Rectangular Waveform Research Articles

Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation

The recently proposed orthogonal time–frequency–space (OTFS) modulation technique was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) over delay-Doppler channels. In this paper, we first derive the explicit input–output relation describing OTFS modulation and demodulation (mod/demod). We then analyze the cases of: 1) ideal pulse-shaping waveforms that satisfy the bi-orthogonality conditions and 2) rectangular waveforms which do not. We show that while only inter-Doppler interference (IDI) is present in the former case, additional inter-carrier interference (ICI) and inter-symbol interference (ISI) occur in the latter case. We next characterize the interferences and develop a novel low-complexity yet efficient message passing (MP) algorithm for joint interference cancellation (IC) and symbol detection. While ICI and ISI are eliminated through appropriate phase shifting, IDI can be mitigated by adapting the MP algorithm to account for only the largest interference terms. The MP algorithm can effectively compensate for a wide range of channel Doppler spreads. Our results indicate that OTFS using practical rectangular waveforms can achieve the performance of OTFS using ideal but non-realizable pulse-shaping waveforms. Finally, simulation results demonstrate the superior error performance gains of the proposed uncoded OTFS schemes over OFDM under various channel conditions.

New Developments to Reduce Arc Blow during SMAW of Pipelines

In some cases, magnetic blow does not allow using direct current for shielded metal arc welding. This is especially true for repair work on pipelines after magnetic flaw detection. Alternating current is useful to control magnetic arc blow during welding. The most promising results give technologies using alternating current with a rectangular waveform. However, the advantages of this method have not been used until now. The main goal of this study is to determine the influence of the parameters of the arc on its stability and the metal transfer mode during shielded metal arc welding under perturbing action of the magnetic field. The proposed methodology of experimental research allowed identifying the cause of arc extinction using direct current electrode positive. This is due to displacement of molten droplets of metal by the magnetic field from of the uneven melted electrode coating and its subsequent separation. This problem was solved using alternating current with the square waveform pulse mode at a frequency of 500 Hz. The amplitude-time parameters of the current pulses provide stabilization of the arc and volume of the molten electrode metal.

Non-rectangular waveforms are more charge-efficient than rectangular one in eliciting network-mediated responses of ON type retinal ganglion cells

Objective. For individuals blinded by outer retinal degenerative diseases, retinal prostheses would be a promising option to restore sight. Unfortunately, however, the best performance of existing devices is still far removed from normal vision. One possible reason for the shortcoming is thought to be suboptimal stimulation conditions such as the waveform shape of electric stimulus. In this study, we explored the effects of varying waveforms on network-mediated responses arising in retinal ganglion cells (RGCs). Approach. We used a cell-attached patch clamp technique to record RGC spiking activities in the isolated mouse retina. ON alpha RGCs were targeted by soma size and their light responses to stationary spot flashes. Spiking in targeted RGCs was measured in response to an epiretinally-delivered cathodal current pulse in four waveforms: rectangular, center triangular, increasing and decreasing ramp shapes. Each waveform was tested at three durations (20, 10, and 5 ms) with adjusted amplitude for a range of total charges (50–400 nC). Main results. ON alpha RGCs always generated two bursts of spikes in responses to all stimuli conditions we tested. However, at a given charge, effects of differing waveforms were distinct in the two bursts. For the first burst, the increasing ramp was most effective among the four waveforms (p < 0.05 for all pairwise comparisons with other waveforms). For example, in responses arising from 20 ms-long stimuli, the increasing ramp evoked ~44% more spikes on average than the rectangular shape which is the typical choice of neural stimulation. Also, the rectangular stimulus evoked the weakest response in the delayed burst arising from pulses of every duration. For instance, 20 ms-long stimuli in the three non-rectangular waveforms showed ~23% or more increment in spike counts compared to response arising from the rectangular one; but there was no statistical difference in response magnitudes across the non-rectangular waveforms. Significance. Although the rectangular waveform has been primarily used in retinal prostheses our results indicate that rectangular stimulus is not optimal for network-mediated responses of ON alpha RGCs. Instead, non-rectangular waveforms evoke stronger responses at a given charge, indicating higher charge-efficiency. Therefore, non-rectangular waveforms are expected to enhance clinical efficacy of retinal prostheses.

