Harmonics Of Fundamental Frequency Research Articles

Enhanced second harmonic generation by an atomically thin MoS2 sheet attached to a resonant metasurface.

Two-dimensional transition metal dichalcogenides have shown large second-order nonlinear responses due to their broken crystal inversion symmetry. However, their nonlinear interaction with light is restricted to an atomically thin layer. Placing a sheet of transition metal dichalcogenides on a resonant metasurface enhances the field interacting with the nonlinear material thus compensating for this shortcoming. But, it remains a challenge to tune resonances such, that they coincide with fundamental and second harmonic frequencies simultaneously. Here we demonstrate two independent methods to achieve that goal and numerically illustrate our findings for a MoS2 layer combined with silicon nitride photonic crystals. We numerically demonstrate 20-fold and 170-fold enhancement of second-harmonic generation compared with a design based on a single resonant structure. Although we focus on that specific configuration our approach can likewise be applied to other dielectrics combined with highly nonlinear 2D materials.

Second harmonic generation for estimating state of charge of lithium-ion batteries

This study applied the nonlinear ultrasonic method, second harmonic generation, to precisely estimate the state of charge (SoC) in lithium-ion batteries. The second harmonic of the longitudinal wave is generated on a pouch cell battery at 5 MHz with a through-transmission setup. The relative nonlinear parameter β′ is determined by analyzing the amplitudes at the fundamental and second harmonic frequencies. To enhance the nonlinear parameter's measurement accuracy, multiple excitation amplitudes are employed. Two separate charge/discharge tests (four-cycle and eight-cycle) are conducted on the battery at a rate of C/10. The nonlinear parameter is measured periodically during the charge/discharge process, and temperature compensation is applied to the measurement. The correlation curves between the nonlinear parameter and the actual SoC align well for the four-cycle and eight-cycle tests, and a robust linear relationship is observed for both correlation curves. A linear model and a second-order polynomial model are applied to fit the correlation using all data points from both tests. The two models are employed to validate the SoC prediction on a second battery by using a four-cycle test. The results indicate that both models can predict the SoC with an accuracy of approximately 3%, whereas the polynomial model demonstrates smaller errors in the regions near 0% and 100% SoC. Therefore, the nonlinear parameter β′, measured through the second harmonic generation, can effectively predict lithium-ion battery SoC with an accuracy of less than 3%.

A novel adaptive filter with a heart-rate-based reference signal for esophageal pressure signal denoising

Esophageal pressure (Peso) is one of the most common and minimally invasive methods used to assess the respiratory and lung mechanics in patients receiving mechanical ventilation. However, the Peso measurement is contaminated by cardiogenic oscillations (CGOs), which cannot be easily eliminated in real-time. The field of study dealing with the elimination of CGO from Peso signals is still in the early stages of its development. In this study, we present an adaptive filtering-based method by constructing a reference signal based on the heart rate and sine function to remove CGOs in real-time. The proposed technique is tested using clinical data acquired from 20 patients admitted to the intensive care unit. Lung compliance ( QUOTE ) and esophageal pressure swings (△Pes) are used to evaluate the performance and efficiency of the proposed technique. The CGO can be efficiently suppressed when the constructional reference signal contains the fundamental, and second and third harmonic frequencies of the heart rate signal. The analysis of the data of 8 patients with controlled mechanical ventilation reveals that the standard deviation/mean of the QUOTE is reduced by 28.4–79.2% without changing the QUOTE and the △Pes measurement is more accurate, with the use of our proposed technique. The proposed technique can effectively eliminate the CGOs from the measured Peso signals in real-time without requiring additional equipment to collect the reference signal.

Simulation of ion cyclotron wave heating in the EXL-50U spherical tokamak based on dispersion relations

This study investigates the single-pass absorption (SPA) of ion cyclotron range of frequency (ICRF) heating in hydrogen plasma of the EXL-50U spherical tokamak, which is an upgraded EXL-50 device with a central solenoid and a stronger magnetic field. The reliability of the kinetic dispersion equation is confirmed by the one-dimensional full-wave code, and the applicability of Porkolab's simplified theoretical SPA model is discussed based on the kinetic dispersion equation. Simulations are conducted to investigate the heating effects of the fundamental and second harmonic frequencies. The results indicate that with the design parameters of the EXL-50U device, the SPA for second harmonic heating is 63%, while the SPA for fundamental heating is 13%. Additionally, the optimal injection frequencies are 23 MHz at 0.9 T and 31 MHz at 1.2 T. The wave vector of the antenna parallel to the magnetic field, with a value of , falls within the optimal heating region. Simulations reveal that the ICRF heating system can play an important role in the ion heating of the EXL-50U.

