- Intermodulated differential immittance spectroscopy (IDIS) is a nonlinear analysis technique that uses two input frequencies (a probe and stimulus signal) to perturb an electrochemical system.
- For a nonlinear system, the output contains not only the probe and stimulus frequencies but also sidebands located at the sum and difference of the frequencies, due to intermodulation.
- The technique defines a transfer function called the differential immittance spectrum, which can be calculated from the sideband amplitudes. This provides information about the system's nonlinearity.
- Testing on a Schottky diode showed that the differential immittance spectrum could accurately determine the diode's flat band voltage and doping level from a single measurement.
Simulation of Nonstationary Processes in Backward-Wave Tube with the Self-Mod...Victor Solntsev
The equations that describe nonlinear nonstationary processes in carcinotrode (backward- wave tube with the emission modulation in the presence of the field of the output signal fed to the cathode via a feedback loop) are derived. An algorithm and the corresponding code are developed to solve the equations with allowance for the modulation of emission using nonuniform (with respect to time) large particles (electrons of equal charge) ejected from the cathode. The effect of the feedback parameter on the intensity and shape of the carcinotrode oscillations is analyzed. It is demonstrated that the carcinotrode efficiency can be increased to about 50% upon the generation of harmonic oscil- lations. A more significant increase in the efficiency to 70% is possible in the regime of the weak self- modulation of oscillations upon an increase in the feedback coefficient in the feedback loop involving the slow-wave structure and the cathode and a decrease in the cathode–grid static field.
Characterization Of Switchable And Multilayered FSS Circuits Using The WCIP M...IJERA Editor
In this paper, we use the Wave Concept Iterative Procedure (WCIP) to study the Switchable and multilayered
FSS (Frequency Selective Surface) circuits. The Switchable part is used for the adjustment of the frequency of
the HF Electronics Circuits. This adjustment is applied by the integration of RF-MEMS switches. This system is
based on the use of circuit fabrication processes included. In order to initialize the iterative procedure, an
incident wave is defined in the spectral domain
Hilbert Vibration Decomposition (HVD) is introduced to the voltage flicker analysis. When voltage flicker accompanies with high order harmonics, the instantaneous frequency of its analytic signal in principle consists of two different parts, power frequency and a rapidly varying asymmetrical oscillating part. The important property of the instantaneous frequency offers a direct way to estimate the power frequency using a low-pass filter and remove the high order harmonics without pre-treatment procedures. Corresponding voltage flicker envelope is estimated using synchronous detection. The HVD method does not involves basic functions that the wavelet transform method needs. It can also adaptively estimate the frequency and amplitude of every modulation frequency component. Simulation results prove that the proposed method could accurately detect voltage flicker with high order harmonics. It has higher calculation efficiency and detection precision than wavelet transform method. Experimental results show that the new algorithm is feasible and efficient.
Ultrasonic transducers are a key element that governs the performances of both generating and receiving ultrasound in an ultrasonic measurement system. Electrical impedance is a parameter sensitive to the environment of the transducer; it contains information about the transducer but also on the medium in which it is immersed. Several practical applications exploit this property. For this study, the model is implemented with the VHDL-AMS behavioral language. The simulations approaches presented in this work are based on the electrical Redwood model and its parameters are deduced from the transducer electroacoustic characteristics.
Accurate Evaluation of Interharmonics of a Six Pulse, Full Wave - Three Phase...idescitation
Interharmonics are the non-integral multiples of
the system’s fundamental frequency. The interharmonic
components can be apprehended as the intermodulation of
the fundamental and harmonic components of the system with
any other frequency components introduced by the load. These
loads include static frequency converters, cyclo-converters,
induction motors, arc furnaces and all the loads not pulsating
synchronously with the fundamental frequency of the system.
The harmonic and interharmonic components inflict common
damage to the system and apart from these damages the
interharmonics also cause light flickering, sideband torques
on motor/generator and adverse effects on transformer and
motor components. To
filter/compensate the interharmonic
components, their accurate evaluation is essential and to
achieve the same the Iterative algorithm has been proposed.
The main cause of spectral leakage errors is the truncation of
the time-domain signal. The proposed adaptive approach
calculates the immaculate window width, eliminating the
spectral leakage errors in the frequency domain and thereby
the interharmonics/harmonics can be calculated accurately.
The algorithm does not require any inputs regarding the
system frequency and interharmonic constituents of the
system. The only parameter required is the signal sequence
obtained by sampling the analog signal at equidistant sampling
interval.
Spatially adiabatic frequency conversion in opto-electro-mechanical arraysOndrej Cernotik
Optoelectromechanical systems offer a promising route towards frequency conversion between microwaves and light and towards building quantum networks of superconducting circuits. Current theoretical and experimental efforts focus on approaches based on either optomechanically induced transparency or adiabatic passage. The former has the advantage of working with time-independent control but only in a limited bandwidth (typically much smaller than the cavity linewidth); the latter can, in principle, be used to increase the bandwidth but at the expense of working with time-dependent control fields and with strong optomechanical coupling. In my presentation, I will show that an array of optoelectromechanical transducers can overcome this limitation and reach a bandwidth that is larger than the cavity linewidth. The coupling rates are varied in space throughout the array so that a mechanically dark mode of the propagating fields adiabatically changes from microwave to optical or vice versa. This strategy also leads to significantly reduced thermal noise with the collective optomechanical cooperativity being the relevant figure of merit. I will also demonstrate that, remarkably, the bandwidth enhancement per transducer element is largest for small arrays. With these features the scheme is particularly relevant for improving the conversion bandwidth in state-of-the-art experimental setups.
Simulation of Nonstationary Processes in Backward-Wave Tube with the Self-Mod...Victor Solntsev
The equations that describe nonlinear nonstationary processes in carcinotrode (backward- wave tube with the emission modulation in the presence of the field of the output signal fed to the cathode via a feedback loop) are derived. An algorithm and the corresponding code are developed to solve the equations with allowance for the modulation of emission using nonuniform (with respect to time) large particles (electrons of equal charge) ejected from the cathode. The effect of the feedback parameter on the intensity and shape of the carcinotrode oscillations is analyzed. It is demonstrated that the carcinotrode efficiency can be increased to about 50% upon the generation of harmonic oscil- lations. A more significant increase in the efficiency to 70% is possible in the regime of the weak self- modulation of oscillations upon an increase in the feedback coefficient in the feedback loop involving the slow-wave structure and the cathode and a decrease in the cathode–grid static field.