Superharmonic vibration and its reduction in SSD control by increase of voltage inversion time

The semi-active synchronized switch damping (SSD) approach has been widely used in vibration suppression owing to its many advantages compared with the active and passive approaches. The SSD method is realized by switching the voltage on the piezoelectric patch embedded in the structure, synchronically with the vibration of the mode to be controlled. Although good control performance can be obtained in the targeted mode, vibrations of high-order harmonic frequencies are usually excited due to the rectangular waveform of the switched actuator voltage because of infinitesimal inversion time, as observed in the previous experiments. This drawback of the SSD method has greatly hindered its application in practical engineering structures. In order to overcome this drawback, the authors propose a new method in this study to suppress the high-order harmonic components in the switched voltage by increasing the inversion time of the voltage. The theoretical expressions of the switched voltage and the dynamic response of the structure were formulated for the cases with finite voltage inversion time. The theoretical results show that increasing the inversion time may weaken the vibration control effect of the targeted mode, but it can significantly reduce the excitation force of the high-order harmonic components. When the inversion time is half of the period of the targeted mode, all the high-order harmonic components in the actuator voltage are completely erased and the control force of the targeted mode decreases by 21%. An experimental setup of a flexible beam was used to verify the theoretical results of the switched voltage and control performance under different inversion time.

A Frequency-Folded ADC Channelizer With Digital Equalization and Relaxed Anti-Alias Filtering

This paper presents a mixed-signal broadband channelizer that employs digital post-processing for reducing the analog anti-aliasing requirement in an N-path frequency-folding receiver architecture. In the approach, a signal of bandwidth $\mathsf {Nf_{LO}/2}$ is downconverted using $\mathsf {N}$ phases of a rectangular pulse waveform at a fundamental frequency of $\mathsf {f_{LO}}$ with a duty-cycle of $\mathsf {1/N}$ . All parts of the input are aliased onto a baseband signal of bandwidth $\mathsf {f_{LO}/2}$ , which is low-pass filtered and applied to an analog-to-digital converter (ADC), with each path employing identical sampling clocks. A digital equalization technique is described that can be utilized to recover the complete broadband input similar to a high-speed ADC, or recover each channelized and down-converted sub-band, similar to a bank of mixers while performing digital-domain harmonic and image rejection. The equalization technique is analyzed in the context of a previously demonstrated channelizer IC. It is shown that the application of the equalization can result in 50-dB broadband SNR over 1-GHz input bandwidth, using eight paths with 10-bit sub-ADCs, with third-order anti-aliasing analog filters. Signal reconstruction methodologies for a multi-tone input and for signals that are aperiodic in the processing window are also described.

Class-E Rectifiers and Power Converters: The Operation of the Class-E Topology as a Power Amplifier and a Rectifier with Very High Conversion Efficiencies

In the late 1970s, interest in reducing the value and size of reactive components motivated power supply specialists to operate dc-to-dc converters at hundreds of kilohertz or even megahertz frequencies. Passive energy storage (mainly magnetics) is the dominant factor in the size of power electronics and also limits its cost, reliability, and dynamic response. With the goals of miniaturization and improved control bandwidth, researchers had to face the frequency-dependent turn-on and turn-off losses associated with the use of rectangular waveforms in the hard-switched topologies of that time. Similar to approaches for RF/microwave power amplifiers (PAs), the introduction of resonant circuits allowed shaping either a sinusoidal voltage or current, with parasitic reactive elements absorbed by the topology in the neighborhood of the switching frequency. The resulting resonant power converters, obtained by cascading a dc-to-ac resonant inverter with a high-frequency rectifier, first transform the dc input power into controlled ac power and then convert it back into the desired dc output [1].

