Elements of power electronics krein pdf download

Rectification is one example e. An- other example is conversion between the 50 Hz system used in about half the world and the 60 Hz system used in the other half. Mobile systems such as aircraft often use higher frequencies. Much higher frequencies are used for induction heating. Waveshape conversion square, sine, triangle, others. Sinusoidal waveforms for power minimize interference with frequency-multiplexed communication systems. They have other advantages in steady-state ac systems.

However, sine waves are not always best for power conversion or motors. Square waves are better for rectification. Triangle or trape- zoid waves are used in some motors. Single-phase ac power is by far the most widely available form of electrical energy. However, polyphase sources are by far the best form when energy is to be converted and transported. This type of conversion is important for introducing speed control and motor efficiency improvements into household appliances, for instance.

How do we accomplish these conversions? Originally, the straightforward way was to link a motor and generator on the same mechanical shaft, as in Figure 1. For example, an ac motor powered with ac electricity could drive a dc generator and thus perform ac to dc conversion. This process converts electricity to mechanical form along the way.

This method sometimes still applies when power levels are very high beyond 1 MW or so , provided that the desired frequencies match available motors and generators. Commercial machines are generally rated for dc, for 50 Hz, and for 60 Hz. There are a few electric railway systems rated for lower frequencies such as Some of the difficulties with this process of electromechanical conversion include:. Limited conversion ranges and functions. Slow response times and limited control capability.

In the past, the distinction was made between rotating converters based on machines, and static converters based on electronic circuits. The term static power conversion has given way to the more general term power. The general nature of the conversion issues at hand can be summarized as follows:. Electricity must always be converted back and forth to the energy forms of interest to people. Electrical engineers are in the business of energy conversion. Whether the issue involves information processing, motors, communication systems, remote sensing, or device fab- rication, electrical energy is the means to an end.

Electricity is easy to control. A light switch, a volume knob, or a cathode ray tube ma- nipulate electrons with speed and precision. Electrical supplies are needed in a variety of subtly different forms: ac, dc, high or low voltage, high or low current, and so on. Some applications of electricity are not compatible. Voltage transformation with magnetic transformers requires ac. Many chemical processes require dc.

Ac motors operate at speeds that depend on the source frequency. Dc motors have speeds that can be adjusted as a function of voltage or current. Conversion of electricity among its various forms is important for a wide range of appli- cations.

Compact electronic components with adequate ratings are available, so that electronic al- ternatives to motor-generator sets can be built. While rectification has always been a key issue, there are many possible conversion objec- tives. The technological significance of many of these is growing as new applications be- come available. In many ways, the search since the s for better rectifier methods has grown into the en- tire field of power electronics.

The basic form of the diode rectifier circuit was discussed in the nineteenth century, and the modem 50 kW rectifier in Figure 1. What makes the early idea significant is the recognition that the underlying process is fundamentally nonlinear, and cannot be done with any combination of linear circuit elements such as resistors, capacitors, and inductors.

One familiar nonlinear device is a rectifying diode-an element that conducts differ- ently depending on the direction of current flow. While the silicon P-N junction diode is the most common example today, many other technologies yield a rectifying two-terminal element. One early example is the selenium diode, used by C. Fritts in a rectifier circuit as early as The development of the vacuum tube diode about twenty years later was essential to practical applications, but it is interesting that semiconductor rectifiers existed well before the invention of vacuum tubes.

The vacuum diode is limited in fundamental ways by the low current density possible in a vacuum system. A major improvement came when mercury was included in rectifier tubes.

The mercury arc tube opened the way to multimegawatt power levels, even at volt- ages as low as a few hundred volts. A paper by Charles Proteus Steinmetz considered the performance of mercury tubes for rectification.

The waveforms in that paper can easily be duplicated in modern rectifier systems, and represent a broad selection of the possibili- ties of power rectification. A typical rectifier system, dating from the s, used mercury arc tubes to convert power from a 50 Hz V bus into V dc for a railway locomotive. Arc tubes are still used in certain specialized circumstances, such as rectification beyond 1 MV. Since before the invention of the transistor, semiconductor diodes have dominated at all but the highest power levels.