Characterization Of Switchable And Multilayered FSS Circuits Using The WCIP M...IJERA Editor
In this paper, we use the Wave Concept Iterative Procedure (WCIP) to study the Switchable and multilayered
FSS (Frequency Selective Surface) circuits. The Switchable part is used for the adjustment of the frequency of
the HF Electronics Circuits. This adjustment is applied by the integration of RF-MEMS switches. This system is
based on the use of circuit fabrication processes included. In order to initialize the iterative procedure, an
incident wave is defined in the spectral domain
Hilbert Vibration Decomposition (HVD) is introduced to the voltage flicker analysis. When voltage flicker accompanies with high order harmonics, the instantaneous frequency of its analytic signal in principle consists of two different parts, power frequency and a rapidly varying asymmetrical oscillating part. The important property of the instantaneous frequency offers a direct way to estimate the power frequency using a low-pass filter and remove the high order harmonics without pre-treatment procedures. Corresponding voltage flicker envelope is estimated using synchronous detection. The HVD method does not involves basic functions that the wavelet transform method needs. It can also adaptively estimate the frequency and amplitude of every modulation frequency component. Simulation results prove that the proposed method could accurately detect voltage flicker with high order harmonics. It has higher calculation efficiency and detection precision than wavelet transform method. Experimental results show that the new algorithm is feasible and efficient.
Ultrasonic transducers are a key element that governs the performances of both generating and receiving ultrasound in an ultrasonic measurement system. Electrical impedance is a parameter sensitive to the environment of the transducer; it contains information about the transducer but also on the medium in which it is immersed. Several practical applications exploit this property. For this study, the model is implemented with the VHDL-AMS behavioral language. The simulations approaches presented in this work are based on the electrical Redwood model and its parameters are deduced from the transducer electroacoustic characteristics.
Accurate Evaluation of Interharmonics of a Six Pulse, Full Wave - Three Phase...idescitation
Interharmonics are the non-integral multiples of
the system’s fundamental frequency. The interharmonic
components can be apprehended as the intermodulation of
the fundamental and harmonic components of the system with
any other frequency components introduced by the load. These
loads include static frequency converters, cyclo-converters,
induction motors, arc furnaces and all the loads not pulsating
synchronously with the fundamental frequency of the system.
The harmonic and interharmonic components inflict common
damage to the system and apart from these damages the
interharmonics also cause light flickering, sideband torques
on motor/generator and adverse effects on transformer and
motor components. To
filter/compensate the interharmonic
components, their accurate evaluation is essential and to
achieve the same the Iterative algorithm has been proposed.
The main cause of spectral leakage errors is the truncation of
the time-domain signal. The proposed adaptive approach
calculates the immaculate window width, eliminating the
spectral leakage errors in the frequency domain and thereby
the interharmonics/harmonics can be calculated accurately.
The algorithm does not require any inputs regarding the
system frequency and interharmonic constituents of the
system. The only parameter required is the signal sequence
obtained by sampling the analog signal at equidistant sampling
interval.
Spatially adiabatic frequency conversion in opto-electro-mechanical arraysOndrej Cernotik
Optoelectromechanical systems offer a promising route towards frequency conversion between microwaves and light and towards building quantum networks of superconducting circuits. Current theoretical and experimental efforts focus on approaches based on either optomechanically induced transparency or adiabatic passage. The former has the advantage of working with time-independent control but only in a limited bandwidth (typically much smaller than the cavity linewidth); the latter can, in principle, be used to increase the bandwidth but at the expense of working with time-dependent control fields and with strong optomechanical coupling. In my presentation, I will show that an array of optoelectromechanical transducers can overcome this limitation and reach a bandwidth that is larger than the cavity linewidth. The coupling rates are varied in space throughout the array so that a mechanically dark mode of the propagating fields adiabatically changes from microwave to optical or vice versa. This strategy also leads to significantly reduced thermal noise with the collective optomechanical cooperativity being the relevant figure of merit. I will also demonstrate that, remarkably, the bandwidth enhancement per transducer element is largest for small arrays. With these features the scheme is particularly relevant for improving the conversion bandwidth in state-of-the-art experimental setups.
High Impedance Fault Detection in Power Distribution Networks with Use of Cur...ijeei-iaes
In very distribution system, physical contact between conductors of a phase and substances around them like trees, walls of the buildings and surfaces below them, always in possible. These conditions known as High Impedance Faults (HIFs), can lead to death due to electricity congestion, burning or ignition via arc or heat of the substances. On the other hand, the whole energy produced by the power company doesn’t achieve by the arbitrary loads and a part of them is lost that this loss is harmful for the power supply companies. Current relaying in distribution systems is only capable of detecting short circuit conditions leads to flowing significant amount of generated electric power to the earth without achieving by the load. It is very difficult to detect HIFs by protection equipments. Because occurrence of them just leads to slight increase in the amount of load current. So it can be considered as a usual increase in the value of load current incorrectly. However various solutions for detecting high impedance faults have been proposed. Most of these approaches are complicated or difficult implementation. In this paper, a novel approach for detecting high impedance faults based on harmonic analysis of current in distribution systems has been presented. Various simulations in PSCAD envirounment have validated that proposed approach in simple in implementation and have great accuracy.
Spintronics refers commonly to phenomena in which
the spin of electrons in a solid state environment
plays the determining role. Spintronics devices are
based on a spin control of electronics, or on an
electrical and optical control of spin or magnetism.
This review provides a new promising science which
has been strongly addressed as Spintronics, the
contracted form of spin based electronics and
presents selected themes of semiconductor
Spintronics, introducing important concepts in spin
transport, spin injection, Silsbee-Johnson spincharge
coupling, and spin dependent tunneling. Most
semiconductor device systems are still theoretical
concepts, waiting for experimental demonstrations.