A History of Switching-Mode Class-E Techniques: The Development of Switching-Mode Class-E Techniques for High-Efficiency Power Amplification

Improving the efficiency of vacuum-tube amplifiers by properly approximating the anode voltage and current waveforms was discussed and first demonstrated in the late 1910s. Researchers found that, if either the tube plate current or voltage is zero when the other is nonzero, then the loss must be zero and the efficiency equal to 100%. The required rectangular waveforms could be achieved by inserting harmonic resonators in the anode circuit and tuning them to the odd and/or even harmonics of the fundamental frequency (now called class-F). Three decades later, however, Model et al. demonstrated that this is not the only way to improve power amplifier efficiency: very high anode efficiency can be achieved without special tuning of the anode circuit at the particular harmonic, provided that the asymmetrical voltage and current waveforms are due to reactive impedances at the harmonics [1].

The Influence of the External Signal Modulation Waveform and Frequency on the Performance of a Photonic Forced Oscillator.

Photonic crystals have been an object of interest because of their properties to inhibit certain wavelengths and allow the transmission of others. Using these properties, we designed a photonic structure known as photodyne formed by two porous silicon one-dimensional photonic crystals with an air defect between them. When the photodyne is illuminated with appropriate light, it allows us to generate electromagnetic forces within the structure that can be maximized if the light becomes localized inside the defect region. These electromagnetic forces allow the microcavity to oscillate mechanically. In the experiment, a chopper was driven by a signal generator to modulate the laser light that was used. The driven frequency and the signal modulation waveform (rectangular, sinusoidal or triangular) were changed with the idea to find optimal conditions for the structure to oscillate. The microcavity displacement amplitude, velocity amplitude and Fourier spectrum of the latter and its frequency were measured by means of a vibrometer. The mechanical oscillations are modeled and compared with the experimental results and show good agreement. For external frequency values of 5 Hz and 10 Hz, the best option was a sinusoidal waveform, which gave higher photodyne displacements and velocity amplitudes. Nonetheless, for an external frequency of 15 Hz, the best option was the rectangular waveform.

Comparison of ambiguity function of eigenwaveform to wideband and pulsed radar waveforms: a comprehensive tutorial

The authors present a comprehensive research tutorial on the ambiguity function (AF) of eigenwaveform for extended targets compared to AFs of common radar waveforms (e.g. wideband and pulsed waveforms). They present new findings of AF properties that contradict classical AF results for the point target assumption. It is shown that the AF properties (peak and volume) for an extended target are not constant thereby contradicting AF properties of waveforms for a point target. They investigate corresponding AFs and note many advantages (or few disadvantages) of using eigenwaveform compared to classical wideband and rectangular-pulsed waveforms. They investigate unambiguous range, range resolution, Doppler resolution, and detection probability of various waveforms for insightful engineering trade-offs. For illustration, they utilise two extended target models to show that these parameters are not only functions of the transmit waveform but also of the nature of the target. They use both single-pulse and pulse-train waveforms to produce AFs to illustrate the effect on Doppler and range ambiguities and resolutions. Finally, they investigate range-Doppler map (RDM) applications of the traditional waveforms and compared them with eigenwaveform RDM. They conclude that the eigenwaveform is superior in probability of detection and Doppler considerations compared to wideband and rectangular waveforms.

Properties of dynamic magnetic loss of ferrite

The B-H loop of ferrite becomes narrower with a decrease in the excitation frequency. However, even at frequencies lower than 1 kHz, the B-H loop exhibits a certain minimum width, which is referred to as the (DC) hysteresis loop, and its area corresponds to the hysteresis loss. The dynamic magnetic loss is obtained by subtracting the hysteresis loss from the B-H loop area measured at a frequency above 1–10 kHz. The temperature characteristics of the hysteresis and dynamic magnetic losses are determined to be experimentally different, which suggests that the mechanism for the generation of dynamic magnetic loss is not exactly the same as that for the hysteresis loss. The dynamic magnetic loss is expressed using the dynamic magnetic loss parameter, which is a function of B and its time derivative, dB/dt. The dynamic magnetic loss parameter is measured under excitation with a rectangular waveform voltage. A ferrite core of TDK PC47 was used and the maximum magnetic flux density Bm, was set to 350 mT. The measured dynamic magnetic loss parameter was experimentally verified to be one of the intrinsic characteristics of ferrite and was also validated for cases of excitation with sinusoidal waveform voltages.

