Electrical: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=194
en-us2022 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 18 Jan 2022 01:30:12 GMTTue, 18 Jan 2022 01:30:12 GMTNew applications in the Electrical categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgElectrical: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=194
Use Optimization for Worst Case Analysis
https://www.maplesoft.com/applications/view.aspx?SID=154769&ref=Feed
In this application, the worst case analysis for a circuit with Three-pin regulator is performed. Usually, Extreme value analysis, Root Sum Square, and Monte Carlo analysis are used for the worst case analysis. As the other approach, the optimization technique can be applied for it, especially to obtain maximum and minimum cases to replace the extreme value analysis. In terms of finding the global optimal solution, the Global Optimization toolbox (add-on) is used in this application.<img src="https://www.maplesoft.com/view.aspx?si=154769/ThreePinRegulator.png" alt="Use Optimization for Worst Case Analysis" style="max-width: 25%;" align="left"/>In this application, the worst case analysis for a circuit with Three-pin regulator is performed. Usually, Extreme value analysis, Root Sum Square, and Monte Carlo analysis are used for the worst case analysis. As the other approach, the optimization technique can be applied for it, especially to obtain maximum and minimum cases to replace the extreme value analysis. In terms of finding the global optimal solution, the Global Optimization toolbox (add-on) is used in this application.https://www.maplesoft.com/applications/view.aspx?SID=154769&ref=FeedWed, 18 Aug 2021 19:46:11 ZTakashi IwagayaTakashi IwagayaCircuit Tolerance Analysis of a Broadband Pulse Transformer
https://www.maplesoft.com/applications/view.aspx?SID=154770&ref=Feed
The application implements three circuit tolerance analysis methods.
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• For the DC analysis<br>
– a full factorial analysis (the approach allows both symmetric and asymmetric tolerances)<br>
– Monte-Carlo simulation, assuming normally distributed component parameters<br>
• For the AC analysis, the symbolic partial derivatives of the circuit equations are used for a sensitivity analysis, with magnitude and phase plots illustrating the frequency-dependent behavior.
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The application also demonstrates how you can generate a customized table of results using Maple's programmatic report generation tools.<img src="https://www.maplesoft.com/view.aspx?si=154770/Broadband_pulse_transformer.png" alt="Circuit Tolerance Analysis of a Broadband Pulse Transformer" style="max-width: 25%;" align="left"/>The application implements three circuit tolerance analysis methods.
<br><br>
• For the DC analysis<br>
– a full factorial analysis (the approach allows both symmetric and asymmetric tolerances)<br>
– Monte-Carlo simulation, assuming normally distributed component parameters<br>
• For the AC analysis, the symbolic partial derivatives of the circuit equations are used for a sensitivity analysis, with magnitude and phase plots illustrating the frequency-dependent behavior.
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The application also demonstrates how you can generate a customized table of results using Maple's programmatic report generation tools.https://www.maplesoft.com/applications/view.aspx?SID=154770&ref=FeedWed, 18 Aug 2021 04:00:00 ZSamir KhanSamir KhanArc Flash Calculation (IEEE 1584-2018)
https://www.maplesoft.com/applications/view.aspx?SID=154713&ref=Feed
An arc flash is a violent eruption of heat and light caused by an electrical explosion. Arc flashes can seriously injure electricians, with fierce burns posing a significant risk to life. Other hazards include shrapnel and a pressure wave (often called an arc blast).
This application determines the minimum safe working distance from an arc flash, following the empirical methodology presented in IEEE 1584 - 2018. Specifically, the application calculates the
<UL>
<LI>intermediate average arcing current
<LI>arcing current variation factor
<LI>box size variation factor
<LI>incident energy - amount of thermal energy on a surface at a specific distance
<LI>arc flash boundary – the minimum distance from an arc flash to prevent 2nd degree burns
</UL><img src="https://www.maplesoft.com/view.aspx?si=154713/arc_flash_image.png" alt="Arc Flash Calculation (IEEE 1584-2018)" style="max-width: 25%;" align="left"/>An arc flash is a violent eruption of heat and light caused by an electrical explosion. Arc flashes can seriously injure electricians, with fierce burns posing a significant risk to life. Other hazards include shrapnel and a pressure wave (often called an arc blast).
