analytic equation
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2021 ◽  
Author(s):  
DENYS ZAIKIN ◽  
Stig Jonasen ◽  
Simon L. Mikkelsen

<div>Being able to predict radiated emissions before using an accredited laboratory can be both time-effective and cost-effective. This study presents a model for predicting radiated emissions from power converters by measuring the common mode current in the attached cable. When power converters are tested for radiated emissions, the attached cables tend to be thick because of the high currents they carry. Ideally, these cables leave the chamber through connectors in an opening positioned precisely at the middle of the bottom of the turntable in keeping with CISPR 32. However, these connectors are typically not intended for currents higher than 16 A. Consequently, such cables are usually inserted through the side wall of the chamber and are necessarily laid horizontally on the chamber floor. When the turntable is to be rotated with a device on it during a test, the length of the cable attached to the device can exceed 10 meters. The proposed model in this study is based on the transmission line model of a cable loaded with reactive impedance and the assumption that the current distribution along the cable follows a sinusoidal distribution law, much like in dipole antenna theory. The analytic equation of the radiation pattern is derived, and a simplified approximation equation has also been presented. The proposed model also works with short, attached cables and is thus universal. The Maxima software code for automated calculation of the radiated field from measurement data is supplied as supplemental material. The proposed model was experimentally validated by running the fuel cell converter module at 5 kW output power.</div>


2021 ◽  
Author(s):  
DENYS ZAIKIN ◽  
Stig Jonasen ◽  
Simon L. Mikkelsen

<div>Being able to predict radiated emissions before using an accredited laboratory can be both time-effective and cost-effective. This study presents a model for predicting radiated emissions from power converters by measuring the common mode current in the attached cable. When power converters are tested for radiated emissions, the attached cables tend to be thick because of the high currents they carry. Ideally, these cables leave the chamber through connectors in an opening positioned precisely at the middle of the bottom of the turntable in keeping with CISPR 32. However, these connectors are typically not intended for currents higher than 16 A. Consequently, such cables are usually inserted through the side wall of the chamber and are necessarily laid horizontally on the chamber floor. When the turntable is to be rotated with a device on it during a test, the length of the cable attached to the device can exceed 10 meters. The proposed model in this study is based on the transmission line model of a cable loaded with reactive impedance and the assumption that the current distribution along the cable follows a sinusoidal distribution law, much like in dipole antenna theory. The analytic equation of the radiation pattern is derived, and a simplified approximation equation has also been presented. The proposed model also works with short, attached cables and is thus universal. The Maxima software code for automated calculation of the radiated field from measurement data is supplied as supplemental material. The proposed model was experimentally validated by running the fuel cell converter module at 5 kW output power.</div>


2021 ◽  
Author(s):  
DENYS ZAIKIN ◽  
Stig Jonasen ◽  
Simon L. Mikkelsen

<div>Being able to predict radiated emissions before using an accredited laboratory can be both time-effective and cost-effective. This study presents a model for predicting radiated emissions from power converters by measuring the common mode current in the attached cable. When power converters are tested for radiated emissions, the attached cables tend to be thick because of the high currents they carry. Ideally, these cables leave the chamber through connectors in an opening positioned precisely at the middle of the bottom of the turntable in keeping with CISPR 32. However, these connectors are typically not intended for currents higher than 16 A. Consequently, such cables are usually inserted through the side wall of the chamber and are necessarily laid horizontally on the chamber floor. When the turntable is to be rotated with a device on it during a test, the length of the cable attached to the device can exceed 10 meters. The proposed model in this study is based on the transmission line model of a cable loaded with reactive impedance and the assumption that the current distribution along the cable follows a sinusoidal distribution law, much like in dipole antenna theory. The analytic equation of the radiation pattern is derived, and a simplified approximation equation has also been presented. The proposed model also works with short, attached cables and is thus universal. The Maxima software code for automated calculation of the radiated field from measurement data is supplied as supplemental material. The proposed model was experimentally validated by running the fuel cell converter module at 5 kW output power.</div>


2021 ◽  
Author(s):  
DENYS ZAIKIN ◽  
Stig Jonasen ◽  
Simon L. Mikkelsen

<div>Being able to predict radiated emissions before using an accredited laboratory can be both time-effective and cost-effective. This study presents a model for predicting radiated emissions from power converters by measuring the common mode current in the attached cable. When power converters are tested for radiated emissions, the attached cables tend to be thick because of the high currents they carry. Ideally, these cables leave the chamber through connectors in an opening positioned precisely at the middle of the bottom of the turntable in keeping with CISPR 32. However, these connectors are typically not intended for currents higher than 16 A. Consequently, such cables are usually inserted through the side wall of the chamber and are necessarily laid horizontally on the chamber floor. When the turntable is to be rotated with a device on it during a test, the length of the cable attached to the device can exceed 10 meters. The proposed model in this study is based on the transmission line model of a cable loaded with reactive impedance and the assumption that the current distribution along the cable follows a sinusoidal distribution law, much like in dipole antenna theory. The analytic equation of the radiation pattern is derived, and a simplified approximation equation has also been presented. The proposed model also works with short, attached cables and is thus universal. The Maxima software code for automated calculation of the radiated field from measurement data is supplied as supplemental material. The proposed model was experimentally validated by running the fuel cell converter module at 5 kW output power.</div>


2021 ◽  
Vol 9 ◽  
Author(s):  
Cheng-Ling Kuo ◽  
Earle Williams ◽  
Toru Adachi ◽  
Kevin Ihaddadene ◽  
Sebastien Celestin ◽  
...  

Recent efforts to compare the sprite ratios with theoretical results have not been successfully resolved due to a lack of theoretical results for sprite streamers in varying altitudes. Advances in the predicted emission ratios of sprite streamers with a simple analytic equation have opened up the possibility for direct comparisons of theoretical results with sprite observations. The study analyzed the blue-to-red ratios measured by the ISUAL array photometer with the analytical expression for the sprite emission ratio derived from the modeling of downward sprite streamers. Our statistical studies compared sprite halos and carrot sprites where the sprite halos showed fair agreement with the predicted ratios from the sprite streamer simulation. But carrot sprites had lower emission ratios. Their estimated electric field has a lower bound of greater than 0.4 times the conventional breakdown electric field (Ek). It was consistent with the results of remote electromagnetic field measurements for short delayed or big/bright sprites. An unexpectedly lower ratio in carrot sprites occurred since sprite beads or glow in carrot sprites may exist and contribute additional red emission.


2021 ◽  
Author(s):  
Davide Nardi

Abstract This paper provides a methodology for the application of a machine learning-based framework for fused deposition modelling manufacturing. The approach was developed to take into account the influence of the material, the part geometry, the process parameters on the maximum part warpage defined by the user. The results showed the effectiveness of machine learning for both classification and regression purposes so that the printability of the part is firstly provided, based on the selected warpage threshold, and secondly, the part warpage can be predicted within the problem design space variables, i.e. part material, part height, part length, and layer thickness. The limitations of the use of the analytic equation as a data-points generator are widely discussed, along with the future research based on the obtained preliminary results. In conclusion, the described methodology represents a concrete step towards a first-time-right strategy in the field of manufacturing processes.


2021 ◽  
pp. 1-7
Author(s):  
Bachir Ouari ◽  
◽  
Malika Madani ◽  
Mohamed Lagraa ◽  
◽  
...  

The magnetization of antiferromagnetic nanoparticles is investigated with the Fokker-Planck equation describing the evolution of the distribution function of the magnetization of an nanoparticle. By solving this equation numerically, the relaxation times, and dynamic susceptibility are calculated for dc field orientations across wide ranges of frequencies, amplitude of the fields and damping. Analytic equation for the dynamic susceptibility is also proposed. It is shown that the damping alters the magnetization in the presence of oblique field applied


2021 ◽  
Vol 18 ◽  
Author(s):  
Aykut Elmas ◽  
Guliz Akyuz ◽  
Ayhan Bergal ◽  
Muberra Andac ◽  
Omer Andac

Background: pH sensitive dendrimers attached to nanocarriers, as one of the drug release systems, has become quite popular due to their ease of manufacture in experimental conditions and ability to generate fast drug release in the targeted area. This kind of fast release behavior cannot be represented properly most of the existing kinetic mathematical models. Besides, these models have either no pH dependence or pH dependence added separately. So, they have remained one dimensional. Objective: The aim of this study was to establish the proper analytic equation to describe the fast release of drugs from pH sensitive nanocarrier systems. Then, to combine it with the pH dependent equation for establishing a two-dimensional model for whole system. Methods: We used four common kinetic models for comparison and we fitted them to the release data. Finding that, only Higuchi and Korsmeyer-Peppas models show acceptable fit results. None of these models have pH dependence. To get a better description for pH triggered fast release, we observed the behavior of the slope angle of the release curve. Then we puroposed a new analytic equation by using relation between the slope angle and time. Result: To add a pH dependent equation, we assumed the drug release is “on” or “off” above/below specific pH value and we modified a step function to get a desired behavior. Conclusion: Our new analytic model shows good fitting, not only one-dimensional time dependent release, but also two-dimensional pH dependent release, that provides a useful analytic model to represent release profiles of pH sensitive fast drug release systems.


2020 ◽  
Vol 13 (10) ◽  
pp. 5259-5275
Author(s):  
Bangsheng Yin ◽  
Qilong Min ◽  
Emily Morgan ◽  
Yuekui Yang ◽  
Alexander Marshak ◽  
...  

Abstract. An analytic transfer inverse model for Earth Polychromatic Imaging Camera (EPIC) observations is proposed to retrieve the cloud-top pressure (CTP) with the consideration of in-cloud photon penetration. In this model, an analytic equation was developed to represent the reflection at the top of the atmosphere from above cloud, in cloud, and below cloud. The coefficients of this analytic equation can be derived from a series of EPIC simulations under different atmospheric conditions using a nonlinear regression algorithm. With estimated cloud pressure thickness, the CTP can be retrieved from EPIC observation data by solving the analytic equation. To simulate the EPIC measurements, a program package using the double-k approach was developed. Compared to line-by-line calculation, this approach can calculate high-accuracy results with a 100-fold computation time reduction. During the retrieval processes, two kinds of retrieval results, i.e., baseline CTP and retrieved CTP, are provided. The baseline CTP is derived without considering in-cloud photon penetration, and the retrieved CTP is derived by solving the analytic equation, taking into consideration in-cloud and below-cloud interactions. The retrieved CTPs for the oxygen A and B bands are smaller than their related baseline CTP. At the same time, both baseline CTP and retrieved CTP at the oxygen B band are larger than those at the oxygen A band. Compared to the difference in baseline CTP between the B band and A band, the difference in retrieved CTP between these two bands is generally reduced. Out of around 10 000 cases, in retrieved CTP between the A and B bands we found an average bias of 93 mb with a standard deviation of 81 mb. The cloud layer top pressure from Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) measurements is used for validation. Under single-layer cloud situations, the retrieved CTPs for the oxygen A band agree well with the CTPs from CALIPSO, the mean difference of which within 5 mb in the case study. Under multiple-layer cloud situations, the CTPs derived from EPIC measurements may be larger than the CTPs of high-level thin clouds due to the effect of photon penetration.


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