Multiple String LED Driver With Flexible and High-Performance PWM Dimming Control

The main objectives in driving multiple LED strings include achieving uniform current control and high performance PWM dimming for all strings. This work proposes a new multiple string LED driver to achieve not only current balance, but also flexible and wide range PWM dimming ratio for each string. A compact single-inductor multiple-output topology is adopted in the driver, accompanied by synchronous integrators and variable dimming frequency, to achieve both high efficiency and high performance dimming. By using the proposed variable dimming frequency scheme, high dimming frequency is applied to a string with high dimming ratio, which helps to maintain the deviation of LED string current in an acceptable range, while low dimming frequency is applied to a string with low dimming ratio, which helps to achieve rectangular LED current waveform. Meanwhile, the new time multiplexing control scheme automatically optimizes the LED string's bus voltages, thus minimizes each string's power loss. A three string LED driver prototype is constructed to validate the effectiveness of the peoposed control scheme, where the three strings can have different dimming ratios between 4% and 100%.

Research of magnetic self-balance used in a repetitive high voltage rectangular waveform pulse adder

Compared with a sinusoidal operation, pulsed operation has more homogeneity and more efficiency in dielectric barrier discharge. In this paper, an improved pulse adder is designed and assembled to create repetitive high voltage rectangular pulses when resistive loads or capacitive loads exist. Beyond the normal pulse adder based on solid-state switches, additional metal–oxide–semiconductor field effect transistors are used in each stage for a faster falling edge. Further, the voltage difference between stages is eliminated by balancing windings. In this paper, we represent our theoretical derivation, software simulations and hardware experiments on magnetic self-balance. The experiments show that the voltage difference between stages is eliminated by balancing windings, which matches the result of simulations with almost identical circuits and parameters.

Photonically assisted microwave waveform generation by gain-transparent SBS-induced carrier processing.

We propose and experimentally demonstrate a new approach to generate microwave waveforms by phase modulation and optical carrier phase processing based on gain-transparent stimulated Brillouin scattering (SBS). By properly adjusting the SBS-induced-phase shift on the carrier and the following group velocity dispersion, microwave waveforms with controllable repetition rates and temporal profiles can be generated. In the experiment, we have successfully generated triangular waveforms at repetition rates of 5.64 and 7.87GHz, and rectangular waveforms at repetition rates of 5.04 and 7.01GHz.

Focus-before-detection radar signal processing: part i—challenges and methods

During the World War II (WWII), radar was invented as an all-day, all-weather, long-range sensor. Over the past 75 years or so, radar has acted as the clairvoyance and clairaudience of humans and has had wide applications in both defense and civilian fields, e.g., surveillance, reconnaissance, fire control, border monitoring, collision avoidance, and traffic control. Along with radar development, radar signal processing (RSP) always plays an important role. In 1943, North pointed out that the matched filter should be the foundation of radar to detect targets from echoes generated by the known transmitting waveform. In 1950, Woodward and Davies introduced the Bayesian statistics theory into the RSP field and proposed the constant false alarm ratio (CFAR) rule for target detection. Based on matched filtering and the CFAR rule, the embryonic framework of classic RSP has been formed and used thus far. In 1953, Woodward further proposed an ambiguity function as a useful tool to evaluate the range and Doppler discrimination abilities of a transmitting waveform, which paves the foundation for radar waveform design. Furthermore, to deal with the tradeoff between large transmitting energy and high range resolution, the early unmodulated rectangular waveform has been replaced by more waveforms with a large time-bandwidth product (TBP), such as linear frequency modulation (LFM) and phase-coded waveforms. These waveforms with large TBP have been widely used to realize the range compression via matched filter.