This application determines the minimum safe working distance from an arc flash, following the empirical methodology presented in IEEE 1584 - 2018. Specifically, the application calculates the
<UL>
<LI>intermediate average arcing current
<LI>arcing current variation factor
<LI>box size variation factor
<LI>incident energy - amount of thermal energy on a surface at a specific distance
<LI>arc flash boundary – the minimum distance from an arc flash to prevent 2nd degree burns
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154713&ref=FeedTue, 09 Mar 2021 05:00:00 ZSamir KhanSamir KhanInduction Motor Analysis for Start-up Protection
https://www.maplesoft.com/applications/view.aspx?SID=154685&ref=Feed
Large currents are generated when induction motors are started. This is called the inrush current, and is much larger than the rated current even if it’s under the normal condition. On the other hand, the motor needs several levels of protection to guard against out-of-specification startup conditions by using the overcurrent relay or the impedance relay. Thus, the appropriate relay settings need to be determined by analyzing the transient trajectories and the impedance of the motor.
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This application shows how to analyze the transient behavior of a motor with impedance and torque characteristics, obtained from an equivalent circuit model of an induction motor. The application also demonstrates a protection scheme study based on these result of analysis.<img src="https://www.maplesoft.com/view.aspx?si=154685/Induction_motor.png" alt="Induction Motor Analysis for Start-up Protection" style="max-width: 25%;" align="left"/>Large currents are generated when induction motors are started. This is called the inrush current, and is much larger than the rated current even if it’s under the normal condition. On the other hand, the motor needs several levels of protection to guard against out-of-specification startup conditions by using the overcurrent relay or the impedance relay. Thus, the appropriate relay settings need to be determined by analyzing the transient trajectories and the impedance of the motor.
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This application shows how to analyze the transient behavior of a motor with impedance and torque characteristics, obtained from an equivalent circuit model of an induction motor. The application also demonstrates a protection scheme study based on these result of analysis.https://www.maplesoft.com/applications/view.aspx?SID=154685&ref=FeedMon, 01 Mar 2021 05:00:00 ZTakashi IwagayaTakashi IwagayaPower Swing Analysis for Out-Of-Step Protection
https://www.maplesoft.com/applications/view.aspx?SID=154684&ref=Feed
Power swings are disturbances in a power system, and are caused by caused by load changes, line switching, loss of generation, and other power faults. These can result in potentially dangerous spikes in current. Electrical power engineers need tools and methods to analyze power swings. This assists them in devising preventative measures that eliminate the potential for costly whole system failures.
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In this application, the transient state defined by swing equation of Two machine system, and the impedance behavior are analyzed to obtain the required information in order to determine the appropriate settings for Out-Of-Step protection.<img src="https://www.maplesoft.com/view.aspx?si=154684/PowerSwingAnalysis.png" alt="Power Swing Analysis for Out-Of-Step Protection" style="max-width: 25%;" align="left"/>Power swings are disturbances in a power system, and are caused by caused by load changes, line switching, loss of generation, and other power faults. These can result in potentially dangerous spikes in current. Electrical power engineers need tools and methods to analyze power swings. This assists them in devising preventative measures that eliminate the potential for costly whole system failures.
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In this application, the transient state defined by swing equation of Two machine system, and the impedance behavior are analyzed to obtain the required information in order to determine the appropriate settings for Out-Of-Step protection.https://www.maplesoft.com/applications/view.aspx?SID=154684&ref=FeedFri, 19 Feb 2021 05:00:00 ZTakashi IwagayaTakashi IwagayaPer Unit Analysis of a Three-Phase Power Distribution System
https://www.maplesoft.com/applications/view.aspx?SID=154679&ref=Feed
This application analyzes the power flows in a three-phase system on a per unit basis.
