Second-order Frequency Response Research Articles

Diagnosis of Voltage Losses of the Proton Exchange Membrane Water Electrolyzer with Nonlinear Frequency Response Method

Proton exchange membrane water electrolyzer (PEMWE) takes a central place in the hydrogen economy as a crucial technology for green hydrogen production. However, this technology still faces challenges, such as the cost of the materials, performance losses at high current densities, and durability. To overcome these obstacles, better comprehension of the phenomena occurring in the PEMWE is necessary. Typical electrochemical methods, such as polarization curves and high-frequency response measurements, lack detailed information about the individual contributions to the overall voltage losses and cannot point out the causes of the performance shortcomings. Therefore, the development of advanced diagnosis techniques for PEMWE is of importance both for the state of health analysis during the operation, as well as for the testing of new materials.In this work, a nonlinear frequency response (NFR) method was applied for the diagnosis of a lab-scale PEMWE. The NFR method represents an extension of the electrochemical impedance spectroscopy to the nonlinear domain by investigating the second-order frequency response function (FRF) in addition to the first-order FRF (equivalent to the impedance) [1]. Typical features corresponding to processes occurring in the PEMWE were observed in both the first- and the second-order FRFs. The experimental observations were interpreted based on a simple nonlinear model. The features observed at frequencies higher than 0.1 Hz were attributed to the electrochemical half-reactions, while a high current density feature observed at lower frequencies, could be attributed to the mass transport. During the analysis, the first-order FRF (impedance) was found not to be sensitive enough for the discrimination of the different sets of parameters and the second-order FRF had to be included for better parameter identification. The obtained parametrized model is dynamic and nonlinear and, thus, it can be utilized for model predictive control of the PEMWE and optimization of the overall green hydrogen production system.[1] Vidaković-Koch, T., Miličić, T., Živković, L.A., Chan, H.S., Krewer, U., Petkovska, M., Cur. Opin. Electrochem., 2021, 30, 100851

Nonlinear frequency response analysis of oxygen reduction reaction on silver in strong alkaline media

Understanding the kinetics of the oxygen reduction reaction on silver in highly concentrated alkaline solutions (e.g., 11 M NaOH) and elevated temperature is of great interest both in terms of technical applications of this reaction (e.g., in chloralkali electrolysis) and in fundamental terms. To gain a better understanding of this process, a nonlinear frequency response analysis was performed in combination with a rotating ring disk analysis. Firstly, the ORR was analyzed under steady-state conditions. The number of exchanged electrons was determined based on rotating ring disk experiments. Secondly, two different dynamic ORR kinetic models have been formulated. These models were used to derive the theoretical first- and second-order frequency response functions (FRFs). Furthermore, the first and second-order FRFs were determined experimentally for both 0.1 M NaOH and 11 M NaOH at different temperatures. In the next step, the kinetic model parameters were numerically estimated from the experimental frequency-domain data. Despite its simplicity, the so-called 1-step model was able to reproduce experimental first- and second-order FRFs in 0.1 M NaOH under different conditions (steady-state potentials and rotation rates). At the same time, this model was able to reproduce the first-order FRF in 11 M NaOH at 60 °C, but not the features observed in the second-order FRF spectra. The more complex 4-step model has shown a better capability in explaining experimental findings, like the first and second-order FRFs, but also experimentally observed change of the Tafel slope as well as the influence of mass transport on the number of exchanged electrons. However, it was also not able to reproduce all experimental features. Possible reasons for these discrepancies are discussed.

Coupled dynamic response analysis of multi-column floating offshore wind turbine with low center of gravity

To realize the application of the floating offshore wind turbine (FOWT) from deep to relatively shallow waters, a new concept of multi-column floating wind turbine platform with low center of gravity (CG) is designed and validated. The multi-column low CG platform is designed to support a 6MW wind turbine class and operated at a water depth of 50m in the South China Sea. The frequency domain software WADAM and time domain software NREL-FAST are used to simulate coupled dynamic responses of the floating wind turbine system with second-order wave loads considering. The dynamic behaviors of multi-column low CG FOWT system under normal operation and parked conditions are presented. The influence of second-order wave force on the motion responses of the multi-column platform, fore-aft force and moment of the tower base and mooring force are researched respectively. The results demonstrate that the coupled dynamic responses at rated operating condition and extreme condition meet the normal operating requirements and extreme survival requirements of FOWT system in the shallow water (50m) of South China Sea. In addition, it is found that, the wave frequency response gradually replaces the second-order low frequency response as the main influencing factor of the coupled dynamic response of the FOWT system with the increasing severity of the sea states. However, in general, the magnitude of second-order low frequency response increases with the increasing severity of the design load case. Thus, in the subsequent design of the shallow water FOWT system, the second-order effects should be paid enough attention.

