Oscillation Waveform Research Articles

DETERMINING NEUTRON STAR MASSES AND RADII USING ENERGY-RESOLVED WAVEFORMS OF X-RAY BURST OSCILLATIONS

Simultaneous, precise measurements of the mass $M$ and radius $R$ of neutron stars can yield uniquely valuable information about the still uncertain properties of cold matter at several times the density of nuclear matter. One method that could be used to measure $M$ and $R$ is to analyze the energy-dependent waveforms of the X-ray flux oscillations seen during some thermonuclear bursts from some neutron stars. These oscillations are thought to be produced by X-ray emission from hotter regions on the surface of the star that are rotating at or near the spin frequency of the star. Here we explore how well $M$ and $R$ could be determined by generating, and analyzing using Bayesian techniques, synthetic energy-resolved X-ray data that we produce assuming a future space mission having 2--30 keV energy coverage and an effective area of 10 m$^2$, such as the proposed \textit{LOFT} or \textit{AXTAR} missions. We find that if the hot spot is within 10$^\circ$ of the rotation equator, both $M$ and $R$ can usually be determined with an uncertainty of about 10% if there are $10^6$ total counts from the spot, whereas waveforms from spots within 20$^\circ$ of the rotation pole provide no useful constraints. These constraints can usually be achieved even if the burst oscillations vary with time and data from multiple bursts must be used to obtain 10$^6$ counts from the hot spot. This is therefore a promising method to constrain $M$ and $R$ tightly enough to discriminate strongly between competing models of cold, high-density matter.

The Electro-Oxidation of Ethylene Glycol on Platinum over a Wide pH Range: Oscillations and Temperature Effects

We report a comprehensive study of the electro-oxidation of ethylene glycol (EG) on platinum with emphasis on the effects exerted by the electrolyte pH, the EG concentration, and temperature, under both regular and oscillatory conditions. We extracted and discussed parameters such as voltammetric activity, reaction orders (with respect to [EG]), oscillation’s amplitude, frequency and waveform, and the evolution of the mean electrode potential at six pH values from 0 to 14. In addition, we obtained the apparent activation energies under several different conditions. Overall, we observed that increasing the electrolyte pH results in a discontinuous transition in most properties studied under both voltammetric and oscillatory regimes. As a relevant result in this direction, we found that the increase in the reaction order with pH is mediated by a minimum (~ 0) at pH = 12. Furthermore, the solution pH strongly affects all features investigated, c.f. the considerable increase in the oscillatory frequency and the decrease in the, oscillatory, activation energy as the pH increase. We suggest that adsorbed CO is probably the main surface-blocking species at low pH, and its absence at high pH is likely to be the main reason behind the differences observed. The size of the parameter region investigated and the amount of comparable parameters and properties presented in this study, as well as the discussion that followed illustrate the strategy of combining investigations under conventional and oscillatory regimes of electrocatalytic systems.

Testing the rotating hotspot model using X-ray burst oscillations from 4U 1636−536

Abstract Precise and accurate measurements of neutron star masses and radii would provide valuable information about the still uncertain properties of cold matter at supranuclear densities. One promising approach to making such measurements involves an analysis of the X-ray flux oscillations often seen during thermonuclear (type 1) X-ray bursts. These oscillations are almost certainly produced by emission from hotter regions on the stellar surface modulated by the rotation of the star. One consequence of the rotation is that the oscillation should appear earlier at higher photon energies than at lower energies. Ford found compelling evidence for such a hard lead in the tail oscillations of one type 1 burst from Aql X-1. Subsequently, Muno, Özel & Chakrabarty analysed oscillations in the tails of type 1 bursts observed using the Rossi X-ray Timing Explorer. They found significant evidence for variation of the oscillation phase with energy in 13 of the 51 oscillation trains they analysed and an apparent linear trend of the phase with energy in six of nine average oscillation profiles produced by folding the energy-resolved oscillation waveforms from five stars and then averaging them in groups. In four of these nine averaged energy-resolved profiles, the oscillation appeared to arrive earlier at lower energies than at higher energies. Such a trend is inconsistent with a simple rotating hotspot model of the burst oscillations and, if confirmed, would mean that this model cannot be used to constrain the masses and radii of these stars and would raise questions about its applicability to other stars. We have therefore re-analysed individually the oscillations observed in the tails of the four type 1 bursts from 4U 1636−536 that, when averaged, provided the strongest evidence for a soft lead in the analysis by Muno et al. We have also analysed the oscillation observed during the superburst from this star. We find that the data from these five bursts, treated both individually and jointly, are fully consistent with a rotating hotspot model. Unfortunately, the uncertainties in these data are too large to provide interesting constraints on the mass and radius of this star.