Full-Bridge Modular Multilevel Submodule-Based High-Voltage Bipolar Pulse Generator With Low-Voltage DC, Input for Pulsed Electric Field Applications

High-voltage (HV) pulse generators (PGs) are the core of pulsed electric field applications. Applying HV pulses produces electrical pores in a biological cell membrane, in which if the size of the pores increases beyond a critical size, the cell will not survive. This paper proposes a new HV-PG based on the modular multilevel converter with full-bridge submodules (FB-SMs). In order to alleviate the need of complicated sensorless or sensor-based voltage balancing techniques for the FB-SM capacitors, a dedicated self-regulating charging circuit is connected across each FB-SM capacitor. The individual capacitor charging voltage level is obtained from three successive stages, namely, convert the low-voltage dc input voltage to a high-frequency square ac voltage, increase the ac voltage level via a nanocrystalline step-up transformer, and rectify the secondary transformer ac voltage via a diode FB rectifier. The HV bipolar pulses are formed across the load in a fourth stage through series connected FB-SMs. The flexibility of inserting and bypassing the FB-SM capacitors allows the proposed topology to generate different pulse-waveform shapes, including rectangular waveforms with specifically reduced ${dv/dt}$ and ramp pulses. The practical results, from a scaled-down experimental rig with five FB-SMs and a 1-kV peak-to-peak pulse output, validate the proposed topology.

Dual use of rectangular and triangular waveforms in voltammetry using a carbon fiber microelectrode to differentiate norepinephrine from dopamine

While dopamine (DA) may be clearly detected by voltammetric techniques such as fast-scan cyclic voltammetry (FSCV) in the heavily-innervated striatum, the differentiation of DA from other monoamines, including norepinephrine (NE) and serotonin (5-HT), is crucial for further applications outside of the striatum. We show that using normal pulse voltammetry (NPV) with 0.1V to 0.3V rectangular pulses can differentiate between NE and DA. While the major electrochemical current of NE and DA is obtained on 0.2V rectangular pulse of NPV, the relative current on 0.1V pulse was higher for DA than NE. It was possible to differentiate NE from DA by electrochemical current on three NPV pulses using simple mathematics of sequential equation. Since FSCV obtains a larger current value and less noisy results than NPV, we alternately recorded both. The electrochemical current data of NPV was combined with FSCV for principal component regression (PCR) analysis. The estimated value was evaluated by percent error and correlation coefficient from the true concentration, and the slope of the linear regression line. Estimation by sequential equation using NPV results could differentiate NE from DA, while PCR without NPV current data could not. PCR including NPV current data also could differentiate NE from DA. In this study, we compared the performance of electrochemical recordings with rectangular and triangular waveforms under the same conditions, and the advantages and disadvantages became very clear. Together with our previous finding of significant differentiation of pH changes from monoamines on rectangular pulses of NPV, the combined use of rectangular and triangular pulses would improve the molecular identification of monoamines in the brain using voltammetric recording.

Computational Stimulation of the Basal Ganglia Neurons with Cost Effective Delayed Gaussian Waveforms.

Deep brain stimulation (DBS) has compelling results in the desynchronization of the basal ganglia neuronal activities and thus, is used in treating the motor symptoms of Parkinson's disease (PD). Accurate definition of DBS waveform parameters could avert tissue or electrode damage, increase the neuronal activity and reduce energy cost which will prolong the battery life, hence avoiding device replacement surgeries. This study considers the use of a charge balanced Gaussian waveform pattern as a method to disrupt the firing patterns of neuronal cell activity. A computational model was created to simulate ganglia cells and their interactions with thalamic neurons. From the model, we investigated the effects of modified DBS pulse shapes and proposed a delay period between the cathodic and anodic parts of the charge balanced Gaussian waveform to desynchronize the firing patterns of the GPe and GPi cells. The results of the proposed Gaussian waveform with delay outperformed that of rectangular DBS waveforms used in in-vivo experiments. The Gaussian Delay Gaussian (GDG) waveforms achieved lower number of misses in eliciting action potential while having a lower amplitude and shorter length of delay compared to numerous different pulse shapes. The amount of energy consumed in the basal ganglia network due to GDG waveforms was dropped by 22% in comparison with charge balanced Gaussian waveforms without any delay between the cathodic and anodic parts and was also 60% lower than a rectangular charged balanced pulse with a delay between the cathodic and anodic parts of the waveform. Furthermore, by defining a Synchronization Level metric, we observed that the GDG waveform was able to reduce the synchronization of GPi neurons more effectively than any other waveform. The promising results of GDG waveforms in terms of eliciting action potential, desynchronization of the basal ganglia neurons and reduction of energy consumption can potentially enhance the performance of DBS devices.