Applications of higher-order frequency response functions to the detection and damage assessment of general structural systems with breathing cracks

Two types of cracks are often encountered in engineering structural systems and these are the open cracks and the breathing cracks. Existence of open cracks often leads to the loss of physical stiffness, resulting in a mostly linear structure with reduced load bearing capacity and vibration frequencies. The development of breathing cracks not only reduces structural stiffness, but tends to render the otherwise linear structure to become nonlinear, due to their bilinear stiffness characteristics associated with open and closed states. The nonlinear structural vibration responses can then be investigated and potentially employed to detect and identify breathing cracks within a structural system. In the present study, breathing cracks are modeled based on fracture mechanics from which bilinear stiffness values are obtained. These values are then incorporated into finite element models to compute the first- and second-order frequency response functions (FRFs) based on a proposed correlation technique which is both very accurate and resilient against measurement uncertainties. The existence of well-defined second-order FRFs has been firmly established for the bilinear oscillator, as well as a cantilevered beam with breathing cracks. By expressing the bilinear restoring force as a polynomial series, analytical derivation of second-order FRFs of general structural systems such as the GARTEUR AG11 structure with breathing cracks has been established for the first time. Further, a method of identification has been developed to identify the physical parameters of breathing cracks using second-order FRFs. With these new developments that are presented in this paper, a solid foundation has been laid for the potential applications of higher-order FRFs to damage identification and assessment of general real structural systems.

High-Performance Wideband Low-Noise Amplifier Using Enhanced $\pi$-Match Input Network

A low noise-figure (NF) and high power gain (S21) 3 ~ 10 GHz ultra-wideband low-noise amplifier (UWB LNA) with excellent phase linearity using 0.18 μm CMOS technology is reported. An enhanced π-match input network is used to achieve wideband input impedance matching as well as high and flat S21. To achieve low and flat NF, the pole frequency and pole quality factor of the second-order NF frequency response are tuned to approximate the maximally flat condition. The LNA consumes 18 mW, achieving S11 better than -10 dB for frequency lower than 12.2 GHz and group-delay (GD) variation smaller than ±14.6 ps for frequencies 3 ~ 10 GHz. Additionally, high and flat S21 of 13.7 ± 1.5 dB is achieved for frequencies 1 ~ 12.5 GHz, which means the corresponding 3-dB bandwidth is 11.5 GHz. Furthermore, the LNA achieves minimum NF of 2.2 dB at 4 GHz and NF of 2.3 ± 0.1 dB for frequencies of 3 ~ 10 GHz, one of the best NF results ever reported for a 3 ~ 10 GHz CMOS LNA.

Highly Linear Wideband LNA Design Using Inductive Shunt Feedback

Low noise amplifier (LNA) is an integral component of RF receiver and frequently required to operate at wide frequency bands for various wireless system applications. For wideband operation, important performance metrics such as voltage gain, return loss, noise figure and linearity have been carefully investigated and characterized for the proposed LNA. An inductive shunt feedback configuration is successfully employed in the input stage of the proposed LNA which incorporates cascaded networks with a peaking inductor in the buffer stage. Design equations for obtaining low and high impedance-matching frequencies are easily derived, leading to a relatively simple method for circuit implementation. Careful theoretical analysis explains that input impedance can be described in the form of second-order frequency response, where poles and zeros are characterized and utilized for realizing the wideband response. Linearity is significantly improved because the inductor located between the gate and the drain decreases the third-order harmonics at the output. Fabricated in 0.18 μm CMOS process, the chip area of this wideband LNA is 0.202 mm2, including pads. Measurement results illustrate that the input return loss shows less than -7dB, voltage gain greater than 8 dB, and a little high noise figure around 6-8 dB over 1.5 - 13 GHz. In addition, good linearity (IIP3) of 2.5 dBm is achieved at 8 GHz and 14 mA of current is consumed from a 1.8 V supply.

Enhanced Second-Order Resonance Actuation and Frequency Response Modulation of Microcantilever by Dual Coplanar Counter Electrodes

We achieve enhanced actuation of the 2nd-order resonance of a microcantilever in a capacitive microcantilever structure featured by a dual coplanar counter electrodes configuration. A torque about the static point of the 2nd eigenmode is generated in this configuration and therefore enables effective actuation of the 2nd-order resonance. It is further confirmed that the torque has the effect of suppressing the 1st-order resonance. As a result, the frequency response curve of the microcantilever beam can be modulated. Our results suggest that electric actuation of any higher-order resonances of the microcantilever can be realized through a rational design of counter electrodes.