PERSONALIZED TRAITS MONITORING USING A NEURAL NETWORK BASED ON OSCILLOMETRIC MEASUREMENTS

Oscillometric method uses a pressure sensor instead of a stethoscope to record the pressure oscillations within the cuff. Oscillations observed from the pressure sensor show personalized traits of systolic pressure, which indicates the maximum amount of work the heart has to perform per stroke in order to move blood through the arteries. For a given person, the oscillation waveforms extracted from the cuff pressure have an oscillation pattern that varies in size over time. Thus, to extract uniform features from a given person, we normalize the variability of the corresponding oscillation patterns for different frequencies, and evaluate systolic blood pressure using a feedforward neural network based on the extracted features. The validity of measuring systolic blood pressure with a neural network was compared with the average values of systolic pressure obtained by two nurses using the auscultatory method. The recognition performance was found to be 98.2% for ±20 mmHg, 93.5% for ±15 mmHg, and 82.3% for ±10 mmHg based on the difference between the systolic pressures measured by the auscultation method and the proposed method with a neural network. The collected database for our experiment includes 85 participants with ages ranging from 10–80 years. In this paper, we present a novel personalized traits monitoring system that can monitor personalized traits of systolic blood pressure. This study can serve as a foundation for the diagnosis and management of isolated systolic hypertension.

Fault Diagnosis of Bearing in Mechanical Drive System Using Wavelet Analysis

Exploring a proper wavelet base function to characterize fault information of mechanical equipment is a big problem when wavelet analysis is applied into the field of fault diagnosis.Improper wavelet base function can dilute fault information, which will cause difficulties in fault diagnosis , based on the principle that the wavelet domain oscillation waveform are similar to the detected signal components, a proper wavelet base function was selected; through wavelet transform on the acceleration signals of the fault bearing, the spectrum chart of fault signals and the frequency characteristics of fault bearing were obtained. The experimental result shows that this method has a great advantage over extracting character signals.

Evaluation of breakdown characteristics of CO2 gas for non-standard lightning impulse waveforms - breakdown characteristics under double-frequency oscillation waveforms and single-frequency oscillation waveforms in the presence of bias voltage

SF6 gas, an insulation medium used for gas insulated switchgear (GIS), has a high global warming potential, hence the search for an effective alternative is required from an environmental perspective. The authors focus particularly on CO2 gas, which has a low global warming potential, as one of these potential alternatives. In order to apply this CO2 gas to actual equipment, the insulation characteristics for overvoltage waveforms generated in an actual field (called non-standard lightning impulse waveforms) must be obtained. Accordingly, in previous studies, the insulation characteristics for single-frequency oscillation waveforms were experimentally obtained in the quasi-uniform electric field, which is the basis when performing the insulation design of GIS, and its evaluation method was examined. In this paper, to further elaborate the evaluation method established thus, the insulation characteristics in relation to complex oscillatory waveforms generated in actual substations, e.g. double-frequency oscillation waveforms and single-frequency oscillation waveforms on which a dc component (bias voltage) that remains due to the superimposed operation of a switching device, were obtained. Consequently, the results obtained indicated that negative polarity waveforms were more severe in terms of electrical insulation under the double frequency oscillation waveforms as well as under the single-frequency oscillation waveforms. Therefore, when considering a dielectric strength, it is reasonable to conduct experiments using negative-polarity waveforms for the complex oscillatory waveforms, such as the double frequency oscillation waveforms. Furthermore, a study was performed on a method of evaluating insulation characteristics for non-standard lightning impulse waveforms of the CO2 gas gap via a comprehensive approach using the results including the previous ones. As a result, as in the case of studies conducted previously on SF6 gas, the insulation characteristics, including complex oscillatory waveforms generated in actual power systems, could be expressed by a single characteristic line by using the parameter of duration.