Performance Comparison of Power Quality Evaluation Using Advanced High Resolu...IOSRJEEE
Most of the conventional methods of power quality assesment in power systems are almost exclusively based on Fourier Transform that suffer from various inherent limitations. First limitation of an FFT based method is that of frequency resolution, whereas the second limitation is due to no coherent signal sampling of the data which proves itself as a leakage in spectrum domain. These two performance limitations of FFT or similar methods are particularly troublesome when analyzing short data records. To overcome from this problem, high regulation spectrum estimation methods can be used where resolution problem is not found. In this thesis, high resolution methods, such as MUSIC, root MUSIC and ESPRIT are discussed that use a different approach to spectral estimation; instead of trying to estimate the power spectral density (PSD) directly from the data, they model the data as the output of a linear system driven by white noise, and then attempt to estimate the parameters of that linear system. Detail Matlab simulations are carried out in order to investigate the performance of MUSIC, Root MUSIC and ESPRIT methods in estimating amplitude, power (squared amplitude) and frequency estimation of synthetic power signal both in clean and noisy conditions. Using mean square error (MSE) as the evaluation criterion, the variation of amplitude, power (squared amplitude) and frequency estimation are shown with respect to data sequence length and SNR and their influences on MSE are compared for the different methods as mentioned above.
Integrated ring resonator system analysis to Optimize the soliton transmissionPremier Publishers
The chaotic signals can be generated within the microring resonator (MRR) system when the Gaussian pulse with input power of 120 mW is inserted into the system. Generation of chaotic signals respect to the ring's radius has been studied. The coupling coefficient affects the output power significantly, thus in order to generate signals with higher output power, the smaller coupling coefficient can be used. Here the output power of the system is characterized with respect to the different coupling coefficients of the system.A series of MRRs connected to an add/drop filter system in order to anaylize the soliton signals. The nonlinear refractive index of the MRR is n2=2.2 x 10-17 m2/W. The capacity of the output signals can be increased through generation of peaks with smaller full width at half maximum (FWHM). Here, we generate and characterize the ultra-short optical soliton pulses respect to the ring's radius and coupling coefficients variation of the system. As result, soliton pulses with FWHM and free spectral range (FSR) of 50 pm and 1440 pm are generated.
The main stake is to detect a defective component or likely to become it during manufacture or inservice inspections, while improving control productivity. In this context, we develop a simulation tool of EC fastened structures testing, integrated to the ANSYS platform, aimed at conceiving testing methods, optimizing and qualifying it. The finite element method has been chosen, it is suitable for this type of problem. Various configurations have been considered for the inspection of a target with a defect in different thicknesses. Due to the impossibility to detect a defect located at a distance much greater than the skin depth δ. Indeed, the eddy currents amplitude are less than 95% of the maximum amplitude beyond a depth greater than 3 δ. We are interested in the detection of defects located at depths higher to three times the skin depth.
Pseudoperiodic waveguides with selection of spatial harmonics and modesVictor Solntsev
A principle of selection of modes and their spatial harmonics in periodic waveguides and, in particular, in spatially developed slowing systems for multibeam traveling-wave tubes (TWTs) is elaborated. The essence of the principle is in the following: varying along the length of the system its period and at least one more parameter that determines the phase shift per period, one can provide constant phase velocity of one spatial harmonic and destroy other spatial harmonics, i.e., reduce their amplitudes substantially. In this case, variations of the period may be significant, and the slowing system becomes nonuniform, or pseudoperiodic; namely, one of the spatial harmonics remains the same as in the initial periodic structure. Relationships are derived for the amplitudes of the spatial-wave harmonics, interaction coefficient, and coupling impedance of the pseudoperiodic system. The possibility of the mode selection in pseudoperiodic slowing systems when the synchronism condition is satisfied for the spatial harmonic of one mode is investigated. The efficiency of suppressing spurious spatial harmonics and modes for linear and abrupt variation of spacing is estimated. The elaborated principle of selection of spatial harmonics and modes is illustrated by an example of a two-section helical-waveguide slowing system.
Some possible interpretations from data of the CODALEMA experimentAhmed Ammar Rebai PhD
The purpose of the CODALEMA experiment, installed at the Nan\c{c}ay Radio Observatory (France), is to study the radio-detection of ultra-high energy cosmic rays in the energy range of 10^{16}-10^{18} eV. Distributed over an area of 0.25 km^2, the original device uses in coincidence an array of particle detectors and an array of short antennas, with a centralized acquisition. A new analysis of the observable in energy for radio is presented from this system, taking into account the geomagnetic effect. Since 2011, a new array of radio-detectors, consisting of 60 stand-alone and self-triggered stations, is being deployed over an area of 1.5 km^2 around the initial configuration. This new development leads to specific constraints to be discussed in term of recognition of cosmic rays and in term of analysis of wave-front.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
High Impedance Fault Detection in Power Distribution Networks with Use of Cur...ijeei-iaes
In very distribution system, physical contact between conductors of a phase and substances around them like trees, walls of the buildings and surfaces below them, always in possible. These conditions known as High Impedance Faults (HIFs), can lead to death due to electricity congestion, burning or ignition via arc or heat of the substances. On the other hand, the whole energy produced by the power company doesn’t achieve by the arbitrary loads and a part of them is lost that this loss is harmful for the power supply companies. Current relaying in distribution systems is only capable of detecting short circuit conditions leads to flowing significant amount of generated electric power to the earth without achieving by the load. It is very difficult to detect HIFs by protection equipments. Because occurrence of them just leads to slight increase in the amount of load current. So it can be considered as a usual increase in the value of load current incorrectly. However various solutions for detecting high impedance faults have been proposed. Most of these approaches are complicated or difficult implementation. In this paper, a novel approach for detecting high impedance faults based on harmonic analysis of current in distribution systems has been presented. Various simulations in PSCAD envirounment have validated that proposed approach in simple in implementation and have great accuracy.
Spintronics refers commonly to phenomena in which
the spin of electrons in a solid state environment
plays the determining role. Spintronics devices are
based on a spin control of electronics, or on an
electrical and optical control of spin or magnetism.