Harmonic Suppressed Wilkinson Power Divider Using Parallel Resonant Shunt Stub

This paper proposes a harmonic-suppressed Wilkinson power divider (HS WPD) utilizing parallel resonant shunt stubs (PRSSs). PRSSs are integrated into the conventional WPD by adding functionalities such as bandpass filtering, harmonic suppression, and physical port separation. The resonance conditions and design equations of the PRSS are theoretically derived and verified through circuit simulations. Using the PRSS, we designed an HS WPD operating at 1 GHz. The fabricated HS WPD demonstrated an insertion loss of 3.2 dB at the fundamental frequency, with a wide 3 dB bandwidth of 129%. The harmonic suppression levels at the 2nd and 3rd harmonic frequencies are measured to be 21.0 dB and 25.8 dB, respectively. The measured input return loss at the fundamental frequency was 27.9 dB, whereas the output return loss was 24.6 dB. Additionally, the HS WPD demonstrates isolation levels at the fundamental, 2nd, and 3rd harmonic frequencies, with levels of 29.2 dB, 17.8 dB, and 47.1 dB, respectively. It also exhibited broadband isolation (>8.7 dB) across the frequency range of 100 kHz to 3.35 GHz. The PRSS design allows for the physical separation of the ports without requiring additional circuitry. Compared to previously reported PDs, the proposed design offers multiple functions in a compact size, making it highly suitable for various microwave systems.

A visual approximation of a Fourier transforms operation using GeoGebra

Many engineering fields use the Fourier Transform. The purpose of the Fourier Transform is to decompose periodic signals into fundamental frequencies and harmonic frequencies. The Fourier transform operation in ordinary textbooks is mathematically analytical, this often makes it difficult for students who study it. This paper describes the mathematical operations that occur in the Fourier transform. Discrete Fourier transform operations consist of conversion operations of continuous-time signals into data sequences, exponential complex number multiplication operations, and integration operations of number data sequences. Visualization of Fourier transform operations using the GeoGebra application. This research obtains visualization results of Fourier transform operations. The resulting visualization includes the effect of increasing signal frequency and the integral limit. The influence of the greater integral limit causes the peak of the frequency spectrum to become larger. The integral result of the pulse signal is in the form of a sinc function and corresponds to the illustration in the textbook. The limitation of the results of this research is that the Fourier transform visualization was carried out at low frequencies

A chip-scale second-harmonic source via self-injection-locked all-optical poling

Second-harmonic generation allows for coherently bridging distant regions of the optical spectrum, with applications ranging from laser technology to self-referencing of frequency combs. However, accessing the nonlinear response of a medium typically requires high-power bulk sources, specific nonlinear crystals, and complex optical setups, hindering the path toward large-scale integration. Here we address all of these issues by engineering a chip-scale second-harmonic (SH) source based on the frequency doubling of a semiconductor laser self-injection-locked to a silicon nitride microresonator. The injection-locking mechanism, combined with a high-Q microresonator, results in an ultra-narrow intrinsic linewidth at the fundamental harmonic frequency as small as 41 Hz. Owing to the extreme resonant field enhancement, quasi-phase-matched second-order nonlinearity is photoinduced through the coherent photogalvanic effect and the high coherence is mapped on the generated SH field. We show how such optical poling technique can be engineered to provide efficient SH generation across the whole C and L telecom bands, in a reconfigurable fashion, overcoming the need for poling electrodes. Our device operates with milliwatt-level pumping and outputs SH power exceeding 2 mW, for an efficiency as high as 280%/W under electrical driving. Our findings suggest that standalone, highly-coherent, and efficient SH sources can be integrated in current silicon nitride photonics, unlocking the potential of χ(2) processes in the next generation of integrated photonic devices.

A Compact Low-Loss Reflection-Type Harmonic Transponder for Battery-Less RFID Sensors Based on Harmonic Backscattering

This study presents a compact reflection-type harmonic transponder with a wide input power range for battery-less radio frequency identification (RFID) sensors based on harmonic backscattering. Miniaturizing the circuit size of conventional harmonic transponders is difficult because the input and output matching stages are configured separately, and two antennas are used for each port. The proposed harmonic transponder based on a dual-band matching network matches the load simultaneously at the fundamental and second harmonic frequencies over a wide input power range, thus enhancing the conversion gain (CG) with a compact size. For verification, the proposed transponder is implemented in a compact size with dimensions of 19 mm × 17.8 mm. The measured CG of the implemented transponder is maintained at over −10 dB in the wide input power range of −6.4 dBm to 10.6 dBm at 2.45 GHz. Th e harmonic transponder is configured with a dual-band chip antenna and measured in free space to verify whether it is suitable for battery-less RFID sensors. The measured detectable effective distance to the proposed circuit is 6.3 m in free space, with an equivalent isotropically radiated power of 42.6 dBm.

Two-section branch-line hybrid couplers based broadband transmit/receive switch

<p>This article introduces a broadband microstripline-based transmit/receive switch for 7-Tesla magnetic resonance imaging. The designed switch aims to handle a signal of multiple frequencies to/from a multi-tuned radio-frequency coil that resonates at frequencies corresponding to the speed of precession of a wide range of atomic X-nuclei, at the same time and without tuning. These include 1H, 23Na, 13C, 31P, 19F, and 7Li used in magnetic resonance spectroscopy as a measure to the existence of many diseases. The fundamental and third harmonic center frequencies of the switch are adjusted to resonate at two broadbands covering a wide range of atomic X-nuclei. Two section branch-line hybrid couplers with phase inverters are designed to build the broadband switch. The designed switch used the minimum trace widths of transmission lines that reveal a compact size without increasing the heat and then the loss beyond specific values. The couplers and the switch S-parameters exhibited good return loss (<-10 dB), high isolation (<-40 dB), less insertion loss (<1 dB) and two clear wide bands covering many atomic X-nuclei used in diagnosis, at the same time and without the need for any tuning circuit during operation.</p>

Highly Efficient Power Amplifier Based on Harmonic-Controlled Matching Network

This study presents a highly efficient power amplifier (PA) based on a compact harmonic-controlled matching network (HCMN). The proposed HCMN with three-stage band-stop matching network (BMN) can simultaneously match to the optimum power matching impedance at fundamental and second harmonic frequencies and suppress second harmonic signals caused by nonlinearity without an additional filter. For verification, the proposed PA was designed, fabricated, and measured. The implemented PA was a compact size of 53.3 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times40$ </tex-math></inline-formula> mm. The measurement results show that the output power is 36–38.6 dBm, and the drain efficiency (DE) is 68.2%–74.3% in the frequency range of 2.9–3.3 GHz. The proposed PA also achieves the low second harmonic level of −44.1 to −67.1 dBc in the frequency range of 2.9–3.3 GHz.

The Identification Method of the Winding Vibration Faults of Dry-Type Transformers

To identify the four typical faults of dry-type transformer winding insulations, looseness, deformation and eccentricity, this study establishes the electric magnetic force multi-physical field simulation model of a dry-type transformer winding under the four typical faults with COMSOL software, based on the vibration mechanism of an SCB10-1000/10 dry-type transformer. Through the multi-physical field coupling calculation, the comparative relationship between the vibration acceleration of the winding under the four kinds of faults and the normal working state is obtained. The results show that the amplitude growth rate of the fundamental frequency or harmonic frequency of the acceleration signal under four kinds of faults is different from that under normal conditions. Therefore, the threshold value of the fundamental frequency or harmonic increment of the acceleration signal is introduced to describe the growth rate of the acceleration signal relative to normal conditions. Finally, four typical faults are identified with different threshold ranges of acceleration increment under faults, laying a foundation for the fault diagnosis of transformer winding vibrations.

A Dual-Frequency WPT Based on Multilayer Self-Decoupled Compact Coil and Dual CLCL Hybrid Compensation Topology

This article proposes a dual-frequency wireless power transfer (WPT) with dual <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CLCL</i> hybrid compensation topology and multilayer self-decoupled compact coils (MLSDCCs). It extends the transmission distance corresponding to stable high transmission power and efficiency. Based on the parameter constraints of compensation capacitances and inductances, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CLCL</i> hybrid compensation topology realizes simultaneous resonance at fundamental and third harmonic frequencies. A typical inverter can meet the requirements of dual-frequency WPT without complex control or more number and improve the utilization rate of square voltage. According to interleaving and rotary stacking of unipolar and bipolar coils in MLSDCCs, the couplings between layers and unnecessary couplings of magnetic coupling mechanism (MCM) are eliminated. Only the main couplings for power transmission are retained and the volume of MCM is reduced. Finally, a 1 kW experimental platform is built. Compared with the typical single-frequency WPT, the maximum transmission power is increased by 2.8%, while the maximum transmission efficiency is only reduced by 0.53%. The main advantage is that the transmission distance corresponding to continuous high-power transmission (in the range of 95%–100% maximum receiving power) is increased by 2.75 times. When the lateral offset distance of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> -axis is one-sixth of the coil side length, the transmission efficiency decreases by only 1.47%.

Broadbands Four-Branch Hybrid Coupler-Based T/R Switch for 7-Tesla Magnetic Resonance Imaging

In this article, we are introducing a new broadband four-branch microstripline hybrid coupler-based switch to transmit/receive signals of a wide range of operating frequencies to/from a single or multi-tuned radio frequency coil. The proposed switch has two ranges of frequencies covering many X-atomic nuclei including: 23Na, 31P, 19F, 13C, 7Li, and 1H when they are exposed to 7 Tesla magnetic field strength in magnetic resonance imaging machines. The introduced switch does not need any type of tuning to cover the X-nuclei. The introduced switch does not exceed the realistic trace width of microstriplines that determine the allowable amount of increase in temperature when being exposed to 1 kW power and 10% duty cycles of the radio frequency pulses. Electromagnetic wave simulator (ADS) is used to characterize the S-parameters. The fundamental and third harmonic center frequencies are adjusted to resonate with two broadbands covering the speed of precession of a wide range of X-nuclei. These atomic nuclei are used as a measure to the existence of cancerous tissues, and their targeting might reduce the need for biopsy in diagnosis. The introduced switch can conduct broadband signals to/from a multi-tuned coil with low return loss values (-15 to -27 dB), low insertion loss (from -0.64 to -1.29 dB), and very good isolation, amounts to -70 dB.

Nonlinear Ultrasonic Inspection of the Effect of Contaminants on Material Properties of Epoxy-Adhesive

Adhesive joints have been an effective alternative to conventional mechanical fasteners for joining materials in the aerospace and automotive industries. Although adhesive joints have various advantages, including uniform stress distribution, lower weight, improved corrosion tolerance, and design flexibility, there can be various defects in adhesive joints, which have limited wider application. This paper investigates the effect of a contaminant on the chemical and mechanical properties of the epoxy-adhesive and seeks to determine if a second harmonic generation method can reliably detect and characterize the degree of contamination in the epoxy-adhesive. A contact based ultrasonic through-transmission method was used to measure nonlinearity and then the nonlinearity parameter was calculated using the measured fundamental and second harmonic frequency components in the signals. It was found that there is higher sensitivity to contaminant concentration, up to 1.5%, of the nonlinearity parameter than that for the sound velocity. These data were also found to correlate with changes in the mechanical hardness, which was measured by the Rockwell hardness testing, with different four levels of contamination. Differential scanning calorimetry (DSC) and the thermogravimetric analysis (TGA) were also conducted to assess the effect of the contaminant on thermal properties of the epoxy-adhesive. The DSC and TGA techniques were used to evaluate the curing reaction and the thermal stability of the epoxy-adhesive respectively.

Large eddy simulations of a turbulent mixing layer periodically excited with fundamental and third harmonic frequency

A better understanding of the mixing behavior of excited turbulent mixing layers is critical to a number of aerospace applications. Previous studies of excited turbulent mixing layers focused on single frequency excitation or the excitation with fundamental and its second harmonic frequency. There is a lack of detailed studies on applying low and higher frequency excitation. In this study, we have performed large-eddy simulations of periodically excited turbulent mixing layers. The excitation consists of a fundamental frequency and its third harmonic. We have used phase-averaging to identify the vortex structure and strength in the mixing layer, and we have studied the vortex dynamics. Two different vortex paring mechanisms are observed depending on the phase shift between the two excitation frequencies. The influence of these two mechanisms on the mixing of a passive scalar is also studied. It is found that exciting the mixing layer with these low and high frequencies has initially an adverse influence on the mixing process; however, it improves the mixing further downstream of the splitter plate with the excitation using a phase shift of Δϕ=π showing the best mixing performance. The present works shed lights on the fundamental vortex dynamics, and has great potential for aeronautical, automotive and combustion engineering applications.

Infrared bands of formaldehyde dissolved in liquid krypton at cryogenic temperatures and the vibrational modes ν1, ν2, and ν5 of H2CO in comets and interstellar clouds

The infrared spectra of formaldehyde (H2CO) dissolved in liquid krypton between 125 K and 137 K have been obtained using a Fourier transform infrared spectrophotometer and a low temperature cryostat. Backing pressures higher than 1.5 atm were necessary to liquefy Kr above 120 K. Monomeric formaldehyde in gas phase was prepared by thermal decomposition of para-formaldehyde. Peak positions (ν), wavenumber shifts between the gas and liquid solution spectra (Δν), and full widths at half maximum (fwhm) are reported. The H2CO vibrational frequencies in liquid Kr are slightly lower than the gas phase frequencies at room temperature because of the inertness of the solvent. The Gaussian 16 software package is used to determine the geometry and lowest energy of H2CO at room temperature and at the temperature of the experiment. Fundamental harmonic and anharmonic vibrational frequencies and relative intensities are calculated. The influence of the solvent on fundamental vibrational frequencies is studied using the polarizable continuum model (PCM). When used in conjunction with calculated anharmonic frequencies, the PCM model shows qualitative agreement with experimental frequency shifts and relative intensities in liquid Kr. The presence of H2CO in space is discussed in reference to the ν1 and ν5 absorption bands observed in comets, the ν1 and ν2 absorptions in interstellar clouds, and the lack of detection of the ν4 and ν6 bands of H2CO in the atmosphere of Titan. The carbonyl stretching mode ν2 is suggested as a possible candidate for confirmation and identification of H2CO in space due to its larger strength in comparison to the other modes that have been studied at low temperatures and its characteristic frequency that is completely removed from CO2, CO, H2O and CH3OH vibrational modes.

A Music Cognition–Guided Framework for Multi-pitch Estimation

As one of the most important subtasks of automatic music transcription (AMT), multi-pitch estimation (MPE) has been studied extensively for predicting the fundamental frequencies in the frames of audio recordings during the past decade. However, how to use music perception and cognition for MPE has not yet been thoroughly investigated. Motivated by this, this demonstrates how to effectively detect the fundamental frequency and the harmonic structure of polyphonic music using a cognitive framework. Inspired by cognitive neuroscience, an integration of the constant Q transform and a state-of-the-art matrix factorization method called shift-invariant probabilistic latent component analysis (SI-PLCA) are proposed to resolve the polyphonic short-time magnitude log-spectra for multiple pitch estimation and source-specific feature extraction. The cognitions of rhythm, harmonic periodicity and instrument timbre are used to guide the analysis of characterizing contiguous notes and the relationship between fundamental frequency and harmonic frequencies for detecting the pitches from the outcomes of SI-PLCA. In the experiment, we compare the performance of proposed MPE system to a number of existing state-of-the-art approaches (seven weak learning methods and four deep learning methods) on three widely used datasets (i.e. MAPS, BACH10 and TRIOS) in terms of F-measure ({F}_{1}) values. The experimental results show that the proposed MPE method provides the best overall performance against other existing methods.

Coherent fundamental-harmonic interactions in a compressible shear layer via integral nonlinear instability approach

A physics-based integral approach is adopted here to develop a theory for studying bi-modal excitation of the shear layer of a Mach 1.5 planar jet. The transverse shapes of the mean flow quantities are given by analytical functions modeling the corresponding jet experiment and Reynolds-averaged Navier–Stokes solution. The transverse shapes of the frequency modes of the coherent large-scale structure are obtained as the eigenfunctions of the locally parallel linear stability theory. The Navier–Stokes equations are then reduced to a set of ordinary differential equations. The solution of this set, subject to the initial conditions, describes the nonlinear interaction among the excited frequency modes, as well as their interaction with the mean flow and the background turbulence. Our analysis shows that the time-averaged interaction among the modes is non-zero only if the two frequency modes are related to each other by the fundamental-harmonic frequency. We label the fundamental mode here, “f,” as the most amplified mode developing nonlinearly along the jet in the absence of other imposed modes. We then use the resulting theory to study the effect of bimodal excitation by harmonically related pairs (f, f/2) or (f, 2f) to see under which conditions this bimodal excitation can suppress the fundamental. We found that the combination of fundamental and harmonic (f, 2f) can effectively reduce the fundamental at an optimized phase lag. By viewing the fundamental as the most dominant sound source in the jet, it is, thus, possible to reduce the jet noise via bi-modal excitation.

Steady-State Visual Evoked Potential-Based Brain-Computer Interface Using a Novel Visual Stimulus with Quick Response (QR) Code Pattern.

Steady-state visual evoked potential (SSVEP)-based brain-computer interface (BCI) systems suffer from low SSVEP response intensity and visual fatigue, resulting in lower accuracy when operating the system for continuous commands, such as an electric wheelchair control. This study proposes two SSVEP improvements to create a practical BCI for communication and control in disabled people. The first is flicker pattern modification for increasing SSVEP response through mixing (1) fundamental and first harmonic frequencies, and (2) two fundamental frequencies for an additional number of commands. The second method utilizes a quick response (QR) code for visual stimulus patterns to increase the SSVEP response and reduce visual fatigue. Eight different stimulus patterns from three flickering frequencies (7, 13, and 17 Hz) were presented to twelve participants for the test and score levels of visual fatigue. Two popular SSVEP methods, i.e., power spectral density (PSD) with Welch periodogram and canonical correlation analysis (CCA) with overlapping sliding window, are used to detect SSVEP intensity and response, compared to the checkerboard pattern. The results suggest that the QR code patterns can yield higher accuracy than checkerboard patterns for both PSD and CCA methods. Moreover, a QR code pattern with low frequency can reduce visual fatigue; however, visual fatigue can be easily affected by high flickering frequency. The findings can be used in the future to implement a real-time, SSVEP-based BCI for verifying user and system performance in actual environments.

Harmonic Balance/Full-Wave Analysis of Wearable Harmonic Transponder for IoT Applications

The article presents a novel design of a compact wearable harmonic transponder with double-plane symmetry, composed of a dual-band patch-type antenna loaded by an HSMS-2820 Schottky diode, operated as a proof of concept at ISM UHF 869 and 1734 MHz frequencies. The antenna is analyzed and optimized for a minimum ground plate size by means of the CST Microwave Studio electromagnetic simulator, and its reflection coefficient is incorporated into the equivalent circuit model for a combined harmonic balance (HB) and full-wave analysis using the AWR Microwave Office commercial simulator. The transponder performance, including the complex input impedance matching and conversion loss (CL) between the fundamental and second harmonic frequencies on the diode, was evaluated both in free space and when attached to a human muscle phantom. The total harmonic transponder CL, including diode CL, antenna transponder gains, and impedance mismatching, is 6.2 dB for an excitation power of −25 dBm at the antenna–diode interface. The measured reading distances are 9.0 and 8.8 m for equivalent isotropically radiated power (EIRP) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=20$ </tex-math></inline-formula> dBm when the transponder is placed in free space and on the human body, respectively. As a means of machine-to-person communication, the transponder is suitable for the Internet of Things (IoT) concept, e.g., for the identification of pedestrians in traffic, i.e., in a complex environment with unwanted radiation clutter and multipath fading.