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Power system parameters (such as voltage, current and impedance) are often normalized to a base power and voltage before an analysis. This simplifies the analysis of the power flow in the system; for example, for a transformer, you can ignore turns ratios of transformers.<img src="https://www.maplesoft.com/view.aspx?si=154679/Per_Unit_Analysis_of_a_Power_Distribution_System.png" alt="Per Unit Analysis of a Three-Phase Power Distribution System" style="max-width: 25%;" align="left"/>This application analyzes the power flows in a three-phase system on a per unit basis.
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Power system parameters (such as voltage, current and impedance) are often normalized to a base power and voltage before an analysis. This simplifies the analysis of the power flow in the system; for example, for a transformer, you can ignore turns ratios of transformers.https://www.maplesoft.com/applications/view.aspx?SID=154679&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanLoad Flow Analysis of a Five-Bus Power System
https://www.maplesoft.com/applications/view.aspx?SID=154675&ref=Feed
This application analyzes a five-bus power system, and calculates the voltages and real and reactive powers at each bus.
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Two approaches to numerically solving the nonlinear load flow equations are demonstrated
<UL>
<LI>The symbolic real and reactive load flow equations are generated, and solved with fsolve (a powerful numerical equation solver).
<LI>The system Jacobian is constructed, and solved with Newton-Raphson iteration.
</UL><img src="https://www.maplesoft.com/view.aspx?si=154675/Five_Bus_Power_System.png" alt="Load Flow Analysis of a Five-Bus Power System" style="max-width: 25%;" align="left"/>This application analyzes a five-bus power system, and calculates the voltages and real and reactive powers at each bus.
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Two approaches to numerically solving the nonlinear load flow equations are demonstrated
<UL>
<LI>The symbolic real and reactive load flow equations are generated, and solved with fsolve (a powerful numerical equation solver).
<LI>The system Jacobian is constructed, and solved with Newton-Raphson iteration.
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154675&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanCable Ampacity using the Nehers-McGrath Method
https://www.maplesoft.com/applications/view.aspx?SID=154677&ref=Feed
Heat is generated when current flows through a cable. The ampacity of a cable is the amount of current a cable can carry without exceeding its temperature rating. Accurately estimating ampacity is critical to minimizing the total lifetime cost of a cable installation.
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This application implements the Nehers-McGrath equations and cross-checks the results against those tabulated in the National Electrical Code (2017); the good agreement means that this worksheet can be the basis of more complex cable ampacity calculations.<img src="https://www.maplesoft.com/view.aspx?si=154677/Cable_Amapacity.png" alt="Cable Ampacity using the Nehers-McGrath Method" style="max-width: 25%;" align="left"/>Heat is generated when current flows through a cable. The ampacity of a cable is the amount of current a cable can carry without exceeding its temperature rating. Accurately estimating ampacity is critical to minimizing the total lifetime cost of a cable installation.
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This application implements the Nehers-McGrath equations and cross-checks the results against those tabulated in the National Electrical Code (2017); the good agreement means that this worksheet can be the basis of more complex cable ampacity calculations.https://www.maplesoft.com/applications/view.aspx?SID=154677&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanCross-Section of Metallic Tape for Substation Earthing
https://www.maplesoft.com/applications/view.aspx?SID=154683&ref=Feed
This application calculates the cross-section of steel tape to earth a conductor for a 110/30 kV substation, correct to IEC 60287-3-1.<img src="https://www.maplesoft.com/view.aspx?si=154683/cross_section.png" alt="Cross-Section of Metallic Tape for Substation Earthing" style="max-width: 25%;" align="left"/>This application calculates the cross-section of steel tape to earth a conductor for a 110/30 kV substation, correct to IEC 60287-3-1.https://www.maplesoft.com/applications/view.aspx?SID=154683&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanUnbalanced Three-Phase Wye-Connected Load
https://www.maplesoft.com/applications/view.aspx?SID=154681&ref=Feed
An unbalanced 3-phase Wye-connected load is connected to a balanced 3-phase four-wire source. The load impedances and line voltage are known.