Evaluation of breakdown characteristics of n2 gas for non-standard lightning impulse waveforms - breakdown characteristics under double-frequency oscillation waveforms and pressure-distance characteristics

SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> gas, an insulation medium used for gas insulated switchgear (GIS), is known for its high global warming potential, hence the search for an effective alternative from an environmental perspective. As a potential alternative, the authors are focusing on N2 gas. To use this N2 gas for actual GIS, the insulation characteristics for actual overvoltage waveforms generated in the field (non-standard lightning impulse waveforms) must be obtained. To do so, the earlier study experimentally obtained and evaluated the insulation characteristics for single-frequency oscillation waveforms as a representative among nonstandard lightning impulse waveforms under the quasi-uniform electric field, which was considered to be a basis for the insulation design of GIS. The present study obtained the insulation characteristics for double-frequency oscillation waveforms to investigate surge waveforms generated in substations in more detail. Consequently, it emerged that negative polarity waveforms were more severe in terms of insulation, as was the case for single-frequency oscillation waveforms. The insulation performance was consistently higher than that for the standard lightning impulse waveforms, which were 1.08 to 1.09 times. In other words, it was confirmed that the insulation specification could be rationalized by about 10%, even for complex oscillation waveforms, such as those of double-frequency oscillation. Furthermore, a study was conducted on the influence of the gas pressure and gap length for single-frequency oscillation waveforms. Consequently, it emerged that the results under the basic experimental conditions were likely to be applicable to actual GIS under wider-ranging conditions.

Laser-Assisted Control of Electrical Oscillation in VO2Thin Films Grown by Pulsed Laser Deposition

By adjusting an optical power of an infrared laser illuminating a vanadium dioxide (VO2) thin film, we have demonstrated a laser-assisted control of a field-induced electrical oscillation (FIEO) in a two-terminal device based on a VO2 thin film fabricated by pulsed laser deposition. Through the control of the laser illumination power, the FIEO could be switched on or off with a fixed low DC bias voltage applied to the device that was connected in series with a standard resistor, and its frequency could be linearly tuned until the extinguishment of the oscillation. The tuning sensitivity of the oscillation frequency was measured as ∼21.28 kHz/mW, showing good linearity with an R-squared value of 0.99288. In addition, the peak-to-peak amplitudes of the oscillation waveforms could also be linearly controlled by adjusting the illumination power.

Laser-Assisted Control of Electrical Oscillation in VO2 Thin Films Grown by Pulsed Laser Deposition

By adjusting an optical power of an infrared laser illuminating a vanadium dioxide (VO2) thin film, we have demonstrated a laser-assisted control of a field-induced electrical oscillation (FIEO) in a two-terminal device based on a VO2 thin film fabricated by pulsed laser deposition. Through the control of the laser illumination power, the FIEO could be switched on or off with a fixed low DC bias voltage applied to the device that was connected in series with a standard resistor, and its frequency could be linearly tuned until the extinguishment of the oscillation. The tuning sensitivity of the oscillation frequency was measured as ∼21.28 kHz/mW, showing good linearity with an R-squared value of 0.99288. In addition, the peak-to-peak amplitudes of the oscillation waveforms could also be linearly controlled by adjusting the illumination power.

Response of a historical short-span railway bridge to passing trains: 3-D deflections and dominant frequencies derived from Robotic Total Station (RTS) measurements

Based on measurements with a Robotic Total Station (RTS), we computed the displacement characteristics (pattern, amplitude, frequency) of the Gorgopotamos Bridge, a short-span, historical bridge in central Greece, in response to passing trains. Vertical deflections of selected points of the midspan were found to range up to 6mm for heavy cargo trains, exceeding the noise level of 1–2mm, and were analyzed in nearly semi-static and dynamic components. Dominant frequencies of the bridge span, in the range 3.18–3.63Hz, were also computed. Evidence of possible lateral and longitudinal deflections was also found. Measurement noise and quality of results were controlled on the basis of the analysis of apparent displacements of reference points during excitation and of non-excitation intervals, as well as on the basis of structural constraints. The amplitude of measured deflections was found to correlate with the load, and a somewhat distinct oscillation waveform was observed in the cases of large oscillations, despite clipping affecting highly dynamic RTS recordings. Observed deflections are large for modern standards, but reasonable for a >100years old bridge partly destroyed and rebuilt twice during World War II.

