This document describes the operation of a DC-DC buck converter, which efficiently reduces DC voltage. It consists of an inductor, capacitor, switch, and diode. When the switch is closed, the inductor stores energy from the input voltage. When open, the diode allows the inductor to discharge its current to the output through the capacitor and load. By rapidly switching at a duty cycle D, the average output voltage is Vin * D. The document analyzes current and voltage waveforms, deriving key equations for output voltage, component ratings, and output ripple voltage. Raising switching frequency or inductance reduces ripple.
1) The document discusses a DC-DC buck converter that efficiently reduces a DC voltage. It examines the operation of buck converters including the input/output voltage relationship and how varying different circuit parameters affects the inductor current waveform.
2) Key circuit elements like the inductor and capacitor are analyzed in the time domain to understand their average voltages and currents. RMS current calculations are also provided for determining proper component ratings.
3) Different operating modes like continuous and discontinuous conduction are covered, and the voltages different components need to withstand are identified to select appropriate voltage ratings.
An inverter converts DC input voltage into AC output voltage. There are various types of inverters including single-phase and three-phase inverters. Single-phase inverters include half-bridge and full-bridge configurations. Current source inverters directly control AC current instead of voltage. They use thyristors and commutating capacitors to generate quasi-square wave output current from a constant DC current source.
This document provides an overview of linear and non-linear wave shaping. It discusses topics such as analog and digital signals, pulse definitions, periodic waveforms, linear wave shaping circuits including high pass RC circuits and low pass RC circuits. It also covers non-linear wave shaping including different types of clippers such as unbiased clippers, series positive clippers, and their working mechanisms. The document is intended to introduce fundamental concepts of signal processing.
The document summarizes experiments on non-linear op-amp circuits, including a comparator, half-wave rectifier, and clipper. It provides the objectives, required equipment, pre-lab questions, and theoretical explanations of how each circuit works. The experiments involve assembling the circuits using op-amps and diodes, observing input and output waveforms on an oscilloscope, and analyzing the output characteristics as circuit parameters are varied. Key points covered include how comparators detect voltage levels, how rectifiers and clippers modify input signals based on reference voltages, and the roles of op-amp gain and diode properties.
The document describes various types of clipping circuits used for non-linear wave shaping. It discusses positive clipping, negative clipping, and slicing circuits. Positive clipping circuits clip the positive portions of a signal that exceed a reference voltage. Negative clipping circuits clip the negative portions above a reference level. A slicing circuit clips both positive and negative portions. The document provides circuit diagrams and expected input and output waveforms for each type of clipping circuit using a diode and resistor. It aims to study these clipping circuits experimentally and verify the theoretical responses.
This chapter describes RC circuits and their behavior when a sinusoidal voltage is applied. Key points include: the current in an RC circuit leads the source voltage; resistor voltage is in phase with current while capacitor voltage lags current by 90 degrees; impedance of a series RC circuit decreases with increasing frequency while the phase angle decreases; and RC circuits can be used as phase shifters or filters.
1) RC circuits involve resistors and capacitors. Charging and discharging of capacitors in such circuits does not occur instantaneously due to the presence of resistors.
2) The time constant, τ, of an RC circuit is equal to RC. It represents the time required for a capacitor's charge or voltage to change by approximately 63.2% of its maximum or initial value.
3) In the long run, the current through a charged capacitor becomes zero as it reaches its maximum charge, acting as an open circuit. For a discharging capacitor, the current becomes zero as its charge reduces to zero.
This document provides an overview of single phase fully controlled rectifiers. It begins by explaining the advantages of fully controlled rectifiers over uncontrolled rectifiers, namely the ability to control output voltage/current and allow bidirectional power flow. It then discusses the operation of a single phase fully controlled half-wave rectifier with resistive and resistive-inductive loads. The full bridge configuration is introduced as the most popular topology. Operation in both continuous and discontinuous conduction modes is analyzed for a full bridge supplying an R-L-E load. Key points like conduction periods, voltage waveforms, and the relationship between firing angle and output voltage/current are explained.
1) The document discusses a DC-DC buck converter that efficiently reduces a DC voltage. It examines the operation of buck converters including the input/output voltage relationship and how varying different circuit parameters affects the inductor current waveform.
2) Key circuit elements like the inductor and capacitor are analyzed in the time domain to understand their average voltages and currents. RMS current calculations are also provided for determining proper component ratings.
3) Different operating modes like continuous and discontinuous conduction are covered, and the voltages different components need to withstand are identified to select appropriate voltage ratings.
An inverter converts DC input voltage into AC output voltage. There are various types of inverters including single-phase and three-phase inverters. Single-phase inverters include half-bridge and full-bridge configurations. Current source inverters directly control AC current instead of voltage. They use thyristors and commutating capacitors to generate quasi-square wave output current from a constant DC current source.
This document provides an overview of linear and non-linear wave shaping. It discusses topics such as analog and digital signals, pulse definitions, periodic waveforms, linear wave shaping circuits including high pass RC circuits and low pass RC circuits. It also covers non-linear wave shaping including different types of clippers such as unbiased clippers, series positive clippers, and their working mechanisms. The document is intended to introduce fundamental concepts of signal processing.
The document summarizes experiments on non-linear op-amp circuits, including a comparator, half-wave rectifier, and clipper. It provides the objectives, required equipment, pre-lab questions, and theoretical explanations of how each circuit works. The experiments involve assembling the circuits using op-amps and diodes, observing input and output waveforms on an oscilloscope, and analyzing the output characteristics as circuit parameters are varied. Key points covered include how comparators detect voltage levels, how rectifiers and clippers modify input signals based on reference voltages, and the roles of op-amp gain and diode properties.
The document describes various types of clipping circuits used for non-linear wave shaping. It discusses positive clipping, negative clipping, and slicing circuits. Positive clipping circuits clip the positive portions of a signal that exceed a reference voltage. Negative clipping circuits clip the negative portions above a reference level. A slicing circuit clips both positive and negative portions. The document provides circuit diagrams and expected input and output waveforms for each type of clipping circuit using a diode and resistor. It aims to study these clipping circuits experimentally and verify the theoretical responses.
This chapter describes RC circuits and their behavior when a sinusoidal voltage is applied. Key points include: the current in an RC circuit leads the source voltage; resistor voltage is in phase with current while capacitor voltage lags current by 90 degrees; impedance of a series RC circuit decreases with increasing frequency while the phase angle decreases; and RC circuits can be used as phase shifters or filters.
1) RC circuits involve resistors and capacitors. Charging and discharging of capacitors in such circuits does not occur instantaneously due to the presence of resistors.
2) The time constant, τ, of an RC circuit is equal to RC. It represents the time required for a capacitor's charge or voltage to change by approximately 63.2% of its maximum or initial value.
3) In the long run, the current through a charged capacitor becomes zero as it reaches its maximum charge, acting as an open circuit. For a discharging capacitor, the current becomes zero as its charge reduces to zero.