This review provides a new promising science which
has been strongly addressed as Spintronics, the
contracted form of spin based electronics and
presents selected themes of semiconductor
Spintronics, introducing important concepts in spin
transport, spin injection, Silsbee-Johnson spincharge
coupling, and spin dependent tunneling. Most
semiconductor device systems are still theoretical
concepts, waiting for experimental demonstrations.
Performance Comparison of Power Quality Evaluation Using Advanced High Resolu...IOSRJEEE
Most of the conventional methods of power quality assesment in power systems are almost exclusively based on Fourier Transform that suffer from various inherent limitations. First limitation of an FFT based method is that of frequency resolution, whereas the second limitation is due to no coherent signal sampling of the data which proves itself as a leakage in spectrum domain. These two performance limitations of FFT or similar methods are particularly troublesome when analyzing short data records. To overcome from this problem, high regulation spectrum estimation methods can be used where resolution problem is not found. In this thesis, high resolution methods, such as MUSIC, root MUSIC and ESPRIT are discussed that use a different approach to spectral estimation; instead of trying to estimate the power spectral density (PSD) directly from the data, they model the data as the output of a linear system driven by white noise, and then attempt to estimate the parameters of that linear system. Detail Matlab simulations are carried out in order to investigate the performance of MUSIC, Root MUSIC and ESPRIT methods in estimating amplitude, power (squared amplitude) and frequency estimation of synthetic power signal both in clean and noisy conditions. Using mean square error (MSE) as the evaluation criterion, the variation of amplitude, power (squared amplitude) and frequency estimation are shown with respect to data sequence length and SNR and their influences on MSE are compared for the different methods as mentioned above.
Integrated ring resonator system analysis to Optimize the soliton transmissionPremier Publishers
The chaotic signals can be generated within the microring resonator (MRR) system when the Gaussian pulse with input power of 120 mW is inserted into the system. Generation of chaotic signals respect to the ring's radius has been studied. The coupling coefficient affects the output power significantly, thus in order to generate signals with higher output power, the smaller coupling coefficient can be used. Here the output power of the system is characterized with respect to the different coupling coefficients of the system.A series of MRRs connected to an add/drop filter system in order to anaylize the soliton signals. The nonlinear refractive index of the MRR is n2=2.2 x 10-17 m2/W. The capacity of the output signals can be increased through generation of peaks with smaller full width at half maximum (FWHM). Here, we generate and characterize the ultra-short optical soliton pulses respect to the ring's radius and coupling coefficients variation of the system. As result, soliton pulses with FWHM and free spectral range (FSR) of 50 pm and 1440 pm are generated.
The main stake is to detect a defective component or likely to become it during manufacture or inservice inspections, while improving control productivity. In this context, we develop a simulation tool of EC fastened structures testing, integrated to the ANSYS platform, aimed at conceiving testing methods, optimizing and qualifying it. The finite element method has been chosen, it is suitable for this type of problem. Various configurations have been considered for the inspection of a target with a defect in different thicknesses. Due to the impossibility to detect a defect located at a distance much greater than the skin depth δ. Indeed, the eddy currents amplitude are less than 95% of the maximum amplitude beyond a depth greater than 3 δ. We are interested in the detection of defects located at depths higher to three times the skin depth.
Pseudoperiodic waveguides with selection of spatial harmonics and modesVictor Solntsev
A principle of selection of modes and their spatial harmonics in periodic waveguides and, in particular, in spatially developed slowing systems for multibeam traveling-wave tubes (TWTs) is elaborated. The essence of the principle is in the following: varying along the length of the system its period and at least one more parameter that determines the phase shift per period, one can provide constant phase velocity of one spatial harmonic and destroy other spatial harmonics, i.e., reduce their amplitudes substantially. In this case, variations of the period may be significant, and the slowing system becomes nonuniform, or pseudoperiodic; namely, one of the spatial harmonics remains the same as in the initial periodic structure. Relationships are derived for the amplitudes of the spatial-wave harmonics, interaction coefficient, and coupling impedance of the pseudoperiodic system. The possibility of the mode selection in pseudoperiodic slowing systems when the synchronism condition is satisfied for the spatial harmonic of one mode is investigated. The efficiency of suppressing spurious spatial harmonics and modes for linear and abrupt variation of spacing is estimated. The elaborated principle of selection of spatial harmonics and modes is illustrated by an example of a two-section helical-waveguide slowing system.
Some possible interpretations from data of the CODALEMA experimentAhmed Ammar Rebai PhD
The purpose of the CODALEMA experiment, installed at the Nan\c{c}ay Radio Observatory (France), is to study the radio-detection of ultra-high energy cosmic rays in the energy range of 10^{16}-10^{18} eV. Distributed over an area of 0.25 km^2, the original device uses in coincidence an array of particle detectors and an array of short antennas, with a centralized acquisition. A new analysis of the observable in energy for radio is presented from this system, taking into account the geomagnetic effect. Since 2011, a new array of radio-detectors, consisting of 60 stand-alone and self-triggered stations, is being deployed over an area of 1.5 km^2 around the initial configuration. This new development leads to specific constraints to be discussed in term of recognition of cosmic rays and in term of analysis of wave-front.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2. Devay, Meszaros, and Rao on a real corrosion system.1,6
They
implemented the treatment, adding some considerations about
the error arising from the uncompensated resistance and the
double layer capacitance. So far the study of nonlinearity was
restricted to the faradic reaction of the electrochemical system.
Antaño-Lopez and co-workers were the first to apply the
intermodulation technique to the study of the double layer.7
They implemented an original setup to perform the experiment
and proposed a new name: the modulation of interface
capacitance transfer function (MICTF) technique. The key
point of this setup was to employ a lock-in amplifier to
demodulate the intermodulation sidebands. Their idea was to
prove that to consider the double layer capacitance as
independent of the potential was an oversimplification. They
applied their model to the study of a system with ion transfer
and to the study of the interface between TiO2 and SnO2 in a
dye-sensitized nanocrystalline solar cell (DSSC).8
Starting from the treatment of Antaño-Lopez and co-
workers,7
this work is focused on the development of a
technique for the analysis of the nonlinear behavior of
electrochemical systems, using a diode as a relatively ideal
nonlinear system; the diode is stable, reproducible, and the
intermodulation can be predicted. In fact, the diode is
equivalent to a conductance in parallel with a capacitance,
which is dependent on the polarization potential. Additionally,
a diode represents a fairly challenging benchmark for
electrochemical instrumentation, due to its high impedance.