Hue shifts produced by temporal asymmetries in chromatic signals depend on the alignment of the first and second harmonics.

When M- or L-cone-isolating sawtooth waveforms flicker at frequencies between 4 and 13.3 Hz, there is a mean hue shift in the direction of the shallower sawtooth slope. Here, we investigate how this shift depends on the alignment of the first and second harmonics of sawtooth-like waveforms. Below 4 Hz, observers can follow hue variations caused by both harmonics, and reliably match reddish and greenish excursions. At higher frequencies, however, the hue variations appear as chromatic flicker superimposed on a steady light, the mean hue of which varies with second-harmonic alignment. Observers can match this mean hue against a variable-duty-cycle rectangular waveform and, separately, set the alignment at which the mean hue flips between reddish and greenish. The maximum hue shifts were approximately frequency independent and occurred when the peaks or troughs of the first and second harmonics roughly aligned at the visual input-consistent with the hue shift's being caused by an early instantaneous nonlinearity that saturates larger hue excursions. These predictions, however, ignore phase delays introduced within the chromatic pathway between its input and the nonlinearity that produces the hue shifts. If the nonlinearity follows the substantial filtering implied by the chromatic temporal contrast-sensitivity function, phase delays will alter the alignment of the first and second harmonics such that at the nonlinearity, the waveforms that produce the maximum hue shifts might well be those with the largest differences in rising and falling slopes-consistent with the hue shift's being caused by a central nonlinearity that limits the rate of hue change.

Repetitive Impulse Withstand Performance of Metal–Oxide Varistors

This study focuses on the relationship between test current waveforms and impulse withstand capability of metal–oxide varistors (MOVs) (withstand energy, current density, and the number of withstand shots) in repetitive impulse application and discusses the mechanical and electrical failure mechanisms. The performance and relationship of withstand energy and withstand shots for conventional 2-ms rectangular waveform, 4/10- $\mu $ s, and newly introduced 10/350- $\mu $ s impulses are investigated. Notably, the 10/350- $\mu $ s waveform has aspects of both steep rise impulse and long duration impulse. In addition, the varistor voltage change after repetitive impulse applications for 10/350- $\mu $ s and 4/10- $\mu $ s waveforms is investigated. There is no direct relationship between varistor voltage drop and repetitive withstand shots. However, ${V}_{1 {\rm mA}}$ and ${V}_{0.01 {\rm mA}}$ changes indicate the degree of MOV damage caused by the impulses and are important factors to monitor progressive damage. Based on these findings, optimal MOV design is discussed.

ANALYTICAL CALCULATIONS OF ELECTROMAGNETIC QUANTITIES FOR SLOTTED BRUSHLESS MACHINES WITH SURFACE-INSET MAGNETS

In this paper, two-dimensional (2-D) analytical magnetic field calculations are used to compute crucial quantities of Brushless permanent-magnet (PM) machines with surface-inset PMs. The analytical magnetic field distribution is based on the subdomain technique in which the slotting and tooth-tip effects have been considered. It includes both different magnetization patterns (e.g., radial, parallel and Halbach) and different spatial distribution of winding (e.g., concentrated and distributed with one or more layers). The saturation effect of the magnetic circuit is neglected. In this investigation, the phase and line induced back electromotive force (EMF) waveforms, electromagnetic/cogging/reluctance torques, self-/mutual-inductances and unbalanced magnetic forces (UMFs) have been analytically calculated. The analytical expressions can be used for Brushless machines having surface-inset PMs with any radius-independent magnetization pattern. In this study, two slotted Brushless PM machines with surface-inset PMs have been selected to evaluate the efficacy of the analytical expressions by comparing the results with those obtained by the finite-element method (FEM). One of the case studies is a 9-slots/8-poles Brushless DC (BLDC) machine with radially magnetized PMs, non-overlapping all teeth wound winding and six-step rectangular armature current waveforms. The other is a 15-slots/4-poles Brushless AC (BLAC) machine with Halbach magnetization PMs, double-layer overlapping winding and sinusoidal armature current waveforms.