By the late s, single devices formed from sele- nium, copper oxide, and other nonlinear materials were manufactured commercially. The P-N junction diode appeared late in the s, and now is the dominant technology, although Schottky barrier diodes offer an alternative in many low-voltage situations.

Devices with ratings up to about 3 A and V are manufactured in huge lots. Diodes rated at more than 15 kV are readily available, and currents up to about A also can be achieved although not both simultaneously.

One figure of merit is the power handling rating-the product of voltage and current ratings. Individual diodes exist with power handling capabil- ities above 36 MW. The fabrication methods for diodes have evolved rapidly. Today, hundreds of diodes with power handling ratings up to perhaps W each can be fabricated on a single silicon wafer. The highest power devices use the opposite method: Individual diodes formed from complete single wafers are available today, even for 20 cm wafers and larger.

One of the biggest challenges with large single devices is packaging: Making a A connection to a thin, brittle disk 20 cm across is a formidable task. Complementing the packaging challenge is the challenge to find improved materials for higher power handling.

Germanium is sometimes used, but it is more sensitive to high tem- peratures than silicon. Gallium arsenide power rectifiers have entered the commercial arena, and other compound materials are being examined for power rectifiers.

Silicon carbide and even diamond film promise new opportunities to reach extreme power levels during the com- ing decades. In many cases, the distinction between a rectifier and an inverter is artificial: In a rectifier, energy flows from an ac source to a dc load.

In an inverter, the flow is from a dc source to an ac load. An inverter thus has much the same function as a rectifier, except for the direc- tion of energy flow.

Such a circuit provides dual rectifier and inverter operation. The example in Figure 1. Although a dual use rectifier and inverter circuit is possible in principle, the rectifier diode does not support such a circuit.

A diode, as a true two-terminal element, is a passive device. This means that its behavior is determined solely by terminal conditions, and there is no direct opportunity for adjustment or other control. One of the most important power electronic devices, the silicon-controlled rectifier or SCR, addresses this need for control.

The SCR, introduced in , provides the function of a diode with the addition of a third terminal for control. The conventional SCR will not con- duct unless a signal is applied to this control terminal, or gate. Once a gate signal is present, the device operates more or less as a conventional diode. In this way, the gate permits ad- justment of the conduction behavior, and leads to the concept of an adjustable diode. The SCR was not the first technology to provide controlled rectifier function.

By the s, passive circuit methods were combined with vacuum diodes to create similar func- tions. Grid control was used with mercury arc tubes to provide controlled rectification by the s.

The cycloconverter-a complicated controlled rectifier adapted for ac-ac con- version-was introduced in about Photographer: Peter S. The device brought about a revolution in electronic power conversion.

Such familiar applications as variable- speed kitchen appliances and lamp dimmers rely on the SCR and its relatives for control. It is sometimes said that power electronics began when the SCR was introduced.

Once a controlled rectifier can be built, the step to inverters is a small one. Inverters are the critical conversion method for most alternative energy resources. Sources as diverse as wind energy, solar panels, battery banks, and superconducting magnetic energy storage SMES rely on inverter circuits to transfer their energy to an ac power grid.

The SCR re- mains crucial for these kinds of systems. Very high power levels have always been an important application for inverters and controlled rectifiers. This is because dc power is the most economical form for transmission of energy over very long distances. Beyond about km or so, wavelength effects begin to bring trouble to ac power networks.

Resonances and reflections can affect behavior or cre- ate failures. Dc power avoids these fundamental problems, and high-voltage dc HVDC power transmission remains an important application. Pacific coast is rated at up to kV and MW. These levels are far beyond the capacity of any individual device, and large series and parallel combinations of devices must be used to provide diode or controlled rectifier functions.

In this particular case, each line terminal can act either as a rectifier or inverter there are two sets of devices at each end so that the line power can be adjusted for seasonal changes in energy flow. Some installations elsewhere in the world sup- port only unidirectional power flow. Two of the fastest-growing inverter applications are not as well served by the SCR. These are circuits for independent backup power and circuits for control of ac motors.