Temporal analysis of vascular smooth muscle cell elasticity and adhesion reveals oscillation waveforms that differ with aging

A spectral analysis approach was developed for detailed study of time-resolved, dynamic changes in vascular smooth muscle cell (VSMC) elasticity and adhesion to identify differences in VSMC from young and aged monkeys. Atomic force microscopy (AFM) was used to measure Young's modulus of elasticity and adhesion as assessed by fibronectin (FN) or anti-beta 1 integrin interaction with the VSMC surface. Measurements demonstrated that VSMC cells from old vs. young monkeys had increased elasticity (21.6 kPa vs. 3.5 kPa or a 612% increase in elastic modulus) and adhesion (86 pN vs. 43 pN or a 200% increase in unbinding force). Spectral analysis identified three major frequency components in the temporal oscillation patterns for elasticity (ranging from 1.7 × 10(-3) to 1.9 × 10(-2) Hz in old and 8.4 × 10(-4) to 1.5 × 10(-2) Hz in young) and showed that the amplitude of oscillation was larger (P < 0.05) in old than in young at all frequencies. It was also observed that patterns of oscillation in the adhesion data were similar to the elasticity waveforms. Cell stiffness was reduced and the oscillations were inhibited by treatment with cytochalasin D, ML7 or blebbistatin indicating the involvement of actin-myosin-driven processes. In conclusion, these data demonstrate the efficacy of time-resolved analysis of AFM cell elasticity and adhesion measurements and that it provides a uniquely sensitive method to detect real-time functional differences in biomechanical and adhesive properties of cells. The oscillatory behavior suggests that mechanisms governing elasticity and adhesion are coupled and affected differentially during aging, which may link these events to changes in vascular stiffness.

Confounding factors in brain death: Cardiogenic ventilator autotriggering and implications for organ transplantation

Brain death is characterised by a flaccid, areflexic neurological examination; fixed, dilated and midpoint pupils and total absence of intrinsic respiratory drive. A non-reversible clinical state or brain lesion must also be identified. Integral to brain death diagnosis is loss of respiratory drive. Following terminal brainstem herniation, a cardiovascular hyperdynamic state often occurs. This hyperdynamic state causes cyclical volume displacement within the chest in phase with the cardiac cycle, causing oscillations in gas flow patterns and may be reflected in ventilator airway pressure and flow waveforms. When these flow/pressure waveform oscillations meet or exceed ventilator flow or pressure trigger sensitivity, ventilator breaths may be triggered in the total absence of intrinsic respiratory drive. In a patient with no apparent neurological function who is still triggering ventilator breaths, detailed analysis of ventilator pressure/flow waveforms in context with neurological assessment findings can identify cardiac autotriggering in a brain-dead patient. Undetected, cardiogenic ventilator autotriggering results in prolonged ICU stay and potential loss of transplantable organs. Collaborative practice and aggressive surveillance to determine loss of all neurologic function and evaluate possible autotriggering in this population is paramount and can minimise ICU stay, reduce costs of care, decrease family stress and facilitate recovery of transplantable organs.

Constant flow-driven microfluidic oscillator for different duty cycles.

This paper presents microfluidic devices that autonomously convert two constant flow inputs into an alternating oscillatory flow output. We accomplish this hardware embedded self-control programming using normally closed membrane valves that have an inlet, an outlet, and a membrane-pressurization chamber connected to a third terminal. Adjustment of threshold opening pressures in these 3-terminal flow switching valves enabled adjustment of oscillation periods to between 57 and 360 s with duty cycles of 0.2-0.5. These values are in relatively good agreement with theoretical values, providing the way for rational design of an even wider range of different waveform oscillations. We also demonstrate the ability to use these oscillators to perform temporally patterned delivery of chemicals to living cells. The device only needs a syringe pump, thus removing the use of complex, expensive external actuators. These tunable waveform microfluidic oscillators are envisioned to facilitate cell-based studies that require temporal stimulation.