Some practical aspects of nonlinear frequency response method for investigation of adsorption equilibrium and kinetics

Some practical aspects regarding application of the nonlinear frequency response (NFR) method for investigation of gas adsorption: choice of the optimal mass of the adsorbent, frequency range and input amplitude, are studied theoretically. For successful application of the NFR method, reliable experimental determination of the second-order frequency response function (FRF) is essential. In order to analyse the influence of the mass of the adsorbent, the frequency range and the input amplitude on the accuracy of the estimated the second-order FRF, frequency responses (FRs) of a batch adsorber with volume modulation are simulated and used for calculation of the second-order FRF. Furthermore, the procedure for estimation of the optimal mass of the adsorbent, required frequency range and input amplitude, based on simple preliminary step responses, is proposed. In order to demonstrate the procedure, responses of the batch adsorber for the step volume change are also simulated. The proposed procedure enables establishment of the efficient experimental plan for application of the NFR method.

A SECOND-ORDER BPF USING A MINIATURIZED-ELEMENT FREQUENCY SELECTIVE SURFACE

A new type of low-proflle frequency selective surface (FSS) with an overall thickness of ‚=40 and a second-order band pass frequency response is presented. The proposed FSS is composed of two metal layers, separated by a thin dielectric substrate. Each layer is a two-dimensional periodic structure with sub-wavelength periodic unit cells. By printing the same topology on each side of the substrate, a second-order frequency response is realized. To provide a physical insight into the operating mechanism, equivalent circuit networks are also investigated in each step of design procedure. Using the proposal technique, low proflle and reduced sensitivity to angle of incident wave for both TE and TM polarizations are obtained and the overall thickness of the substrate is fairly thin. FSS samples are designed, fabricated, and installed in waveguide operating at X-band and a good agreement between the simulated and measured results is achieved.

Analysis and Design of CMOS Distributed Amplifier Using Inductively Peaking Cascaded Gain Cell for UWB Systems

A low-power, high-gain (HG), and low-noise (LN) CMOS distributed amplifier (DA) using cascaded gain cell, formed by an inductively parallel-peaking cascode-stage with a low- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> RLC load and an inductively series-peaking common-source stage, is proposed. Flat and high <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> and flat and low noise figure (NF) are achieved simultaneously by adopting a slightly under-damped <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> factor for the second-order transconductance frequency response. A single-stage and a two-stage DA for ultra-wideband (UWB) systems are demonstrated. In the LN mode, the two-stage DA consumes 22 mW and achieves flat and high <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> of 14.07 ± 1.69 dB with an average NF of only 2.8 dB over the 3-10-GHz band of interest, one of the best reported NF performances for a CMOS UWB DA or LN amplifier in the literature. In addition, in the low-gain mode, the two-stage DA consumes 6.86 mW and achieves <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> of 11.03 ± 0.98 dB and an average NF of 4.25 dB. In the HG mode, the two-stage DA consumes 37.8 mW and achieves <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> of 20.47 ± 0.72 dB and an average NF of 3.3 dB. The analytical, simulated, and measured results are mutually consistent.

Nonlinear Frequency Response Analysis of the Ferrocyanide Oxidation Kinetics. Part I. A Theoretical Analysis

In this work, a nonlinear frequency response (NLFR) analysis was used for a first time in a theoretical study of nonlinear behavior of electrochemical (EC) ferrocyanide oxidation as a simple model reaction. Analytical expressions of the first- and second-order frequency response functions (FRFs) are derived. The first-order FRF is equivalent to the EC admittance and contains information about the linear behavior of the system, whereas the second-order FRF contains additional nonlinear information. The influence of different parameters, such as the heterogeneous rate constant, solution resistance, double-layer capacitance, diffusion coefficients of the reacting species, and electrode rotation rate on the characteristics of the first- and second-order FRFs was checked and discussed. It was found that the second-order FRF is more sensitive to the changes of the studied parameters than the first-order FRF. Experimental verification of the NLFR analysis of EC ferrocyanide oxidation is presented in Part II of this work.

Versatile analog squarer and multiplier free from body effect

This paper proposes the analog CMOS squarer and the four-quadrant analog CMOS multiplier. The major advantages of the proposed circuits are low voltage supply, multifunction of output, and insensitive to the threshold voltage variation caused by body effect. The versatile squarer has two inputs (V in and I in ). Its output can be the square of V in or the square of I in . The versatile four-quadrant multiplier has four inputs (V X , I X , V Y , and I Y ). Its output can be the product of V X and V Y , the product of I X and I Y , the product of V X and I Y , or the product of V Y and I X . Therefore, the proposed circuits can be applied more than conventional circuits and have good performance. Second-order effects and frequency response are analyzed. Simulation results have verified the workability of the circuits. Experimental results are done to confirm the operation of the circuits.