Two small modem commercial units are shown in Figure 1. The most straightforward inverter cir- cuits use timing information from the ac voltage source to control their operation. Backup circuits and motor controllers do not have access to this qort of time reference information.

Without such timing information, inverter control can be complicated. Motor control and backup applications were difficult to build from electronic circuits until relatively recently. One early ex'ample was the Stir-Lec I, an experimental electric vehicle built by General Mo- tors in This car used SCRs in an innovative but Complicated arrangement to convert dc power from batteries for an ac motor. Both backup power and ac motor control systems were considered to be classical ap- plications of motor-generator sets prior to the semiconductor revolution.

Diesel-driven gen- erator systems remain the standard choice for large backup power sources. Battery backup is common in dc applications, such as telephone networks and communication equipment. Batteries are becoming more common in small backup applications.

Equipment rated for the kW range is now readily available. The growth in low-power battery-backup inverters can be attributed in part to devel- opments in transistor technology. Power BJTs were first developed for the U. By the late s, power handling capacities had reached 1 kW. These ratings were well-matched to small so- lar panel units. Ratings quickly reached 5 kW early in the s-sufficient to meet the needs of small computers and other light commercial backup applications. By the early s, an experimental device with 1 MW power handling level had been constructed on a single 7.

They are more convenient to use in many circuits. After the power FET was intro- duced commercially in , it rapidly came into use for low-level conversion applica- tions. This device offers an interesting contrast to other power semiconductors.

Recent FETs have power handling levels well beyond 10 kW, and have been being applied to inverters for computer power, and even for heavier loads such as AM broadcast transmitters and inverters for ac motors up to about 50 HP.

They dominate motor control inverters. Motor control and motor drives are often considered a separate field related to power electronics. The most important long-term goal of engineers designing motor controls has been to supplant dc motors with ac machines.

In a typical commercial ac motor controller, the in- coming ac power is rectified to create a dc source. This dc voltage supplies an inverter virtu- ally identical to that used in a backup power application. Control of ac motors has been an im- portant technological objective since Tesla introduced the polyphase induction motor in the late s. Dc motors are common in control applications, because their speed can be altered sim- ply by adjusting the input dc voltage level, and their output torque can be manipulated through control of their main winding current.

They have major disadvantages in cost and reliability: a true dc motor has brushes and a mechanical commutator which must be maintained. Ac mo- tors, and especially induction motors, are inherently cheaper to build and maintain than dc ma- chines. They have better power-to-weight ratio than dc machines, and can operate at higher speeds. Moving parts are few, and only the bearings themselves require upkeep if motor rat- ings are observed. However, the speed of an ac machine is tied to the input frequency, and the torque is adjusted by altering the magnetic field levels in the device.

The difficult challenge of providing adjustable magnetic field and input frequency makes ac motors hard to control. Before about , the extra cost of control equipment far. In a few cases, the reliability ad- vantages of ac machines were critically important. Motor-generator sets provided adjustable frequency for these applications. Examples include the Scherbius combination, a combined ac motor-ac generator-ac motor, and the Ward-Leonard combination, a dc or ac motor-dc generator-dc motor combination.

These are summarized in Figure 1. The SCR can be used with some difficulty in electronic converters for ac motor con- trols, as mentioned above in the example of the electric car drive. One of the first ex- amples was the so-called static Scherbius system, in which combinations of SCRs substi- tuted for the functions of the Scherbius motor-generator arrangement.

The SCR is hard to use in such a system because its gate controls only the turn-on behavior. It is possible to al- ter an SCR so that current can be turned off by means of a negative gate signal. This device, called a gate turn-of SCR, or GTO, is used in some large motor control circuits today, par- ticularly those on ac locomotives.

More recent electronic circuits built from power FETs or IGBTs meet the basic func- tional requirements of ac motor control with inverters. In the early s, the cost of these electronic drives began to drop so dramatically that now the combination of a power elec- tronic circuit and an ac motor is cheaper than the cost of an equivalent dc motor system.

This development is bringing extraordinarily rapid change in manufacturing and industrial pro- cessing. Advanced ac motion control equipment has reached the cost and performance level at which almost any automation application can be addressed. This application dominates the power electronics industry in many ways, because of the huge quantities involved. