resistance segments of microstrip transmission lines that allow configuring small-sized topologies of multi-pole devices with acceptable electrical characteristics. Results. A number of basic topologies of loop structures designed to function in given frequency bands have been studied. With the help of electrodynamic modeling and parametric optimization, according to a number of criteria (given wave resistance, phase shift, reflection coefficient), the necessary geometric dimensions of the modified topologies were determined. The dependence of the frequency band on the geometric dimensions of the low-resistance loop of the T-section is revealed. By the level of “minus” 20 dB from the maximum of the reflection coefficient, the values of the frequency band width of two types of T-structures – symmetrical and counter-pin - were determined and compared. It is shown that the U-shaped section is characterized by an increased frequency band due to better matching, however, its geometric dimensions exceed the dimensions of the basic T-structures. Practical significance. Modified microstrip loop structures in some cases are able to effectively replace quarter-wave segments of transmission lines, on the basis of which most microwave devices are formed (directional couplers, power dividers, electric filters, phase shifters, crossovers, etc.). The use of combinations of T- and U-shaped structures leads to a significant reduction in the area of microstrip devices designed to operate in the UHF and Microwave bands.

Analysis of optimized phase locked loop for grid synchronization of solar PV system under grid disturbances

AbstractIn this work, an optimal phase locked loop (PLL) is employed to estimate the fundamental grid frequency and phase angle under grid disturbances, which largely reduces the frequency and phase error. Conventional synchronous reference frame (SRF) offers considerable results for balanced grid conditions but has poor performance under grid disturbances with improper phase detection. In this regard, gravitational search algorithm (GSA)‐based optimization is utilized to optimally tune the proportional and integral (PI) gain values of conventional SRF PLL, which ensures the proper tracking of fundamental phase angle and frequency even during abnormal grid conditions, that is, voltage unbalance, frequency variations, high‐frequency harmonics, and phase variations. Further, integral square error (ISE) criteria, settling time, and overshoot are considered as objective functions to obtain the optimal value of current gain, present in the control loop of a grid‐tied solar photovoltaic (PV) system. The supremacy of the proposed work, compared to SRF and optimal SRF PLL, is tested with MATLAB®/Simulink studies and verified by dSPACE‐1104‐based hardware‐in‐loop (HIL) results for real‐time validation.

High pressures as an effective tool to separate different contributions to the electrode polarization of polar liquids and solids

Electrode polarization effects are an important issue in electrochemistry. Here we report investigation of electrode polarization effects in ethanol (used as a model material), in solid and liquid phases at high pressures. Application of pressure has dramatic effect on electrode polarization. Firstly, it significantly reduces the fractional power exponent, which dominates the low-frequency electrode polarization impedance, from approximately 1 at ambient pressure to less than 0.1 at 1.3 GPa. At pressure we can observe transition of electrode polarization impedance from fractional frequency law to inversely proportional to frequency relationship. This transition observed for the first time solves the problem with analytical limitation of electrode polarization effects at higher frequencies. Experimental data fitting by the procedure proposed by us, enables extracting the temperature dependencies of dielectric constant and dielectric relaxation frequency in the solid phase of ethanol at high pressures.

Traveling salesman problem solution using magnonic combinatorial device

Traveling salesman problem (TSP) is a decision-making problem that is essential for a number of practical applications. Today, this problem is solved on digital computers exploiting Boolean-type architecture by checking one by one a number of possible routes. In this work, we describe a special type of hardware for the TSP solution. It is a magnonic combinatorial device comprising magnetic and electric parts connected in the active ring circuit. There is a number of possible propagation routes in the magnetic mesh made of phase shifters, frequency filters, and attenuators. The phase shifters mimic cities in TSP while the distance between the cities is encoded in the signal attenuation. The set of frequency filters makes the waves on different frequencies propagate through the different routes. The principle of operation is based on the classical wave superposition. There is a number of waves coming in all possible routes in parallel accumulating different phase shifts and amplitude damping. However, only the wave(s) that accumulates the certain phase shift will be amplified by the electric part. The amplification comes first to the waves that possess the minimum propagation losses. It makes this type of device suitable for TSP solution, where waves are similar to the salesmen traveling in all possible routes at a time. We present the results of numerical modeling illustrating the TSP solutions for four and six cities. Also, we present experimental data for the TSP solution with four cities. The prototype device is built of commercially available components including magnetic phase shifters/filters, coaxial cables, splitters, attenuators, and a broadband amplifier. There are three examples of finding the shortest route between the cities for three different sets of city-to-city distances. The proposed approach is scalable to TSP with a larger number of cities. Physical limits and challenges are also discussed.

Mathematical modelling and simulation of a wideband PLL for application in frequency synthesizers

In this paper the mathematical modelling of the Voltage Controlled Oscillator, Phase Frequency Detector, Low Pass Filter, Charge pump for designing a PLL circuit is proposed. Based on the modelling schematics are designed and proposed for the application in frequency synthesizer. The main design feature of this modelling is that VCO tunning switches are controlled digitally. The behaviour of PLL under its region of operation is simulated. The effect of temperature variations and insufficient bandgap overlapping on the output frequency of PLL is also presented and discussed. To avoid the current mismatching and residual phase errors the charge pump is modelled as to calibrate by its own circuit. Various simulations are done for the performance analysis of wideband PLL. The proposed design will have its application in frequency synthesizers suitable for multi band transceivers.