Based on the intermodulation sidebands, we defined a general
transfer function called differential immittance spectrum.
Results from a dummy cell containing only passive elements
(linear system) were used to validate the results and to show
the resolution limit of our instrumentation.
■ THEORETICAL BACKGROUND
In the intermodulated differential immittance spectroscopy
(IDIS), the system is perturbed by an input that contains two
sine waves: the probe signal at angular frequency Ω and the
stimulus signal at angular frequency ω. Following Figure 1f and
removing the higher-order harmonics of the probe and
stimulus, but keeping the sidebands, one can describe the
output as composed by four sine waves: the probe response at
frequency fp, the stimulus response at frequency fs, and the two
sidebands generated by the intermodulation at frequencies fp −
fs and fp + fs. If the input is the potential and the output is the
current, the admittance at the angular frequencies Ω and ω can
be calculated at once from
Ω =
Ω
Ω
Y( )
I( )
U( ) (1)
ω
ω
ω
=
Y( )
I( )
U( ) (2)
where I and U represent the Fourier transforms of the current
and potential at the angular frequencies Ω or ω. We want to
stress that the conductance, G, is equal to Re(Y), and the
susceptance, B, is equal to Im(Y). From eqs 1 and 2, the
differential conductance, dG, differential susceptance, dB, and
differential admittance, dY, can be defined in a general sense as
ω
ω
ω
Ω = Ω
G
d ( , )
G ( )
U( ) (3)
ω
ω
ω
Ω = Ω
B
d ( , )
B ( )
U( ) (4)
ω ω ω
Ω = Ω + Ω
Y G B
d ( , ) d ( , ) jd ( , ) (5)
where GΩ, BΩ, and YΩ are the Fourier transforms of the probe
conductance, susceptance, and admittance at the stimulus
angular frequency ω, respectively, and j is the imaginary unit. It
has to be stressed that Re(dY) is equal to Re(dG) − Im(dB),
and Im(dY) is equal to Im(dG) + Re(dB). The conductance
Figure 1. Schematic of the Fourier transform for a single (first row) and double input measurement (second row) on a linear (second column) and
nonlinear system (third column). Δ represents the fundamental harmonic, □ the higher-order harmonics, and ○ the intermodulation sidebands.
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3. and susceptance can be measured in the time domain by the
lock-in amplifier, as done by Antaño-Lopez and co-workers.7
However, their Fourier transform at ω can be calculated
directly from the sidebands rising from the intermodulation
(see appendix A of the Supporting Information). The general
term intermodulated differential immittance spectroscopy was
used to describe both differential admittance and differential
impedance. In appendix B of the Supporting Information, the
treatment for the intermodulated differential impedance
spectroscopy is reported. The differential conductance and
the differential susceptance both respond to the Kramer−
Kronig relations.
The equivalent circuit of a diode in reverse bias is
represented by a capacitance in parallel to a conductance.
The capacitance takes into account the accumulation of charge
in the space charge region, and its dependence on the
polarization potential is given by the Mott−Schottky equation.9
The parallel conductance represents the leakage current due to
thermo-emission of electrons and movement of the holes in the
valence band; the conductance is weakly dependent on the
polarization potential. The stimulus affects the potential across
the diode, and as consequence, the value of the capacitance of
the diode, which is the origin of the amplitude modulation of
the probe current at the stimulus frequency. The Fourier
transform of the current is very similar to that depicted by
Figure 1f. Following eqs 3, 4, and 5 and the equivalent circuit of
the Schottky diode, dG should be negative and imaginary, and
dB should be negative and real (see appendix C of the
Supporting Information). Both terms are correlated to the
variation of the capacitance with the potential; however, the
value of dG is proportional to ω, while the value of dB is
proportional to Ω. From the Mott−Schottky analysis, it is
possible to derive the flat band voltage and, knowing the
relative permittivity εr, the dopant concentration of the
semiconductor in the diode. The same information is obtained
by the intermodulated differential admittance spectroscopy. We
want to stress that Mott−Schottky analysis is done acquiring
several EIS at different potential values and plotting the
reciprocal of the square of the calculated capacitance against the
potential, while the differential admittance spectrum is obtained
at a single potential.
■ EXPERIMENTAL SECTION
The Instrument. The instrument was composed by a
potentiostat PG_310USB (HEKA Elektronik), a 2-channel
lock-in amplifier HF2LI (Zurich Instruments), a 4-channel
oscilloscope PicoScope 4424 (Pico Technology), two sine wave
generators (included in the lock-in amplifier), and a personal
computer equipped with Matlab. The main characteristic of the
potentiostat is a wide bandwidth associated with a low noise
level, so that only small distortions are introduced at high
frequencies. Figure 2 shows a schematic of the instrument.
Generator 1 provides the sine wave of the stimulus at frequency
fs and generator 2 the sine wave of the probe at frequency fp (fp
> fs); the latter was also used as a reference for the lock-in
amplifier. The signals produced by the generators were
summed and sent to the potentiostat, which was connected
to the investigated system. The current and potential outputs of
the potentiostat were sent to the first two channels of the
oscilloscope; the current output was sent also to the lock-in
amplifier, where it was demodulated according to the reference
signal (the probe signal). The in-phase and out-of-phase
components of the current were amplified and sent to the
remaining two channels of the oscilloscope. The immittance
and the differential immittance are obtained by the PC, using
homemade Matlab-based software and calculating the Fourier
transform of the signals recorded by the four channels of the
oscilloscope.