Quantitative dynamical relationships for the effect of rotation rate on frequency and waveform of electrochemical oscillations

We investigate the effect of changing mass transfer conditions through variation of rotation rate of a rotating disk electrode on features of oscillatory dynamics of negative differential resistance electrochemical systems. The theoretical analysis and numerical simulation of a prototype two-variable electrochemical model show that for oscillations close to a Hopf bifurcation the frequency (ω) increases with increase in rotation rate (d) following an approximate square root formula ω∝d1/2. For relaxation oscillations, the oscillations maxima, minima, and transition points between the high- and low-current states do not depend on rotation rate; the oscillation waveform invariance is explained using nullcline analysis by showing that the rotation does not affect the nullcline of the fast variable (electrode potential) along which the oscillations occur. The numerical and theoretical predictions are confirmed in experiments with copper electrodissolution in phosphoric acid electrolyte using a rotating electrode setup. The results thus indicate that simplifying concepts related to invariant manifolds and parameter dependence of bifurcation points (principle of critical simplification) are efficient approaches to obtaining quantitative dynamical relationships for decoding complexity in electrochemical reaction systems.

Evaluation of breakdown characteristics of N2 gas for non-standard lightning impulse waveforms - breakdown characteristics under single-frequency oscillation waveforms and with bias voltages

SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> gas, an insulation medium used for gas insulated switchgear (GIS), has a high global warming potential, hence the search for an effective alternative is required from an environmental perspective. As one of its potential alternatives, the authors are focusing on N2 gas, which has relatively good insulation characteristics among natural gases and a low environmental impact. However, to use this N2 gas for actual GIS, the insulation characteristics for actual overvoltage waveforms generated in the field (non-standard lightning impulse waveforms; non-standard-LIWs) must be obtained. The present study, with single-frequency oscillation waveforms as a representative basis among non-standard LIWs, experimentally obtained the insulation characteristics of an N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gas gap by changing the frequency and the damping factor. Consequently, the breakdown voltage (BDV) was lower for the negative polarity under a quasi-uniform electric field, hence the conclusion that it was reasonable to conduct experiments using negative polarity waveforms in order to discuss the dielectric strength. In addition, even if the frequency and damping factor changed, the BDV remained relatively constant, and that is consistently higher than that for the standard lightning impulse waveforms (standard-LIWs) at a level of 1.14 to 1.24 times. As a result, it was also confirmed for GIS using N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gas that the insulation specification could be rationalized by about 20% by converting lightning impulse waveforms from non-standard to equivalent standard-LIWs of 1.2/50 μs. Furthermore, insulation characteristics were obtained under the pattern in which a disconnector switching surges are superposed on residual dc elements generated through the operation of disconnectors (bias voltages). Consequently, the bias voltage had only a minor influence on the insulation characteristics and it emerged that insulation characteristics were likely to be evaluated using a single polarity waveform.

Evaluation of overshoot rate of lightning impulse withstand voltage test waveform based on new base curve fitting methods - study on overshoot waveform in an actual test circuit

In a lightning impulse withstand voltage test for large-sized electric power equipment, voltage waveforms sometimes contain overshoot due to the capacitance of the test equipment and the residual inductance of the test circuit including the power source. The authors have been studying fitting methods for extracting a reasonable base curve from this overshoot waveform. In the previous study, each of the fitting methods was applied to the overshoot waveform simulated using a mathematical equation to evaluate the respective merits and demerits. As the test waveform, the present paper used the overshoot waveform actually generated using a large-scale test circuit. This actual waveform was determined as one over which an oscillation waveform of several hundred kHz, which was actually at issue, was superimposed. The correct base curve of the actual waveform was derived through detailed analysis of the equivalent circuit of the test circuit and the overshoot rate was calculated based on this correct value. This correct overshoot rate was compared with that calculated using each of the fitting methods to evaluate which was an optimum fitting method. Consequently, it was found that an overshoot rate close to the correct value could be derived using the new base curve extraction method for the actual waveform. Meanwhile, it should be noted that the kfactor filtering scheme was implemented after the application of various fitting methods, and then the shape parameters of the test voltage waveforms, such as the crest value, wavefront duration, and wavetail duration, were almost identical, which confirmed that fitting methods had only a minor influence on the test voltage waveform.