This document provides an overview of single phase fully controlled rectifiers. It begins by explaining the advantages of fully controlled rectifiers over uncontrolled rectifiers, namely the ability to control output voltage/current and allow bidirectional power flow. It then discusses the operation of a single phase fully controlled half-wave rectifier with resistive and resistive-inductive loads. The full bridge configuration is introduced as the most popular topology. Operation in both continuous and discontinuous conduction modes is analyzed for a full bridge supplying an R-L-E load. Key points like conduction periods, voltage waveforms, and the relationship between firing angle and output voltage/current are explained.
Chopper basically uses a Thyristor for high power applications. The process of turning off a conducting Thyristor is known as commutation. Here Thyristor is turned off by a current pulse that is why it is called a Current Commutated Chopper.
This chapter discusses principles of steady-state analysis of DC-DC power converters. It introduces inductor volt-second balance and capacitor charge balance, which relate the average inductor voltage and capacitor current to be zero during steady-state. A small ripple approximation is used to simplify analysis by ignoring output voltage ripple. Examples of steady-state analysis of the buck and boost converters are presented using these principles to determine output voltage, inductor current, and capacitor sizing for given ripple levels.
This document discusses various types of phase controlled converters including single-phase and three-phase semiconverters, full converters, and dual converters. It provides equations for the average and RMS output voltage of single-phase converters with resistive and RL loads. It also derives an expression for the average output voltage of a three-phase half wave converter with continuous and constant load current. Key aspects of three-phase half wave, full wave, and dual converters are summarized.
1) The document discusses transmission lines and their characteristics. It describes different types of transmission lines including coaxial lines, two-wire lines, and microstrip lines.
2) It presents the telegrapher's equations which model voltage and current on a transmission line as a function of position and time. These equations include parameters like inductance and capacitance per unit length.
3) Waves can propagate down transmission lines, maintaining their shape as they travel at a characteristic velocity. The wavelength depends on the wave velocity and frequency. Phasors are used to represent sinusoidal waves independent of time.
Two leg three-phase inverters (FSTPIs) have been proposed to be used in low-power; low-cost applications because of the reduced number of semiconductor devices, and space vector pulse width modulation (SVPWM) techniques have also been introduced to control FSTPIs. However, high-performance controllers are needed to implement complicated SVPWM algorithms, which limit their low-cost applications. To simplify algorithms and reduce the cost of implementation, an equivalent scalar method for SVPWM of FSTPIs is proposed. SVPWM for FSTPIs is actually a sine PWM by modulating two sine waves of 600 phase difference with a triangle wave, but in this method third harmonics doesn’t eliminated. So as to eliminate the third harmonics we have to compose a high frequency sine wave to on existing sine waves. So such a special sine PWM can be used to control FSTPIs. The Mathematical and simulation results demonstrate the validity of the proposed method.
http://www.mathworks.com/matlabcentral/fileexchange/authors/126814
This document discusses RC circuits and filters. It describes parallel and series RC circuits and different types of filters including low-pass and high-pass filters. The frequency response of these filters is examined for sinusoidal, step, pulse and square wave inputs. RC low-pass filters consist of a resistor and capacitor in series and output is taken across the capacitor. High-pass filters have the components interchanged with output across the resistor. The time constant RC determines the rate of exponential change in output for different input signals in these simple first-order RC circuits.
The document discusses various types of phase-controlled converters including single-phase and three-phase semiconverters, full converters, and dual converters. It provides details on their operating characteristics, modes, and derivations of output voltages and currents. Specifically, it describes a three-phase half-wave converter with an RL load and derives an expression for the average output voltage under continuous load current conditions. Trigonometric relationships between the three-phase supply voltages are used in the derivation.
DC power supplies work by taking an AC voltage from a transformer, rectifying it using diodes to convert it to DC, filtering it using capacitors to smooth the output, and regulating it using integrated circuits to maintain a steady voltage level. Common rectification methods include half-wave and full-wave rectification using either single-phase or three-phase inputs. The rectification process converts the AC voltage to a pulsing DC voltage that is then filtered and regulated.
The document discusses quasi-resonant converters and the half-wave zero-current-switching quasi-resonant switch cell. The switch cell uses a small resonant inductor and capacitor to achieve zero-current switching of the transistor. It operates in four subintervals per switching period: 1) transistor on, 2) resonant ringing, 3) capacitor discharging, 4) diode on. Mathematical analysis determines the waveforms and durations of each subinterval. Averaging the switch cell currents and voltages gives the conversion ratio, allowing the cell to be analyzed and incorporated into converter circuits.
This document outlines an experiment to construct and test positive and negative clamper circuits using a PN junction diode. The objectives are to build each clamper circuit, observe the input and output waveforms using an oscilloscope, and study the application of diodes as clampers. Components needed include a diode, power supply, function generator, oscilloscope, probes, and capacitor. Input and output waveforms are plotted for each clamper circuit type.
This document discusses op-amp clipper circuits. It begins by introducing op-amps and their applications. It then defines a clipper as a circuit that prevents an output from exceeding a voltage level without distorting the waveform. The document discusses positive and negative clipper circuits using op-amps and diodes. It provides examples of clipped waveforms and describes applications of clipper circuits such as protecting radio transmitters and integrated circuits.
This document discusses various types of filters used in power electronics, including L, C, and LC filters. It also discusses capacitor filters and how they smooth the DC output voltage of a rectifier. Finally, it discusses firing circuits for thyristors, including resistance and RC firing circuits, and provides equations for calculating voltage and current in half-wave converter circuits with resistive and RL loads.
17b transformer class exercise solution_r13MecmedMomod
This document provides solutions to exercises related to transformer protection. Exercise 1 asks students to determine typical distribution and generator step-up transformer connections. Exercise 2 involves calculating currents and selecting CT ratios and relay taps for a 138/22 kV transformer. Exercise 3 repeats these calculations for a 138/12 kV transformer. The exercises help students learn to analyze transformer connections and settings for differential relay protection.
The document discusses the objectives of designing various linear wave shaping circuits including a low pass filter, integrator, high pass filter, and differentiator. It provides details on the design, components, procedure, and results for each objective. For the low pass filter and integrator objectives, it discusses the expected output waveforms for different conditions. The key points are:
1) Objectives are to design four linear wave shaping circuits with cut-off frequencies of 1kHz.
2) Details on the design, components, procedure, and results are provided for a low pass filter and integrator.
3) The behavior of the low pass filter and integrator are studied under different conditions to observe their wave shaping capabilities.
The document describes different types of single phase converters. It discusses:
1) A single phase full bridge converter that uses 4 SCRs to provide controllable DC output from a single phase AC supply. It is mainly used for speed control of DC motors.
2) The working of a single phase full bridge converter with a resistive load, including the firing angles of the SCRs and the resulting output waveform.
3) A single phase semi converter or half bridge converter that uses 2 SCRs and 2 diodes to provide DC output from a single phase AC supply for a resistive or RL load.
Clippers and clampers are electronic circuits that shape waveforms. Clippers limit output voltage by clipping portions of the input signal without distortion. Clampers shift the DC level of the output voltage by adding a fixed DC potential. Some key differences are that clippers limit output while clampers shift the DC level. Both have various applications including waveform generation and shaping, signal separation, protection from transients, and as components in television receivers. Clippers clip unwanted portions while clampers add a DC level to maintain black and white reference levels lost during signal processing.
This document describes experiments to design a differentiator and integrator circuit using an op-amp IC 741. It provides the aim, apparatus required, theory of operation, design steps, circuit diagrams, observations and results for both the differentiator and integrator circuits. The differentiator circuit performs mathematical differentiation to produce an output waveform that is the derivative of the input. The integrator circuit performs integration to produce an output waveform that is the integral of the input.
The document discusses three tasks analyzing a full wave uncontrolled rectifier circuit with different load types: resistive, resistive-inductive, and a DC motor load. In task 1, the rectifier supplied a resistive load and output waveforms showed the expected pulsating DC. Task 2 added an inductive load, causing the output current waveform to exhibit a lag and cutoff before reaching zero. Task 3 replaced the inductive load with a DC motor, further reducing the output voltage and current. Measurements, calculations, and analyses of the circuits aimed to observe the effects of load type on rectifier performance.
The document summarizes a seminar presentation on AC-DC converters given by Ankur Mahajan. The presentation covered single phase half wave and full wave converters. It discussed various rectifier types including uncontrolled, half controlled, and fully controlled bridges. It provided calculations for average and RMS voltage values for different converter configurations under resistive and inductive loads. The presentation also covered single phase half controlled and fully controlled bridge converters in both continuous and discontinuous conduction modes.
le roludes the tiofuture research directionsARNABPAL81
ully distributed formation-containment control protocol for networked MASs with timevarying formation reference. Two detailed case studies are considered in Section 4.4 to
show the effectiveness of the proposed methodology. One of them deals with the formationcontainment of a team of networked satellites, and the other one shows experimental validation using nonholonomic mobile robots. Section 4.5 concludes the chapter mentioning the
future research directions
This document discusses DC-DC buck converters. It begins by introducing different types of DC-DC converters and their applications. It then explains the objective of a buck converter is to efficiently reduce DC voltage. It discusses how a simple inefficient converter can achieve only 33% efficiency. Through the addition of an inductor and diode, lossless conversion becomes possible. The document explains the operating principles of the buck converter through examination of the inductor voltage and capacitor current in steady state. It derives the input-output voltage relationship and discusses how varying different circuit parameters affects the inductor current waveform. Finally, it covers RMS calculations for common periodic waveforms seen in converter circuits.
Chopper basically uses a Thyristor for high power applications. The process of turning off a conducting Thyristor is known as commutation. Here Thyristor is turned off by a current pulse that is why it is called a Current Commutated Chopper.
This chapter discusses principles of steady-state analysis of DC-DC power converters. It introduces inductor volt-second balance and capacitor charge balance, which relate the average inductor voltage and capacitor current to be zero during steady-state. A small ripple approximation is used to simplify analysis by ignoring output voltage ripple. Examples of steady-state analysis of the buck and boost converters are presented using these principles to determine output voltage, inductor current, and capacitor sizing for given ripple levels.
This document discusses various types of phase controlled converters including single-phase and three-phase semiconverters, full converters, and dual converters. It provides equations for the average and RMS output voltage of single-phase converters with resistive and RL loads. It also derives an expression for the average output voltage of a three-phase half wave converter with continuous and constant load current. Key aspects of three-phase half wave, full wave, and dual converters are summarized.
1) The document discusses transmission lines and their characteristics. It describes different types of transmission lines including coaxial lines, two-wire lines, and microstrip lines.
2) It presents the telegrapher's equations which model voltage and current on a transmission line as a function of position and time. These equations include parameters like inductance and capacitance per unit length.
3) Waves can propagate down transmission lines, maintaining their shape as they travel at a characteristic velocity. The wavelength depends on the wave velocity and frequency. Phasors are used to represent sinusoidal waves independent of time.
Two leg three-phase inverters (FSTPIs) have been proposed to be used in low-power; low-cost applications because of the reduced number of semiconductor devices, and space vector pulse width modulation (SVPWM) techniques have also been introduced to control FSTPIs. However, high-performance controllers are needed to implement complicated SVPWM algorithms, which limit their low-cost applications. To simplify algorithms and reduce the cost of implementation, an equivalent scalar method for SVPWM of FSTPIs is proposed. SVPWM for FSTPIs is actually a sine PWM by modulating two sine waves of 600 phase difference with a triangle wave, but in this method third harmonics doesn’t eliminated. So as to eliminate the third harmonics we have to compose a high frequency sine wave to on existing sine waves. So such a special sine PWM can be used to control FSTPIs. The Mathematical and simulation results demonstrate the validity of the proposed method.
http://www.mathworks.com/matlabcentral/fileexchange/authors/126814
This document discusses RC circuits and filters. It describes parallel and series RC circuits and different types of filters including low-pass and high-pass filters. The frequency response of these filters is examined for sinusoidal, step, pulse and square wave inputs. RC low-pass filters consist of a resistor and capacitor in series and output is taken across the capacitor. High-pass filters have the components interchanged with output across the resistor. The time constant RC determines the rate of exponential change in output for different input signals in these simple first-order RC circuits.
The document discusses various types of phase-controlled converters including single-phase and three-phase semiconverters, full converters, and dual converters. It provides details on their operating characteristics, modes, and derivations of output voltages and currents. Specifically, it describes a three-phase half-wave converter with an RL load and derives an expression for the average output voltage under continuous load current conditions. Trigonometric relationships between the three-phase supply voltages are used in the derivation.
DC power supplies work by taking an AC voltage from a transformer, rectifying it using diodes to convert it to DC, filtering it using capacitors to smooth the output, and regulating it using integrated circuits to maintain a steady voltage level. Common rectification methods include half-wave and full-wave rectification using either single-phase or three-phase inputs. The rectification process converts the AC voltage to a pulsing DC voltage that is then filtered and regulated.
The document discusses quasi-resonant converters and the half-wave zero-current-switching quasi-resonant switch cell. The switch cell uses a small resonant inductor and capacitor to achieve zero-current switching of the transistor. It operates in four subintervals per switching period: 1) transistor on, 2) resonant ringing, 3) capacitor discharging, 4) diode on. Mathematical analysis determines the waveforms and durations of each subinterval. Averaging the switch cell currents and voltages gives the conversion ratio, allowing the cell to be analyzed and incorporated into converter circuits.
This document outlines an experiment to construct and test positive and negative clamper circuits using a PN junction diode. The objectives are to build each clamper circuit, observe the input and output waveforms using an oscilloscope, and study the application of diodes as clampers. Components needed include a diode, power supply, function generator, oscilloscope, probes, and capacitor. Input and output waveforms are plotted for each clamper circuit type.
This document discusses op-amp clipper circuits. It begins by introducing op-amps and their applications. It then defines a clipper as a circuit that prevents an output from exceeding a voltage level without distorting the waveform. The document discusses positive and negative clipper circuits using op-amps and diodes. It provides examples of clipped waveforms and describes applications of clipper circuits such as protecting radio transmitters and integrated circuits.
This document discusses various types of filters used in power electronics, including L, C, and LC filters. It also discusses capacitor filters and how they smooth the DC output voltage of a rectifier. Finally, it discusses firing circuits for thyristors, including resistance and RC firing circuits, and provides equations for calculating voltage and current in half-wave converter circuits with resistive and RL loads.
17b transformer class exercise solution_r13MecmedMomod
This document provides solutions to exercises related to transformer protection. Exercise 1 asks students to determine typical distribution and generator step-up transformer connections. Exercise 2 involves calculating currents and selecting CT ratios and relay taps for a 138/22 kV transformer. Exercise 3 repeats these calculations for a 138/12 kV transformer. The exercises help students learn to analyze transformer connections and settings for differential relay protection.
The document discusses the objectives of designing various linear wave shaping circuits including a low pass filter, integrator, high pass filter, and differentiator. It provides details on the design, components, procedure, and results for each objective. For the low pass filter and integrator objectives, it discusses the expected output waveforms for different conditions. The key points are:
1) Objectives are to design four linear wave shaping circuits with cut-off frequencies of 1kHz.
2) Details on the design, components, procedure, and results are provided for a low pass filter and integrator.
3) The behavior of the low pass filter and integrator are studied under different conditions to observe their wave shaping capabilities.
The document describes different types of single phase converters. It discusses:
1) A single phase full bridge converter that uses 4 SCRs to provide controllable DC output from a single phase AC supply. It is mainly used for speed control of DC motors.
2) The working of a single phase full bridge converter with a resistive load, including the firing angles of the SCRs and the resulting output waveform.
3) A single phase semi converter or half bridge converter that uses 2 SCRs and 2 diodes to provide DC output from a single phase AC supply for a resistive or RL load.
Clippers and clampers are electronic circuits that shape waveforms. Clippers limit output voltage by clipping portions of the input signal without distortion. Clampers shift the DC level of the output voltage by adding a fixed DC potential. Some key differences are that clippers limit output while clampers shift the DC level. Both have various applications including waveform generation and shaping, signal separation, protection from transients, and as components in television receivers. Clippers clip unwanted portions while clampers add a DC level to maintain black and white reference levels lost during signal processing.
This document describes experiments to design a differentiator and integrator circuit using an op-amp IC 741. It provides the aim, apparatus required, theory of operation, design steps, circuit diagrams, observations and results for both the differentiator and integrator circuits. The differentiator circuit performs mathematical differentiation to produce an output waveform that is the derivative of the input. The integrator circuit performs integration to produce an output waveform that is the integral of the input.
The document discusses three tasks analyzing a full wave uncontrolled rectifier circuit with different load types: resistive, resistive-inductive, and a DC motor load. In task 1, the rectifier supplied a resistive load and output waveforms showed the expected pulsating DC. Task 2 added an inductive load, causing the output current waveform to exhibit a lag and cutoff before reaching zero. Task 3 replaced the inductive load with a DC motor, further reducing the output voltage and current. Measurements, calculations, and analyses of the circuits aimed to observe the effects of load type on rectifier performance.
The document summarizes a seminar presentation on AC-DC converters given by Ankur Mahajan. The presentation covered single phase half wave and full wave converters. It discussed various rectifier types including uncontrolled, half controlled, and fully controlled bridges. It provided calculations for average and RMS voltage values for different converter configurations under resistive and inductive loads. The presentation also covered single phase half controlled and fully controlled bridge converters in both continuous and discontinuous conduction modes.
le roludes the tiofuture research directionsARNABPAL81
ully distributed formation-containment control protocol for networked MASs with timevarying formation reference. Two detailed case studies are considered in Section 4.4 to
show the effectiveness of the proposed methodology. One of them deals with the formationcontainment of a team of networked satellites, and the other one shows experimental validation using nonholonomic mobile robots. Section 4.5 concludes the chapter mentioning the
future research directions
This document discusses DC-DC buck converters. It begins by introducing different types of DC-DC converters and their applications. It then explains the objective of a buck converter is to efficiently reduce DC voltage. It discusses how a simple inefficient converter can achieve only 33% efficiency. Through the addition of an inductor and diode, lossless conversion becomes possible. The document explains the operating principles of the buck converter through examination of the inductor voltage and capacitor current in steady state. It derives the input-output voltage relationship and discusses how varying different circuit parameters affects the inductor current waveform. Finally, it covers RMS calculations for common periodic waveforms seen in converter circuits.
1. The document discusses DC-DC buck converters and their operation. A buck converter efficiently steps down DC voltage through lossless conversion using a switch, inductor, diode, and capacitor.
2. When the switch is closed, the inductor current rises and energy is stored in the inductor's magnetic field. When the switch opens, the inductor current flows through the diode to the load. By rapidly switching on and off, the output voltage is the average of the input voltage over many switching cycles.
3. Key aspects covered include inductor and capacitor behavior, the input/output voltage relationship, effects of varying duty cycle and switching frequency, and RMS current calculations. Proper component selection is important for continuous
The document describes the operation and design considerations of a buck/boost DC-DC converter circuit. It provides equations to calculate component ratings for the input inductor, output capacitor, MOSFET, diode, and other parts. Design examples are given to illustrate how to select appropriate component values and ratings to ensure continuous inductor currents and minimize output voltage ripple.
The document describes the operation and design considerations of a buck/boost DC-DC converter circuit. It provides equations to calculate component ratings for the input inductor, output capacitor, MOSFET, diode, and other parts. Design examples are given to illustrate how to select appropriate component values and ratings to ensure continuous inductor currents and minimize output voltage ripple.
The document describes the operation and design considerations of a buck/boost DC-DC converter circuit. It provides equations to calculate component ratings for the input inductor, output capacitor, MOSFET, diode, and other parts. Design examples are given to illustrate how to select appropriate component values and ratings to ensure continuous inductor currents and minimize output voltage ripple.
The document discusses the design and operation of a buck-boost DC-DC converter circuit. It provides details on component sizing, current and voltage ratings, and worst-case analyses. Key aspects covered include inductor and capacitor sizing to limit ripple current and voltage, MOSFET and diode voltage and current ratings, and concluding that 50kHz may be too low a switching frequency for this buck-boost converter design.
The SEPIC converter is a type of DC-DC converter that allows the output voltage to be greater than, less than, or equal to the input voltage. It uses two inductors and two capacitors in a unique configuration to achieve this. While more complex than a basic boost or buck converter, the SEPIC converter has advantages like having no average current pass through one of the capacitors and allowing impedance matching across the full operating range of a solar panel. Key components are rated for higher voltages and currents than a basic buck-boost converter.
1) DC-DC converters control the output voltage by converting the unregulated DC input voltage to a regulated DC output voltage. Switching regulators have near zero power loss by rapidly opening and closing a switch to transfer power from input to output in pulses.
2) A buck converter is a type of step-down DC-DC converter that produces an output voltage lower than the input voltage. It contains a switch, diode, and inductor. The inductor current ripples between a maximum and minimum value depending on the duty cycle of the switch.
3) Key parameters in buck converter design include duty cycle, switching frequency, inductor value, and capacitor value. These are selected to achieve the desired output voltage
This document provides an introduction to DC-DC converters known as choppers. It discusses the principle of operation where a chopper uses a switching device to vary the duty cycle and produce a chopped DC voltage at the load. This allows obtaining a variable DC output voltage from a constant DC source. Specific converter circuits are described including buck converters for stepping down voltage, boost converters for stepping up voltage, and buck-boost converters for both stepping up or down voltage. The operation and analysis of these converters is explained through diagrams and waveforms.
This document provides an overview of pulse-width modulated (PWM) DC/DC converters. It discusses typical applications, topologies including non-isolated converters like buck, boost and buck-boost converters. The principles of DC/DC converters like conversion ratio and voltage/current waveforms are introduced. Modes of operation for buck converters in continuous and discontinuous mode are examined. Component ratings for voltage and current are also covered.
This document discusses the design and operation of a boost converter circuit. It notes that boost converters are more unforgiving than buck converters if components fail or the load is disconnected. The document derives the input-output voltage relationship for boost converters and calculates important design parameters like inductor and capacitor current ratings, voltage ratings for components, and impedance matching considerations. It provides an example of using a boost converter to extract maximum power from a solar panel by modifying the effective load resistance seen by the panel. Tables compare worst-case component ratings and output capacitor ripple voltages for boost converters.
1. The document discusses the steady-state analysis of basic DC-DC converters like the Buck, Boost, and Buck-Boost converters in continuous conduction mode.
2. It introduces analysis methods based on the average values of inductor voltages and capacitor currents to determine output voltage expressions in terms of input voltage and duty cycle.
3. The analysis yields expressions for average and peak inductor and switch currents as well as maximum switch voltages.
1. The document discusses the steady-state analysis of DC-DC converters operating in continuous conduction mode (CCM), including the buck, boost, and buck-boost converters.
2. The analysis involves determining the main waveforms, applying Kirchhoff's laws to the average values of voltages and currents, and ensuring power balance at the input and output.
3. For the buck converter, the output voltage is less than the input voltage and equals the duty cycle times the input voltage. For the boost converter, the output voltage is greater than the input voltage and equals the input voltage divided by one minus the duty cycle.
Zero voltage switching resonant power conversionPham Hoang
The document summarizes the technique of zero voltage switching (ZVS) in power conversion. It explores several ZVS topologies and applications. It presents the benefits of ZVS which include lossless switching transitions, reduced switching losses, and ability to operate at high voltages and frequencies with high efficiency. The document then provides equations to analyze the voltage and current waveforms in a ZVS buck converter during the different intervals of the switching cycle. It analyzes the capacitor charging, resonant, and inductor charging states that occur between the switch turning off and back on. The analysis aims to understand how ZVS facilitates switching at zero voltage to reduce switching losses.
A document about DC choppers is summarized as follows:
1) DC choppers are static devices that provide a variable DC voltage from a constant DC source and are widely used for motor control and regenerative braking. Choppers come in two types - step-down and step-up.
2) In a step-down chopper, the output voltage is less than the input voltage. When the thyristor switch is ON, the supply voltage appears across the load. When it is OFF, the voltage across the load is zero.
3) In a step-up chopper, the output voltage is higher than the input voltage. Energy is stored in an inductor when the chopper is
The document discusses DC-DC power conversion using choppers. It describes step-down, step-up, and buck-boost chopper circuits. Step-down choppers, also called buck converters, produce a lower output voltage than the input voltage. Step-up choppers, also called boost converters, produce a higher output voltage than the input voltage. Buck-boost choppers can produce either higher or lower output voltages depending on duty cycle. Choppers are used in applications like DC motor drives and switch-mode power supplies to efficiently convert DC voltages.
This document discusses uncontrolled rectifiers, which use diodes to convert alternating current (AC) to direct current (DC). It covers the operation and analysis of single-phase half-wave and full-wave rectifiers, as well as three-phase rectifiers, with both resistive and inductive loads. Key points covered include the output voltage and current calculations, effects of adding capacitors or inductors, and how source inductance can affect rectifier operation. The objectives are to understand different rectifier circuits and analyze their performance parameters.
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
This document provides an introduction to switched-capacitor circuits. It discusses:
1) How switched-capacitor circuits sample input signals using capacitors and switches to create discrete-time systems, unlike continuous-time systems.
2) Key considerations for sampling switches including speed, precision, and input signal range limitations.
3) Common switched-capacitor circuit topologies like amplifiers, integrators, and common-mode feedback that replace resistors with capacitors and switches.
Necessity of starter in induction motorjohny renoald
The starter is a device required for three-phase induction motors to limit the high starting current, which can be 6 to 8 times the full load current and damage the motor windings. A starter works by controlling the induced electromotive force in the rotor circuit and thereby controlling the rotor current during start-up. Common types of starters include stator rheostat starters, autotransformer starters, star-delta starters, and direct on line starters.
This document discusses three phase induction motors. It describes their operating principle of rotating magnetic fields produced by three phase currents in the stator. Key points include:
- Induction motors operate on rotating magnetic fields and can run on single or three phase power, with three phase preferred.
- Advantages over DC motors include low maintenance, ruggedness, low cost, and ability to operate in harsh environments.
- Speed is controlled by varying supply frequency using variable frequency drives to maintain constant flux.
- Starters like star-delta are used to limit starting current and torque by initially applying reduced voltage.
This document discusses special electrical machines, specifically permanent magnet synchronous motors (PMSM). It describes PMSM as a brushless DC motor with permanent magnets on the rotor that create magnetic poles instead of a field winding. The document outlines the basic construction and working principle of PMSM, noting that a rotating magnetic field from the stator interacts with the permanent rotor magnets to produce torque. Applications mentioned include servo drives, robotics, traction systems, and railway transportation.
This document contains a presentation on transformers given by Dr. B. Gopinath, Professor of Electrical and Electronics Engineering. It discusses the principle of operation of transformers, their basic construction, equivalent circuit, regulation and efficiency. It provides equations for transformer operation and covers topics like single phase transformer referred to primary and secondary, transformer losses, practical transformer equivalent circuit, and components like conservator tank, silica gel breather, and Buchholz relay.
The MOSFET is a four-terminal semiconductor device used for switching and amplifying electronic signals. It comes in two basic forms, P-channel and N-channel, and two modes, depletion and enhancement. MOSFETs exhibit three operating regions - cut-off, where no current flows; ohmic or linear, where current increases with drain-source voltage; and saturation, where current reaches a maximum. MOSFETs are voltage-controlled, unipolar devices that can switch or amplify depending on their operating region.
The document discusses different methods for triggering an SCR (silicon controlled rectifier) to turn on. There are four main triggering methods: forward voltage triggering, thermal/temperature triggering, radiation/light triggering, and gate triggering. Forward voltage triggering involves applying an additional forward voltage until avalanche breakdown occurs. Thermal triggering relies on increased temperature reducing the depletion layer. Radiation triggering uses light to generate charge carriers. Gate triggering, the most common method, injects charge carriers from the gate terminal to reduce the depletion layer thickness.
The document discusses insulated gate bipolar transistors (IGBTs). It describes IGBTs as having MOSFET-like input characteristics and bipolar junction transistor-like output characteristics. The document summarizes IGBT structure, working principles, characteristics including transfer and switching characteristics, and methods of connecting IGBTs in series and parallel. It also discusses protection of IGBTs from overvoltage, overcurrent, high dv/dt, and overheating.
This document discusses DC-DC converters, which convert a fixed DC source into a variable DC source like an AC transformer. It describes step-down converters, which use a switch like a BJT, MOSFET, or IGBT to alternately connect and disconnect the voltage source to produce a lower average output voltage. Key concepts covered include duty cycle, pulse-width modulation, modes of operation, generation of the switching signal, and analysis of a step-down converter with an RL load in continuous conduction mode.
1) There are several methods to control the output voltage of single phase inverters including external control of AC output voltage, external control of DC input voltage, and internal control of the inverter.
2) Internal control of the inverter through pulse width modulation is commonly used as it requires no additional components. Pulse width modulation controls the output voltage by adjusting the ON and OFF periods of the inverter components.
3) Harmonic reduction can be achieved through techniques like multiple pulse modulation, sinusoidal pulse modulation, and combining output voltages from multiple inverters with transformer connections. Internal control of the inverter through advanced PWM techniques is effective in minimizing harmonics in the output voltage.
An inverter is a static device that converts DC power from a source like batteries into AC power at a desired output voltage and frequency. There are different types of inverters classified by their commutation method, component connections, and the nature of the DC source. Voltage source inverters have a constant voltage input and output voltage does not depend on the load, while current source inverters have a constant current input and output voltage depends on the load. Common inverter configurations include single phase half and full bridge inverters, and three phase inverters that can operate in 180 or 120 degree modes.
This document discusses different types of phase controlled converters including single-phase and three-phase semiconverters, full converters, and dual converters. It provides equations and diagrams to describe the operation and analyze the performance of single-phase semiconverters and full converters with resistive-inductive loads. It also describes the operation of a three-phase half-wave converter with continuous and constant load current.
This document provides information on a Power System Protection course taught at Vivekanandha College of Engineering for Women. The syllabus covers 5 units: introduction to protection schemes, relay operating principles and characteristics, apparatus protection, theory of circuit interruption, and circuit breakers. It lists textbooks and presents details on each unit, including topics like relay types, transformer/generator/motor protection, arc phenomena, and different circuit breaker types. The last section provides references for textbooks, websites, and presentations on related topics.
This document provides information about a power system protection course, including:
1. The syllabus covers 5 units - introduction to protection schemes, operating principles of relays, apparatus protection, theory of circuit interruption, and circuit breakers.
2. The theory of circuit interruption unit discusses arc phenomena, interruption of DC and AC circuits. It explains the physics behind arc initiation, maintenance and methods of arc extinction.
3. Interruption of capacitive current can produce high transient voltages across the circuit breaker contacts. This occurs when unloaded transmission lines or capacitor banks are switched off.
This document provides information about power system protection for a course. It includes:
1. A syllabus covering introduction to protection schemes, operating principles of relays, apparatus protection, circuit interruption theory, and circuit breakers.
2. Details on apparatus protection including considerations for protecting generators, transformers, and transmission lines with zones of protection.
3. An overview of generator protection including faults that can occur and classifications of protective relays into categories based on their response time.
This document contains information about a power system protection course, including:
1. The syllabus covers 5 units - introduction to protection schemes, operating principles of electromagnetic and static relays, apparatus protection, circuit interruption theory, and circuit breakers.
2. Unit 2 discusses the operating principles of electromagnetic relays like overcurrent, directional, distance, differential and under frequency relays. It also introduces static relays.
3. Directional relays use both current and voltage inputs to operate only for a specific direction of power flow, while non-directional relays operate based only on current.
This document outlines the syllabus for a Power System Protection course, including 5 units: introduction, relay operating principles and characteristics, apparatus protection, theory of circuit interruption, and circuit breakers. It provides an overview of key concepts like faults and fault currents in power systems, the importance of protective schemes, and components of protection systems like relays, circuit breakers, and batteries. The document also shares diagrams to illustrate power system configurations and protective devices.
This document provides an introduction to basic electrical concepts including charge, current, voltage, resistors, and capacitors. It defines each concept, provides examples and analogies to explain them, and discusses how components such as resistors and capacitors are constructed and operate in electrical circuits. Key points covered include that charge is carried by electrons and protons, current is the flow of electrons, voltage is needed to push charge through a circuit, and resistors and capacitors can store and control the flow of electric charge and energy.
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This document discusses management from several perspectives: as an activity, process, academic discipline, and group. It also covers the nature, importance, and functions of management. Management involves planning, organizing, directing, and controlling resources to achieve organizational goals. There are three levels of management - first-line managers who directly oversee production, middle managers who coordinate activities and set objectives, and top managers who provide overall direction. Different skills are important at each level, including communication, teamwork, planning, and leadership.
This document discusses communication skills and effective communication. It defines communication as a series of senses and describes the most common ways to communicate as speaking, writing, visuals, images, and body language. It then covers types of communication based on organization, flow, and expression. The document also discusses formal channels of communication like downward, upward, and horizontal communication. It identifies barriers to communication such as semantic, emotional, organizational, and personal barriers. Finally, it provides tips for developing good communication skills through exploring related skills, maintaining eye contact, using gestures, practicing, and ensuring communication is two-way, involves listening, utilizes feedback, and is clear and free of stress.
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMSIJNSA Journal
The smart irrigation system represents an innovative approach to optimize water usage in agricultural and landscaping practices. The integration of cutting-edge technologies, including sensors, actuators, and data analysis, empowers this system to provide accurate monitoring and control of irrigation processes by leveraging real-time environmental conditions. The main objective of a smart irrigation system is to optimize water efficiency, minimize expenses, and foster the adoption of sustainable water management methods. This paper conducts a systematic risk assessment by exploring the key components/assets and their functionalities in the smart irrigation system. The crucial role of sensors in gathering data on soil moisture, weather patterns, and plant well-being is emphasized in this system. These sensors enable intelligent decision-making in irrigation scheduling and water distribution, leading to enhanced water efficiency and sustainable water management practices. Actuators enable automated control of irrigation devices, ensuring precise and targeted water delivery to plants. Additionally, the paper addresses the potential threat and vulnerabilities associated with smart irrigation systems. It discusses limitations of the system, such as power constraints and computational capabilities, and calculates the potential security risks. The paper suggests possible risk treatment methods for effective secure system operation. In conclusion, the paper emphasizes the significant benefits of implementing smart irrigation systems, including improved water conservation, increased crop yield, and reduced environmental impact. Additionally, based on the security analysis conducted, the paper recommends the implementation of countermeasures and security approaches to address vulnerabilities and ensure the integrity and reliability of the system. By incorporating these measures, smart irrigation technology can revolutionize water management practices in agriculture, promoting sustainability, resource efficiency, and safeguarding against potential security threats.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
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represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
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Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
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Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
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This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
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K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
2. Objective – to efficiently reduce DC voltage
DC−DC Buck
Converter
+
Vin
−
+
Vout
−
IoutIin
Lossless objective: Pin = Pout, which means that VinIin = VoutIout and
The DC equivalent of an AC transformer
out
in
in
out
I
I
V
V
3. Here is an example of an inefficient DC−DC
converter
21
2
RR
R
VV inout
+
Vin
−
+
Vout
−
R1
R2
in
out
V
V
RR
R
21
2
If Vin = 39V, and Vout = 13V, efficiency η is only 0.33
The load
Unacceptable except in very low power applications
4. Another method – lossless conversion of
39Vdc to average 13Vdc
If the duty cycle D of the switch is 0.33, then the average
voltage to the expensive car stereo is 39 ● 0.33 = 13Vdc. This
is lossless conversion, but is it acceptable?
Rstereo
+
39Vdc
–
Switch state, Stereo voltage
Closed, 39Vdc
Open, 0Vdc
Switch open
Stereo
voltage
39
0
Switch closed
DT
T
!
5. Convert 39Vdc to 13Vdc, cont.
Try adding a large C in parallel with the load to
control ripple. But if the C has 13Vdc, then
when the switch closes, the source current
spikes to a huge value and burns out the
switch.
Rstereo
+
39Vdc
–
C
Try adding an L to prevent the huge
current spike. But now, if the L has
current when the switch attempts to
open, the inductor’s current momentum
and resulting Ldi/dt burns out the switch.
By adding a “free wheeling” diode, the
switch can open and the inductor current
can continue to flow. With high-
frequency switching, the load voltage
ripple can be reduced to a small value.
Rstereo
+
39Vdc
–
C
L
Rstereo
+
39Vdc
–
C
L
A DC-DC Buck Converter
lossless
6. C’s and L’s operating in periodic steady-state
Examine the current passing through a capacitor that is operating
in periodic steady state. The governing equation is
dt
tdv
Cti
)(
)( which leads to
tot
ot
o dtti
C
tvtv )(
1
)()(
Since the capacitor is in periodic steady state, then the voltage at
time to is the same as the voltage one period T later, so
),()( oo tvTtv
The conclusion is that
Tot
ot
oo dtti
C
tvTtv )(
1
0)()(or
0)(
Tot
ot
dtti
the average current through a capacitor operating in periodic
steady state is zero
which means that
7. Now, an inductor
Examine the voltage across an inductor that is operating in
periodic steady state. The governing equation is
dt
tdi
Ltv
)(
)( which leads to
tot
ot
o dttv
L
titi )(
1
)()(
Since the inductor is in periodic steady state, then the voltage at
time to is the same as the voltage one period T later, so
),()( oo tiTti
The conclusion is that
Tot
ot
oo dttv
L
tiTti )(
1
0)()(or
0)(
Tot
ot
dttv
the average voltage across an inductor operating in periodic
steady state is zero
which means that
8. KVL and KCL in periodic steady-state
,0)(
loopAround
tv
,0)(
nodeofOut
ti
0)()()()( 321 tvtvtvtv N
Since KVL and KCL apply at any instance, then they must also be valid
in averages. Consider KVL,
0)()()()( 321 titititi N
0)0(
1
)(
1
)(
1
)(
1
)(
1
321
dt
T
dttv
T
dttv
T
dttv
T
dttv
T
Tot
ot
Tot
ot
N
Tot
ot
Tot
ot
Tot
ot
0321 Navgavgavgavg VVVV
The same reasoning applies to KCL
0321 Navgavgavgavg IIII
KVL applies in the average sense
KCL applies in the average sense
9. Capacitors and Inductors
In capacitors:
dt
tdv
Cti
)(
)(
Capacitors tend to keep the voltage constant (voltage “inertia”). An ideal
capacitor with infinite capacitance acts as a constant voltage source.
Thus, a capacitor cannot be connected in parallel with a voltage source
or a switch (otherwise KVL would be violated, i.e. there will be a
short-circuit)
The voltage cannot change instantaneously
In inductors:
Inductors tend to keep the current constant (current “inertia”). An ideal
inductor with infinite inductance acts as a constant current source.
Thus, an inductor cannot be connected in series with a current source
or a switch (otherwise KCL would be violated)
The current cannot change instantaneously
dt
tdi
Ltv
)(
)(
10. Vin
+
Vout
–
iL
L
C iC
Ioutiin
Buck converter
+ vL –
Vin
+
Vout
–
L
C
Ioutiin
+ 0 V –
What do we learn from inductor voltage and capacitor
current in the average sense?
Iout
0 A
• Assume large C so that
Vout has very low ripple
• Since Vout has very low
ripple, then assume Iout
has very low ripple
11. The input/output equation for DC-DC converters
usually comes by examining inductor voltages
Vin
+
Vout
–
L
C
Ioutiin
+ (Vin – Vout) –
iL
(iL – Iout)
Reverse biased, thus the
diode is open
,
dt
di
Lv L
L
L
VV
dt
di outinL
,
dt
di
LVV L
outin ,outinL VVv
for DT seconds
Note – if the switch stays closed, then Vout = Vin
Switch closed for
DT seconds
12. Vin
+
Vout
–
L
C
Iout
– Vout +
iL
(iL – Iout)
Switch open for (1 − D)T seconds
iL continues to flow, thus the diode is closed. This
is the assumption of “continuous conduction” in the
inductor which is the normal operating condition.
,
dt
di
Lv L
L
L
V
dt
di outL
,
dt
di
LV L
out ,outL Vv
for (1−D)T seconds
13. Since the average voltage across L is zero
01 outoutinLavg VDVVDV
outoutoutin VDVVDDV
inout DVV
From power balance, outoutinin IVIV
D
I
I in
out
, so
The input/output equation becomes
Note – even though iin is not constant
(i.e., iin has harmonics), the input power
is still simply Vin • Iin because Vin has no
harmonics
14. Examine the inductor current
Switch closed,
Switch open,
L
VV
dt
di
VVv outinL
outinL
,
L
V
dt
di
Vv outL
outL
,
sec/A
L
VV outin
DT (1 − D)T
T
Imax
Imin
Iavg = Iout
From geometry, Iavg = Iout is halfway
between Imax and Imin
sec/A
L
Vout
ΔI
iL
Periodic – finishes
a period where it
started
15. Effect of raising and lowering Iout while
holding Vin, Vout, f, and L constant
iL
ΔI
ΔI
Raise Iout
ΔI
Lower Iout
• ΔI is unchanged
• Lowering Iout (and, therefore, Pout ) moves the circuit
toward discontinuous operation
16. Effect of raising and lowering f while
holding Vin, Vout, Iout, and L constant
iL
Raise f
Lower f
• Slopes of iL are unchanged
• Lowering f increases ΔI and moves the circuit toward
discontinuous operation
17. iL
Effect of raising and lowering L while
holding Vin, Vout, Iout and f constant
Raise L
Lower L
• Lowering L increases ΔI and moves the circuit toward
discontinuous operation
18. RMS of common periodic waveforms, cont.
TTT
rms t
T
V
dtt
T
V
dtt
T
V
T
V
0
3
3
2
0
2
3
2
0
2
2
3
1
T
V
0
3
V
Vrms
Sawtooth
Taken from “Waveforms and Definitions” PPT
19. RMS of common periodic waveforms, cont.
Using the power concept, it is easy to reason that the following waveforms
would all produce the same average power to a resistor, and thus their rms
values are identical and equal to the previous example
V
0
V
0
V
0
0
-V
V
0
3
V
Vrms
V
0
V
0
Taken from “Waveforms and Definitions” PPT
20. RMS of common periodic waveforms, cont.
Now, consider a useful example, based upon a waveform that is often seen in
DC-DC converter currents. Decompose the waveform into its ripple, plus its
minimum value.
minmax II
0
)(ti
the ripple
+
0
minI
the minimum value
)(ti
maxI
minI
=
2
minmax II
Iavg
avgI
Taken from “Waveforms and Definitions” PPT
21. RMS of common periodic waveforms, cont.
2
min
2
)( ItiAvgIrms
2
minmin
22
)(2)( IItitiAvgIrms
2
minmin
22
)(2)( ItiAvgItiAvgIrms
2
min
minmax
min
2
minmax2
2
2
3
I
II
I
II
Irms
2
minmin
2
2
3
III
I
I PP
PP
rms
minmax IIIPP Define
Taken from “Waveforms and Definitions” PPT
22. RMS of common periodic waveforms, cont.
2
min
PP
avg
I
II
22
2
223
PP
avgPP
PP
avg
PP
rms
I
II
I
I
I
I
423
2
2
22
2 PP
PPavgavg
PP
PPavg
PP
rms
I
III
I
II
I
I
2
22
2
43
avg
PPPP
rms I
II
I
Recognize that
12
2
22 PP
avgrms
I
II
avgI
)(ti
minmax IIIPP
2
minmax II
Iavg
Taken from “Waveforms and Definitions” PPT
23. Inductor current rating
22222
12
1
12
1
IIIII outppavgLrms
2222
3
4
2
12
1
outoutoutLrms IIII
Max impact of ΔI on the rms current occurs at the boundary of
continuous/discontinuous conduction, where ΔI =2Iout
outLrms II
3
2
2Iout
0
Iavg = Iout
ΔI
iL
Use max
24. Capacitor current and current rating
22222
3
1
02
12
1
outoutavgCrms IIII
iL
L
C
Iout
(iL – Iout)
Iout
−Iout
0
ΔI
Max rms current occurs at the boundary of continuous/discontinuous
conduction, where ΔI =2Iout
3
out
Crms
I
I
Use max
iC = (iL – Iout) Note – raising f or L, which lowers
ΔI, reduces the capacitor current
25. MOSFET and diode currents and current ratings
iL
L
C
Iout
(iL – Iout)
outrms II
3
2
Use max
2Iout
0
Iout
iin
2Iout
0
Iout
Take worst case D for each
26. Worst-case load ripple voltage
Cf
I
C
IT
C
I
T
C
Q
V outout
out
44
22
1
Iout
−Iout
0
T/2
C charging
iC = (iL – Iout)
During the charging period, the C voltage moves from the min to the max.
The area of the triangle shown above gives the peak-to-peak ripple voltage.
Raising f or L reduces the load voltage ripple
28. There is a 3rd state – discontinuous
Vin
+
Vout
–
L
C
Iout
• Occurs for light loads, or low operating frequencies, where
the inductor current eventually hits zero during the switch-
open state
• The diode opens to prevent backward current flow
• The small capacitances of the MOSFET and diode, acting in
parallel with each other as a net parasitic capacitance,
interact with L to produce an oscillation
• The output C is in series with the net parasitic capacitance,
but C is so large that it can be ignored in the oscillation
phenomenon
Iout
MOSFET
DIODE
29. Inductor voltage showing oscillation during
discontinuous current operation
650kHz. With L = 100µH, this corresponds
to net parasitic C = 0.6nF
vL = (Vin – Vout)
vL = –Vout
Switch open
Switch
closed
30. Onset of the discontinuous state
sec/A
L
Vout
fL
DV
TD
L
V
I
onset
out
onset
out
out
1
12
2Iout
0
Iavg = Iout
iL
(1 − D)T
fI
V
L
out
out
2
guarantees continuous conduction
use max
use min
fI
DV
L
out
out
onset
2
1
Then, considering the worst case (i.e., D → 0),
31. Impedance matching
out
out
load
I
V
R
equivR
DC−DC Buck
Converter
+
Vin
−
+
Vout = DVin
−
Iout = Iin / DIin
+
Vin
−
Iin
22
D
R
DI
V
DI
D
V
I
V
R load
out
out
out
out
in
in
equiv
Equivalent from
source perspective
Source
So, the buck converter
makes the load
resistance look larger
to the source
32. Example of drawing maximum power from
solar panel
PV Station 13, Bright Sun, Dec. 6, 2002
0
1
2
3
4
5
6
0 5 10 15 20 25 30 35 40 45
V(panel) - volts
I-amps
Isc
Voc
Pmax is approx. 130W
(occurs at 29V, 4.5A)
44.6
5.4
29
A
V
Rload
For max power from
panels at this solar
intensity level, attach
I-V characteristic of 6.44Ω resistor
But as the sun conditions
change, the “max power
resistance” must also
change
33. Connect a 2Ω resistor directly, extract only 55W
PV Station 13, Bright Sun, Dec. 6, 2002
0
1
2
3
4
5
6
0 5 10 15 20 25 30 35 40 45
V(panel) - volts
I-amps
130W
55W
56.0
44.6
2
,
2
equiv
loadload
equiv
R
R
D
D
R
R
To draw maximum power (130W), connect a buck converter between the
panel and the load resistor, and use D to modify the equivalent load
resistance seen by the source so that maximum power is transferred
34. Vpanel
+
Vout
–
iL
L
C iC
Ioutipanel
Buck converter for solar applications
+ vL –
Put a capacitor here to provide the
ripple current required by the
opening and closing of the MOSFET
The panel needs a ripple-free current to stay on the max power point.
Wiring inductance reacts to the current switching with large voltage spikes.
In that way, the panel current can be ripple
free and the voltage spikes can be controlled
We use a 10µF, 50V, 10A high-frequency bipolar (unpolarized) capacitor
35. Worst-Case Component Ratings Comparisons
for DC-DC Converters
Converter
Type
Input Inductor
Current
(Arms)
Output
Capacitor
Voltage
Output Capacitor
Current (Arms)
Diode and
MOSFET
Voltage
Diode and
MOSFET
Current
(Arms)
Buck
outI
3
2 1.5 outV
outI
3
1 2 inV
outI
3
2
10A 10A10A 40V 40V
Likely worst-case buck situation
5.66A 200V, 250V 16A, 20A
Our components
9A 250V
Our M (MOSFET). 250V, 20A
Our L. 100µH, 9A
Our C. 1500µF, 250V, 5.66A p-p
Our D (Diode). 200V, 16A
BUCK DESIGN
36. Comparisons of Output Capacitor Ripple Voltage
Converter Type Volts (peak-to-peak)
Buck
Cf
Iout
4
10A
1500µF 50kHz
0.033V
BUCK DESIGN
Our M (MOSFET). 250V, 20A
Our L. 100µH, 9A
Our C. 1500µF, 250V, 5.66A p-p
Our D (Diode). 200V, 16A
37. Minimum Inductance Values Needed to
Guarantee Continuous Current
Converter Type For Continuous
Current in the Input
Inductor
For Continuous
Current in L2
Buck
fI
V
L
out
out
2
–
40V
2A 50kHz
200µH
BUCK DESIGN
Our M (MOSFET). 250V, 20A
Our L. 100µH, 9A
Our C. 1500µF, 250V, 5.66A p-p
Our D (Diode). 200V, 16A