Investigated Systems. Two systems were investigated: a
Schottky diode 80SQ040 (International Rectifier), as an ideal
nonlinear system and a dummy cell composed by a 9.4 MΩ
resistor in parallel with a 2 nF capacitor, as an ideal linear
system. Cyclic voltammetry and electrochemical impedance
spectroscopy (EIS) were performed on the Schottky diode
using a Zahner Zennium (Zahner) potentiostat between 0 and
2 V. A scan rate of 10 mV s−1
was used for the cyclic
voltammetry. The impedance spectra were measured between
100 kHz and 100 mHz, with 10 points per decade, using a 10
mV amplitude voltage sine wave, and an impedance spectrum
was recorded each 100 mV. The diode was connected to the
potentiostat using the IUPAC official setup, with the cathode
attached to the working electrode and the anode to the
reference and counter electrodes. For the measurement of the
differential immittance, the probe frequency was kept constant
at 1 kHz, and the stimulus frequency was scanned between 100
Hz and 100 mHz, at 10 points per decade. The amplitude of
the probe and the stimulus were 20 and 40 mV, respectively.
These are optimized values that provide good signal-to-noise
ratios. Ten cycles of the stimulus signal were recorded with 20
points per period of the probe signal. A polarization voltage of
0.5 V was chosen for both systems.
■ RESULTS AND DISCUSSION
Cyclic Voltammetry and EIS on the Diode. Figure 3a
shows the cyclic voltammogramm of the diode at a scan rate of
10 mV s−1
, performed between 0 and 2 V. This voltage window
corresponds to the inverse region of the diode; its flat band
voltage is a located at −0.53 V. The leakage current is equal to
ca. 400 nA at a 0.5 V polarization voltage. In the same voltage
window an impedance spectrum was recorded each 100 mV.
Calculating the parallel capacitance from the imaginary part of
the admittance at 100 kHz for each potential, it was possible to
use the Mott−Schottky analysis to obtain the flat band voltage
Figure 2. Schematic of the instrument setup. Generator 1 outputs the
stimulus signal and generator 2 the probe signal. The potentiostat
sends the potential output and the current output to the first two
channels of the oscilloscope and current output to the input of the
lock-in amplifier. The lock-in demodulates the current and sends the
in-phase and out-of-phase components to the second two channels of
the oscilloscope.
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4. and the dopant concentration. The Mott−Schottky analysis is
based on the following equation (for n-type semiconductors):
ε ε
=
| |
− −
| |
−
⎛
⎝
⎜
⎞
⎠
⎟
C N
U U
k T
1 2
e e
SC
2
r 0 D
E fb
B
(6)
where CSC is the capacitance of the Schottky diode, εr the
relative dielectric constant, ε0 the permittivity of vacuum, e the
charge of the electron, ND the concentration of dopants, UE the
polarization voltage, Ufb the flat band voltage, kB the Boltzmann
constant, T the absolute temperature. In Figure 3b, the Mott−
Schottky plot for the diode is reported. From the linear
regression, a flat band potential of −0.536 ± 0.005 V and a
dopant concentration of 3.61 × 1017
± 1015
cm−3
were
calculated (εr = 11.68). The same results were achieved using
lower frequencies (down to 1 kHz) and restricting the potential
range from 0.2 to 2 V.
Intermodulated Differential Immittance Spectrosco-
py (IDIS) on the Schottky Diode. For measuring the
differential immitance spectra, two configurations are possible:
the current and potential output of the potentiostat are
connected to a 2-channel oscilloscope and the differential
immittance is calculated from the Fourier transform of the
current at Ω − ω and Ω + ω (oscilloscope setup) or the current
output is demodulated at angular frequency Ω by a lock-in
amplifier and the in-phase and out-of-phase components are
recorded by an oscilloscope (lock-in setup). In the latter case, a
4-channel oscilloscope is necessary: potential, current, in-phase
component, and out-of-phase component have to be recorded
as a function of time, and the differential immittance is
calculated from the Fourier transform of the in-phase and out-
of-phase components at ω. In the next paragraph, we will
discuss the oscilloscope setup and its limitations.
The differential immittance spectra were measured at a
polarization voltage of 0.5 V, using a probe frequency of 1 kHz
and a stimulus frequency scanning from 100 Hz to 100 mHz,
with 10 points per decade. Ten cycles of the stimulus signal and
20 points per period of the probe signal were recorded with two
channels of the oscilloscope. The Fourier transform was
performed on the potential at angular frequencies Ω and ω and
on the current at angular frequencies Ω, ω, Ω − ω, and Ω + ω,
using a Blackman−Harris window function (see appendix D of
the Supporting Information). The result of the Fourier
transform of the current in the whole range of frequencies is
reported in Figure 4b for the stimulus frequency of 10 Hz. The
sidebands are located at 990 and 1010 Hz, as expected for the
intermodulation effect. The impedance spectrum at 0.5 V can
be calculated from the Fourier transform of the potential and
current at ω. This is reported in the Nyquist plot of Figure 4a,
together with the impedance measured previously at 0.5 V with
the Zahner Zennium. The two curves are very close, thus
indicating the good quality of data. The resistance measured by
the IDIS is smaller because of the higher amplitude of the
stimulus oscillation. By fitting the impedance spectrum with a
capacitance parallel to a resistance, the values of 1.76 nF and
7.74 MΩ are obtained. The good quality of the fitting also
confirms that the data respond to the Kramer−Kronig relations.
The measurement of IDIS can be affected by the control
loop of the potentiostat and bandwidth of the current follower.
First, the control loop of the potentiostat can introduce a delay
and an attenuation of the applied sine wave potential at high
frequencies (the probe frequency) with respect to the
Figure 3. (a) Cyclic voltammetry of the diode between 0 and 2 V at 10
mV s−1
. (b) Mott−Schottky plot of the capacitance of the diode
measured at 100 kHz and linear regression.
Figure 4. (a) Nyquist plot of the EIS of the diode performed with a
commercial instrument and that recorded with the oscilloscope setup.
(b) Fourier transform of the current of the diode with a stimulus
frequency of 10 Hz and a probe frequency of 1 kHz.
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5. generated one; this error is easily compensated because the real
applied potential is measured. The bandwidth of the current
follower also introduces a delay and an attenuation of the
measured current with respect to the real current flowing
through the system. The correction of this distortion requires
the knowledge of the transfer function of the current followers.
In general, the lower is the current range (the higher is the
current amplification), the lower is the bandwidth of the
current follower. In this work, rather low current ranges (10
μA) had to be used to enhance the signal of the sidebands. The
transfer function of the current amplifier is obtained by means
of a calibrated resistor and measuring its impedance in the
frequency range from 100 kHz to 100 mHz. The normalized
admittance represents the transfer function of the current
follower.
In Figure 5a, the differential conductance, dG, and the
differential susceptance, dB, are reported in their real and
imaginary part, as a function of the stimulus frequency. As
expected (see appendix C of the Supporting Information), the
value of dG is imaginary, negative, and increases with increasing
fs, while the value of dB is real, negative, and constant with fs. In
Figure 5b, the differential admittance, dY, is reported as a
function of the stimulus frequency. dY is composed only by the
imaginary part, while the real part remains mostly near 0.
Im(dY) increases at higher stimulus frequencies, in accordance
with the value of Im(dG) becoming larger. The differential
susceptance for the diode is given by:
ε ε
= −Ω
| |
− −
| |
−
⎛
⎝
⎜
⎞
⎠
⎟
B
N
U U
k T
d
1
2
e
2 e
r 0 D
E fb
B
3/2
(7)
More details on eq 7 can be found in appendix C of the
Supporting Information. Equation 7 can be used together with
eq 6 for calculating the flat band voltage and the dopant level,
with results equal to −0.535 ± 0.01 V and 3.92 × 1017
± 8 ×
1015
cm−3
, respectively. Table 1 presents a summary of the
results obtained with the different techniques compared with
the tabulated data. They all show to be in good agreement.
The advantage of using the oscilloscope setup is of course a
reduction of the costs and connections required. However, care
has to be taken that high resolution in the F-domain is
obtained, which is achieved by long time recording; this is
necessary to visualize precisely the sidebands and separate them
from the sidelobes of the probe frequency, as explained in more
detail in appendix D of the Supporting Information. For this
reason, up to 10 cycles of the stimulus signal are acquired.
Moreover, to avoid the high frequency noise, 20 points per
period of the probe signal are recorded. The restriction in the
ratio Ω/ω rises from the fact that the number of points
recorded at each stimulus frequency is equal to some 200 Ω/ω,
and that due to limitations in the calculation power of the PC,
files larger than 10 million points are difficult to handle. If lower
frequencies have to be reached, the lock-in amplifier in
combination with four low-pass filters has to be used to
demodulate the current with respect to the probe frequency.
Moreover, as will be shown below, the lock-in amplifier has a
slightly higher resolution and better signal-to-noise ratio, with
respect to the oscilloscope and could be necessary for extremely
low values of the differential immittance.
Use of the Lock-in Amplifier for Measuring the IDIS. A
lock-in amplifier can be used to measure directly the
conductance and the susceptance of the system at the probe
frequency. Under these conditions, additionally to the current
and potential at fs, the measured conductance and susceptance
can also be recorded by a 4-channels oscilloscope (lock-in
setup). After the acquisition, the differential conductance and
susceptance can be calculated from the Fourier transform of the
conductance and susceptance at angular frequency, ω,
respectively, as explained in the Theoretical Background by
eqs 3−5. However, a lock-in amplifier may be a source of
distortion in the measured differential immittance: first, the
phase of the demodulator of the current has to be adjusted to
avoid delays between the real current flowing through the
system and the measured current; moreover, the lock-in
amplifier tries to cut off the intermodulation, as it considers it as
noise. The advantage of using the lock-in amplifier is that the
conductance and the susceptance are directly measured and it
allows exploring a larger range of stimulus frequencies because
Figure 5. (a) Bode plot of the real (empty symbols) and imaginary
part (solid symbols) of the differential conductance (● and ○) and of
the differential susceptance (△ and ▲). (b) Bode plot of the real (○)
and imaginary part (●) of the differential admittance.
Table 1. Flat Band Potential, Ufb, and Dopant
Concentration, ND, of the Diode Calculated with the
Differential Admittance Measured by the Oscilloscope Setup
and the Lock-in Setup, with the Mott-Schottky (M-S)
Analysis, and Reported in the Datasheet
Ufb (V) ND (1017
cm−3
)
oscilloscope setup −0.535 ± 0.01 3.92 ± 0.08
lock-in setup −0.527 ± 0.006 3.88 ± 0.01
M-S analysis −0.536 ± 0.005 3.61 ± 0.01
tabulated data −0.53 not reported
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6. high frequency signals do not need to be recorded. The setup in
this paper consists of a 2-channel lock-in amplifier; before
starting the experiment, the software automatically forces the
lock-in to detect the phase shift between the generated and the
applied probe signal (the delay introduced by the control loop
of the potentiostat) and then adds it to the shift in phase of the
current follower (measured as in paragraph 4.2) and sets it as
the phase of the demodulator. In this way, the distortion
between the measured and the real current flowing through the
system is removed, apart from a proportional factor that can be
calculated later from the transfer function of the potentiostat.
A lock-in amplifier is designed to demodulate the input signal
with respect to a reference signal, which can be external or
internal. The demodulation consists in measuring the
correlation between the input and reference signal (in a
mathematical sense). The correlation can be then used to
calculate the in-phase and out-of-phase components of the
input signal with respect to the reference signal. After the
demodulation, the in-phase and out-of-phase components pass
through a low-pass filter and an amplifier. The series of the
demodulation and low-pass filter is equivalent to a band-pass
filter. Because of the low-pass filter, the lock-in amplifier
introduces a distortion to the differential immittance through
its own transfer function. The low-pass filter has a bandwidth
that is given by the time constant of the lock-in amplifier and
the order of the filter: a long time constant and a high-order
filter attenuate all the signals away from the reference, including
the intermodulation effect and a short time constant and a low
order filter allow demodulating the sidebands properly at
expenses of high noise level. This effect generates a limitation
on the higher stimulus frequency that can be measured: in the
proposed setup, with a fourth-order filter (24 db/octave), the
upper limit in fs is equal to 0.1fp.
If we name Δω the bandwidth of the lock-in in rad s−1
, the
relevant parameter that controls the transfer function of the
lock-in amplifier with respect to the stimulus frequency is given
by ω/Δω. The relation between the time constant, tC, and the
bandwidth is
ω
Δ =
A
tC (8)
where A is a constant that depends on the low-pass filter order.
The transfer function of the lock-in, H(ω/Δω), was obtained
from the ratio of the differential admittance measured from the
lock-in setup and the one measured by the oscilloscope setup
for the Schottky diode, recorded for different values of Δω and
ω/Δω. In Figure 6, the measured transfer function of the lock-
in amplifier is reported in the Bode representation. The
experimental data (empty dots) were fitted with a fourth-order
inverse polynomial (line), which was thereafter used for the
proper correction. For ω/Δω = 1, the attenuation is 3 db, and
the phase-shift is ca. 90 degrees. For ω/Δω > 1, H attenuates
and strongly delays the intermodulation signal; however, larger
frequencies are measurable. For ω/Δω < 1, H tends to unity
and the phase-shift tends to 0 degrees, but frequencies near fp
are not accessible. A good compromise was obtained with ω/
Δω = 0.2. The homemade software automatically sets Δω = 5ω
each time the stimulus frequency is changed. In this way, it is
possible to measure dG and dB with higher precision than by
using the oscilloscope setup. In Table 1, the analysis of the
differential immitance of the diode measured with the lock-in
setup, maintaining Δω = 5ω is reported and is in very good
agreement with the previous results obtained with the
oscilloscope setup, with the Mott−Schottky analysis and
reported in the database.
The Ideal Linear System: The Dummy Cell. A dummy
cell composed by passive elements is the ideal linear system. A
dummy cell consisting of a 9.4 MΩ resistor in parallel to a 2 nF
capacitor was built and tested. The differential admittance was
measured at 0.5 V potential using a probe signal of 1 kHz,
having amplitude of 20 mV and a stimulus signal ranging from
100 Hz to 100 mHz, with 40 mV of amplitude. The
measurement was performed with both oscilloscope setup
and lock-in setup. In Figure 7a, the Fourier transform of the
current signal in a large range of frequencies is reported for fs
equal to 10 Hz. For comparison, the same result for the
Schottky diode is reported. It can be immediately observed that,
while for the Schottky diode the intermodulation sidebands are
clearly visible, for the dummy cell, the intermodulation
sidebands are completely buried under the noise level. The
differential admittance of the dummy cell is a measure of the
noise level of the device. In Figure 7b, the noise level of the
IDIS for the oscilloscope setup and for the lock-in setup,
measured though the differential admittance of the dummy cell,
is shown. We want to stress that the noise level is very low and
less than 1% of the measured value in the diode. Also, it can be
observed that in the range between 1 and 10 Hz, the lock-in
setup works better than the oscilloscope setup. Under these
conditions, the limit of detectability of the differential
admittance is equal to ca. 20 nS V−1
.
■ CONCLUSIONS
The intermodulation effect can be used to study the
nonlinearity of electrochemical and electronic systems. To
measure it, it is possible to proceed with a simplified approach,
using a 2-channel oscilloscope to record the current and the
Figure 6. Bode plots of the lock-in amplifier transfer function H,
experimental data (○), and fourth-order inverse polynomial fit (line):
(a) absolute value and (b) phase-shift of H.
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7. potential in the system (oscilloscope setup), or measure directly
the conductance and susceptance of the system by demodulat-
ing the current with a lock-in amplifier and recording the
signals with a 4-channel oscilloscope (lock-in setup). Both
configurations have advantages and disadvantages. The
oscilloscope setup is less complicated, but a limitation rises in
the maximum value of Ω/ω that can be explored, mainly due to
the limited calculation power of the personal computer. The
lock-in setup has the advantage to make lower stimulus
frequencies accessible; however, it has a limited higher stimulus
frequency (fs < 0.1fp) due to the correlation between the time
constant of the lock-in amplifier and noise rejection. Moreover,
the transfer function of the lock-in amplifier, H, has to be
measured. We proposed to measure H by comparison of the
differential immittances of a Schottky diode obtained by the
lock-in setup and the oscilloscope setup in the range of stimulus
frequencies that are available for both configurations. The
differential immittance of a diode (an ideal nonlinear system)
was measured. From the data, it was possible to obtain the flat
band voltage and the dopant concentrations, which showed
good agreement with the values tabulated and obtained with
classical techniques (such as the Mott−Schottky analysis).
Measuring the differential admittance on a dummy cell
composed by passive elements, it was possible to quantify the
detectability limit of the setups; the error on the values of dY
obtained for the diode was estimated to be less than 1%. We
can foresee the importance of such a technique to study the
reaction mechanism of electro-catalytic reactions, the transport
and trapping of carriers in semiconductors, the electron transfer
in surface-confined species, the corrosion behavior of metals,
and in other fields.
■ ASSOCIATED CONTENT
*
S Supporting Information
The Supporting Information contains four appendixes: A,
correlation between differential admittance and sidebands; B,
correlation between differential impedance and differential
admittance; C, differential admittance of the Schottky diode;
and D, the window function and the sidelobes. This material is
available free of charge via the Internet at http://pubs.acs.org.
■ AUTHOR INFORMATION
Corresponding Author
*A.B.: e-mail, alberto.battistel@rub.de. F.L.M.: e-mail, fabio.
lamantia@rub.de.
Notes
The authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
The financial support by the Federal Ministry of Education and
Research (BMBF) in the framework of the project “Energies-
peicher” (Grant FKZ 03EK3005) and the funding of the
Centre for Electrochemical Sciences (CES) by the European
Commission and the state North Rhine-Westphalia (NRW) in
the framework of the HighTech.NRW program are gratefully
acknowledged.
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Figure 7. (a) Fourier transform of the current of the diode (line) and
of the dummy cell (○) with a stimulus frequency of 10 Hz and a probe
frequency of 1 kHz. (b) Bode plot of the absolute value of the
differential admittance measured by the oscilloscope setup (○) and
the lock-in setup (line).
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