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This application calculates the currents in the system, and the total power drawn by the load.<img src="https://www.maplesoft.com/view.aspx?si=154681/Three Phase Wye Connected Load2.png" alt="Unbalanced Three-Phase Wye-Connected Load" style="max-width: 25%;" align="left"/>An unbalanced 3-phase Wye-connected load is connected to a balanced 3-phase four-wire source. The load impedances and line voltage are known.
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This application calculates the currents in the system, and the total power drawn by the load.https://www.maplesoft.com/applications/view.aspx?SID=154681&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanTransmission Line Simulation via Numerical Inversion of Laplace Transforms
https://www.maplesoft.com/applications/view.aspx?SID=154674&ref=Feed
This application numerically inverts the Laplace transforms that describe the voltage and current in a transmission line.
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The Laplace transforms are based on the Telegrapher’s Equations, a pair of coupled partial differential equations.
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The results describe the transient variation of current and voltage at any point on the transmission line.<img src="https://www.maplesoft.com/view.aspx?si=154674/Transmission_Line.png" alt="Transmission Line Simulation via Numerical Inversion of Laplace Transforms" style="max-width: 25%;" align="left"/>This application numerically inverts the Laplace transforms that describe the voltage and current in a transmission line.
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The Laplace transforms are based on the Telegrapher’s Equations, a pair of coupled partial differential equations.
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The results describe the transient variation of current and voltage at any point on the transmission line.https://www.maplesoft.com/applications/view.aspx?SID=154674&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanCross-Section of Metallic Steel Tape for Earthing of 110/30 kV Substation: Interactive Application
https://www.maplesoft.com/applications/view.aspx?SID=154682&ref=Feed
This interactive tool helps electrical power systems engineer calculate the cross-sectional area of metallic tape needed to adequately earth a substation.
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The equations and parameters are correct to EN 50522:2010 (Earthing of Power Installations Exceeding 1 kV A.C.)<img src="https://www.maplesoft.com/view.aspx?si=154682/Substation_Earthing_Interactive_Application.png" alt="Cross-Section of Metallic Steel Tape for Earthing of 110/30 kV Substation: Interactive Application" style="max-width: 25%;" align="left"/>This interactive tool helps electrical power systems engineer calculate the cross-sectional area of metallic tape needed to adequately earth a substation.
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The equations and parameters are correct to EN 50522:2010 (Earthing of Power Installations Exceeding 1 kV A.C.)https://www.maplesoft.com/applications/view.aspx?SID=154682&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanAntenna Arrays
https://www.maplesoft.com/applications/view.aspx?SID=154671&ref=Feed
This application calculates the far-field, electromagnetic radiation pattern for antenna arrays that repeat in the x, y and z directions, and includes several examples. This worksheet could also serve as the basis for developing tools to work with circular or triangular arrays.<img src="https://www.maplesoft.com/view.aspx?si=154671/arrays.png" alt="Antenna Arrays" style="max-width: 25%;" align="left"/>This application calculates the far-field, electromagnetic radiation pattern for antenna arrays that repeat in the x, y and z directions, and includes several examples. This worksheet could also serve as the basis for developing tools to work with circular or triangular arrays.https://www.maplesoft.com/applications/view.aspx?SID=154671&ref=FeedThu, 28 Jan 2021 05:00:00 ZSteve RoperSteve RoperLight, Chroma & Lamp Engineering Applications
https://www.maplesoft.com/applications/view.aspx?SID=154656&ref=Feed
Emulation of the spectral distributions of many non-LED popular lamps, allows for direct utility calculations based on many different parameters including chromaticity, space type, lifetime, occasion, application, cost and efficiency. 7 such parameters are used with constrained weight optimization to fish out some of the more popular lamp types used in many situations today. Will be modified some time later to deal with LEDs. Based on elemental spectral data published by NIST.<img src="https://www.maplesoft.com/view.aspx?si=154656/L14(1).jpg" alt="Light, Chroma & Lamp Engineering Applications" style="max-width: 25%;" align="left"/>Emulation of the spectral distributions of many non-LED popular lamps, allows for direct utility calculations based on many different parameters including chromaticity, space type, lifetime, occasion, application, cost and efficiency. 7 such parameters are used with constrained weight optimization to fish out some of the more popular lamp types used in many situations today. Will be modified some time later to deal with LEDs. Based on elemental spectral data published by NIST.https://www.maplesoft.com/applications/view.aspx?SID=154656&ref=FeedFri, 04 Dec 2020 05:00:00 ZYiannis GalidakisYiannis GalidakisDouble Stub Matching
https://www.maplesoft.com/applications/view.aspx?SID=154628&ref=Feed
This application will calculate the lengths of two shunt stubs that match the load to the impedance of a transmission line.<img src="https://www.maplesoft.com/view.aspx?si=154628/double_stub.png" alt="Double Stub Matching" style="max-width: 25%;" align="left"/>This application will calculate the lengths of two shunt stubs that match the load to the impedance of a transmission line.https://www.maplesoft.com/applications/view.aspx?SID=154628&ref=FeedThu, 02 Apr 2020 04:00:00 ZSamir KhanSamir KhanFitting the Steinhart-Hart Equation to Thermistor Data
https://www.maplesoft.com/applications/view.aspx?SID=154594&ref=Feed
The Steinhart-Hart equation is an empirical relationship between the temperature and resistance of a thermistor with a negative temperature coefficient (that is, a thermistor whose resistance decreases with temperature).
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1/T = A + B*ln(R) + C*ln(R)^3
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A, B and C are determined by calibrating the equation against experimental data. This application fits data for a A-10K3A1 thermistor to the Steinhart-Hart Equation.
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Specifically, this application implements the method of determining A, B and C described on the Wikipedia page for the Steinhart-Hart equation. This approach uses three pairs of values of temperature and resistance.<img src="https://www.maplesoft.com/view.aspx?si=154594/thumb.png" alt="Fitting the Steinhart-Hart Equation to Thermistor Data" style="max-width: 25%;" align="left"/>The Steinhart-Hart equation is an empirical relationship between the temperature and resistance of a thermistor with a negative temperature coefficient (that is, a thermistor whose resistance decreases with temperature).
<BR><BR>
1/T = A + B*ln(R) + C*ln(R)^3
<BR><BR>
A, B and C are determined by calibrating the equation against experimental data. This application fits data for a A-10K3A1 thermistor to the Steinhart-Hart Equation.
<BR><BR>
Specifically, this application implements the method of determining A, B and C described on the Wikipedia page for the Steinhart-Hart equation. This approach uses three pairs of values of temperature and resistance.https://www.maplesoft.com/applications/view.aspx?SID=154594&ref=FeedFri, 20 Dec 2019 05:00:00 ZSamir KhanSamir KhanComplex Nonlinear Least Squares Fitting of Immittance Data
https://www.maplesoft.com/applications/view.aspx?SID=154540&ref=Feed
This worksheet provides a procedure immfit that carries out complex nonlinear least squares fitting of experimental data to an arbitrary function of s = Iω. This can be used to fit impedance, admittance or other similar data, in which real and imaginary parts are measured as a function of frequency, to theoretical expressions such as expressions for the impedance of an electrical circuit.<img src="https://www.maplesoft.com/view.aspx?si=154540/Immfit.png" alt="Complex Nonlinear Least Squares Fitting of Immittance Data" style="max-width: 25%;" align="left"/>This worksheet provides a procedure immfit that carries out complex nonlinear least squares fitting of experimental data to an arbitrary function of s = Iω. This can be used to fit impedance, admittance or other similar data, in which real and imaginary parts are measured as a function of frequency, to theoretical expressions such as expressions for the impedance of an electrical circuit.https://www.maplesoft.com/applications/view.aspx?SID=154540&ref=FeedSat, 22 Jun 2019 04:00:00 ZDr. David HarringtonDr. David HarringtonWorst Case Circuit Analysis with Monte Carlo Simulation
https://www.maplesoft.com/applications/view.aspx?SID=154534&ref=Feed
Electrical components are manufactured in large quantities. Inconsistencies in the raw materials and the manufacturing process means that component parameters have a statistical distribution. That is, the resistance of a batch of resistors might be described by a normal distribution.