3.7 mW 24 GHz LNA with 10.1 dB gain and 4.5 dB NF in 0.18 µm CMOS technology

A low-power 24 GHz low-noise amplifier (LNA) with flat and low noise figure (NF) using standard 0.18 µm CMOS technology is demonstrated. The low-power LNA consists of three cascaded common-source stages biased in the weak inversion region. To achieve sufficient gain, a series peaking inductor (LG3) was added to the input terminal of the third stage to boost the gain (simulation shows a 78.9% improvement (from 5.7 to 10.2 dB) at 24 GHz). Flat and low NF was achieved by adopting a slightly under-damped Q-factor for the second-order NF frequency response. Shunt RC feedback in conjunction with a low-Q RL load were adopted in the third stage to achieve excellent output impedance matching. The 24 GHz LNA achieved S21 of 10.1 dB and NF of 4.5 dB with a power dissipation (PDC) of only 3.7 mW, the lowest PDC ever reported for a 24 GHz-band CMOS LNA with S21 greater than 10 dB.

3.1 dB NF 20–29 GHz CMOS UWB LNA using a T-match input network

A 20–29 GHz CMOS ultra-wideband (UWB) low-noise amplifier (LNA) with excellent input return loss (S11), flat and high power gain (S21), and flat and low noise figure (NF) is demonstrated. Wideband input impedance matching was achieved by using the proposed T-match input network to generate two S11 dips. Flat and high S21 was achieved because the inductive-peaking second stage and the current-reused final two stages can compensate the gain degradation of the source-degenerative first stage at medium and high frequencies, respectively. Flat and low NF was achieved by adopting a slightly under-damped Q-factor for the second-order NF frequency response. The LNA consumed 22.07 mW and achieved S11 of −15.5 to −26.8 dB, S21 of 16.2±2.5 dB, minimum NF (NFmin) of 3.1 dB (at 20 GHz), and an average NF of 3.6 dB over the 20–29 GHz band of interest, one of the best reported average NF performances for a 24 GHz band CMOS LNA with bandwidth wider than 6 GHz in the literature.

Nonlinear Frequency Response of Electrochemical Methanol Oxidation Kinetics: A Theoretical Analysis

In this theoretical contribution, nonlinear frequency response analysis was applied for the investigation of electrochemical methanol oxidation. This technique expresses the input–output behavior of any weakly nonlinear system with the help of the Volterra series expansion and generalized Fourier transform into so-called higher order frequency response functions. These functions contain the system’s nonlinear fingerprint. They can be derived analytically from a nonlinear model. These functions can be obtained experimentally from the measurement of higher harmonics induced by a high amplitude sinusoidal perturbation of the system of interest. Frequency response functions up to the second order have been derived analytically for four different model varieties describing the kinetics of the electrochemical methanol oxidation. The first-order frequency response function corresponds to the reciprocal value of the well-known electrochemical impedance, which represents the linear part of the frequency response. This function does not contain sufficient information for discrimination between the different kinetic models. In contrast, the symmetrical second-order frequency response functions show differences in shape, which substantiate the availability of the theoretical prerequisites for model discrimination. A detailed parametric study for all four model variants has been performed. The results show that the basic features of the shapes of the amplitude spectra corresponding to the four models remain unique. The ubiquitousness of the qualitative differences between the competing models, for the whole set of parameters chosen for our analysis, suggests that the aforementioned amplitude spectra contain sufficient information for an unequivocal model discrimination.

Design and study of second-order Y-loop frequency selective surfaces

The multiband properties of self-similar fractals can be used to design multiband single-layer frequency selective surfaces (FSS). Combined with Floquet periodic boundary conditions, the moments method is applied to characterize the second-order Y-loop fractal FSS frequency response to different valuses of iterative scaling factor F and lattice as the incidence varies, and then the estimated empirical constant is obtained. Experimental results show good correlation to the calculations, indicating that the resonant frequencies are mainly determined by the iteration factor and the initial unit size,while the lattice impacts the transmission coefficient and bandwidth apparently.