Discrete-Time Modelling of the Moog Sawtooth Oscillator Waveform

Discrete-time modelling strategies of analogue Moog sawtooth oscillator waveforms are presented. Two alternative approaches suitable for real-time implementation are proposed, one modelling the analogue waveform in time domain using phase distortion synthesis and another matching the spectrum of an existing antialiasing sawtooth oscillator to the corresponding analogue spectrum using a first-order IIR post-equalising filter. A parameter estimation procedure for both approaches is explained and performed. Performance evaluation using polynomial fits for the estimated parameters is carried out, and good matches between the model outputs and recorded waveforms are obtained. The best match of the tested algorithms is produced by the phase distortion model and by post-equalising the fourth-order B-spline bandlimited step function sawtooth oscillator.

The Design and Analysis of Dual-Delay-Path Ring Oscillators

A dual-operation-mode ring oscillator that employs dual-delay paths is presented. The two operation modes, referred to as the differential and common modes, have different output waveform characteristics and oscillation frequencies. A nonlinear model for the dual-delay-path ring oscillator and the analysis of the stability of each operation mode are proposed to confirm both simulation and measurement results. Furthermore, a method for operation-mode selection is presented. The differential four-stage dual-delay-path ring oscillator is fabricated in a 0.18-μm CMOS technology. Measurements show that the tuning ranges are from 1.77 to 1.92 GHz and from 1.01 to 1.055 GHz for differential- and common-mode operations, respectively.

Evaluation of breakdown characteristics of CO2 gas for non-standard lightning impulse waveforms - breakdown characteristics under single-frequency oscillation waveforms of 5.3 MHz to 20.0 MHz

SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> gas, an insulation medium used for gas insulated switchgear (GIS), has a high global warming potential, hence the search for an effective alternative means from the environmental perspective. The authors are focusing on CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gas, which has a lower global warming potential (GWP), as one of its potential alternatives. In order to use this CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gas for actual GIS, the insulation characteristics for actual overvoltage waveforms generated in the field (called non-standard lightning impulse waveforms) must be obtained. For this purpose, the preceding study experimentally obtained and evaluated the insulation characteristics for relatively low frequency oscillation waveforms in disconnector switching surges generated in the actual field. In this paper, the insulation characteristics of the CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gas gap for higher frequency oscillation waveforms were experimentally obtained while changing the frequency and damping rate. Consequently, in the high frequency area, if the frequency was raised or the damping rate increased, the dielectric breakdown voltage tended to increase, consistently remaining higher than that for standard lightning impulse waveforms at a level of 1.08 to 1.36 times. Accordingly, it was found that the insulation specification could be rationalized by approximately 10% by converting non-standard lightning impulse waveforms to equivalent standard lightning impulse waveforms. In addition, the influence of gas pressure and gap length was examined and it emerged that the results obtained under basic experimental conditions were likely to be applicable to the conditions close to actual GIS conditions.

Evaluation of breakdown characteristics of CO2 gas for non-standard lightning impulse waveforms - breakdown characteristics under single-frequency oscillation waveforms of 1.3 MHz to 4.0 MHz

SF6 gas, an insulation medium used for gas insulated switchgear (GIS), has a high global warming potential, hence the search for an effective alternative means from the environmental perspective. One of the alternative candidates is CO2 gas, which has a lower global warming potential. In order to use this CO2 gas for actual GIS, the insulation specification must be rationalized by lowering the lightning impulse withstand voltage because the dielectric strength of CO2 gas is lower than that of SF6 gas. To lower the lightning impulse withstand voltage of GIS while maintaining the high reliability of its insulation performance, it is important to define in an organized way the insulation characteristics for non-standard lightning impulse voltage waveforms (non-standard-LIWs) that represent actual surge waveforms in the field and compare them with the characteristics for the standard lightning impulse waveform (standard-LIW) quantitatively. In this paper, with single-frequency oscillations as typical examples of non-standard-LIWs, the insulation characteristics for the CO2 gas gap were experimentally obtained while changing the frequency and damping rate. Consequently, even if the frequency and damping rate were changed, the dielectric breakdown voltage varied little, consistently remaining higher than that with standard-LIW at a level of 1.08 to 1.17 times. Accordingly, it was found that, for GIS using CO2 gas, the insulation specification could be rationalized by approximately 10% by converting non-standard-LIWs to equivalent standard-LIWs. In addition, the influence of gas pressure and gap length was examined and it emerged that the results obtained under basic experimental conditions were likely to be applicable to the conditions close to actual GIS conditions.