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Given the components in a circuit their parameter distribution, the circuit may not perform as specified. This is a risk that must be identified and mitigated early in the design process.
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Worst Case Circuit Analysis is a set of techniques used to analyze how variations in parameters influence circuit performance. One approach is Monte Carlo analysis, in which parameters are randomly selected from a distribution, and the circuit simulated, anywhere from 1000 to 100000 times.
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This application performs a worst case circuit analysis of an electrical circuit using a Monte Carlo approach.<img src="https://www.maplesoft.com/view.aspx?si=154534/WCCA_MC.png" alt="Worst Case Circuit Analysis with Monte Carlo Simulation" style="max-width: 25%;" align="left"/>Electrical components are manufactured in large quantities. Inconsistencies in the raw materials and the manufacturing process means that component parameters have a statistical distribution. That is, the resistance of a batch of resistors might be described by a normal distribution.
<BR><BR>
Given the components in a circuit their parameter distribution, the circuit may not perform as specified. This is a risk that must be identified and mitigated early in the design process.
<BR><BR>
Worst Case Circuit Analysis is a set of techniques used to analyze how variations in parameters influence circuit performance. One approach is Monte Carlo analysis, in which parameters are randomly selected from a distribution, and the circuit simulated, anywhere from 1000 to 100000 times.
<BR><BR>
This application performs a worst case circuit analysis of an electrical circuit using a Monte Carlo approach.https://www.maplesoft.com/applications/view.aspx?SID=154534&ref=FeedWed, 29 May 2019 04:00:00 ZSamir KhanSamir KhanExtreme Value Analysis of an Electrical Circuit
https://www.maplesoft.com/applications/view.aspx?SID=154533&ref=Feed
An electrical component, such as a resistor or capacitor, is usually quantified with a nominal value and a tolerance. Given the number of components in a circuit and their compounded tolerances, the actual performance of a circuit may not necessarily match its desired performance.
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Extreme Value Analysis (EVA) is a process in which the behavior of a circuit is simulated for every permutation of extreme component parameters in combination with every permutation of extreme values for all other components. This application performs an extreme value analysis of a circuit with a photodiode-generated current and an op-amp, though the principles can be extended to any circuit.<img src="https://www.maplesoft.com/view.aspx?si=154533/circuit.png" alt="Extreme Value Analysis of an Electrical Circuit" style="max-width: 25%;" align="left"/>An electrical component, such as a resistor or capacitor, is usually quantified with a nominal value and a tolerance. Given the number of components in a circuit and their compounded tolerances, the actual performance of a circuit may not necessarily match its desired performance.
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Extreme Value Analysis (EVA) is a process in which the behavior of a circuit is simulated for every permutation of extreme component parameters in combination with every permutation of extreme values for all other components. This application performs an extreme value analysis of a circuit with a photodiode-generated current and an op-amp, though the principles can be extended to any circuit.https://www.maplesoft.com/applications/view.aspx?SID=154533&ref=FeedTue, 28 May 2019 04:00:00 ZSamir KhanSamir KhanCoaxial Cable Transmission Line Design
https://www.maplesoft.com/applications/view.aspx?SID=154401&ref=Feed
An electrical engineer is asked to design a coaxial transmission line with a characteristic impedance of 50 Ω and a phase velocity of at least 1.8 x 108 m s-1
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This application will calculate the outer radius of the line.<img src="https://www.maplesoft.com/view.aspx?si=154401/image.png" alt="Coaxial Cable Transmission Line Design" style="max-width: 25%;" align="left"/>An electrical engineer is asked to design a coaxial transmission line with a characteristic impedance of 50 Ω and a phase velocity of at least 1.8 x 108 m s-1
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This application will calculate the outer radius of the line.https://www.maplesoft.com/applications/view.aspx?SID=154401&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir Khan