Low-power, high-gain and low-noise CMOS distributed amplifier for UWB systems

A 3-10-GHz CMOS distributed amplifier (DA) with flat and low noise figure (NF) and flat and high power gain (S 21 ) is demonstrated. A flat and low NF was achieved by adopting an RL terminating network for the gate transmission line, and a slightly under-damped Q -factor for the second-order NF frequency response. Besides, an flat and high S 21 was achieved by using the proposed cascade gain cell, which constitutes a cascode-stage with a low- Q RLC load and an inductive-peaking common-source stage. In the high-gain mode, the DA consumed 37.8 mW and achieved a flat and high S 21 of 20.47plusmn0.72 dB with an average NF of 3.29plusmndB over the 3plusmn10plusmnGHz band of interest, one of the best reported NF performances for a CMOS UWB DA or low-noise amplifier. In the low-gain mode, the DA achieved S 21 of 11.03plusmn0.98plusmndB and an average NF of 4.25plusmndB with a power dissipation ( PD ) of 6.86 mW, the lowest PD ever reported for a CMOS UWB DA or LNA with an average S 21 of greater than 10 dB.

Tailored Current—Voltage Relationships of Droplet-Interface Bilayers Using Biomolecules and External Feedback Control

The development of a new class of active material based on the ion transport properties of functional biomolecules is introduced in this work. The new class of materials utilizes a recently developed technique known as the droplet-interface bilayer (DIB) to enable the reconstitution of biomolecules into a durable matrix. Methods to modify the current— voltage relationship across the bilayer, including the incorporation of proteins and the use of an external feedback loop, are explored. Electrical impedance spectroscopy and cyclic voltammetry measurements are used to characterize the bilayers and indicate that a single DIB can be modeled as a resistor in parallel with a capacitor. Alpha-hemolysin proteins from Staphyloccus aureus cause a reduction in the resistance of the bilayer and exhibit current-rectification at positive cis potentials. Alamethicin proteins from Trichoderma viride produce a voltage-dependent conductance allowing the specific resistance (MΩ cm2) of the bilayer to be varied reversibly by 2—3 orders of magnitude. Feedback integral current control is demonstrated on pure 1,2-diphytanoyl-sn-glycero-3-phosphocholine DIBs and provides accurate current tracking at a driving rate of 10 mHz and less. Proportional—integral voltage control applied to a DIB establishes a second-order frequency response where the natural frequency and damping ratio of the resonance can be selected.

Resolving Controversies in the Application of the Method of Multiple Scales and the Generalized Method of Averaging

I compare application of the method of multiple scales with reconstitution and the generalized method of averaging for determining higher-order approximations of three single-degree-of-freedom systems and a two-degree-of-freedom system. Three implementations of the method of multiple scales are considered, namely, application of the method to the system equations expressed as second-order equations, as first-order equations, and in complex-variable form. I show that all of these methods produce the same modulation equations. I address the problem of determining higher-order approximate solutions of the Duffing equation in the case of primary resonance. I show that the conclusions of Rahman and Burton that the method of multiple scales, the generalized method of averaging, and Lie series and transforms might lead to incorrect results, in that spurious solutions occur and the obtained frequency–response curves bear little resemblance to the actual response, is the result of their using parameter values for which the neglected terms are the same order as the retained terms. I show also that spurious solutions cannot be avoided, in general, in any consistent expansion and their presence does not constitute a limitation of the methods. In particular, I show that, for the Duffing equation, the second-order frequency–response equation does not possess spurious solutions for the case of hardening nonlinearity, but possesses spurious solutions for the case of softening nonlinearity. For sufficiently small nonlinearity, the spurious solutions are far removed from the actual response. But as the strength of the nonlinearity increases, these solutions move closer to the backbone and eventually distort it. This is not a drawback of the perturbation methods but an indication of an application of the analysis for parameter values outside the range of validity of the expansion. Also, I address the problem of obtaining non-Hamiltonian modulation equations in the application of the method of multiple scales to multi-degree-of-freedom Hamiltonian systems written as second-order equations in time and how this problem can be overcome by attacking the state-space form of the governing equations. Moreover, I show that application of a variation of the method of Rahman and Burton to multi-degree-of-freedom systems leads to results that do not agree with those obtained with the generalized method of averaging.

Data translation and order reduction for turbine-generator models used in network studies

This paper develops suitable procedures for translating high-order networks into conventional stability constants. The approach is computer-oriented and imposes no restriction on the number of equivalent damper windings per axis. Optimum order reduction is used to demonstrate that second-order networks have a bandwidth limited to between 1 and 5 Hz while third-order models may extend this bandwidth beyond 100 Hz. The latter are therefore mandatory for subsynchronous resonance and harmonic studies. In the course of this investigation, the need for a precise definition of the so-called stability constants arises and it is concluded that only a second-order standstill frequency response (SSFR)-based model yields constants that are consistent with the latest, short-circuit test bound, IEEE standard definitions.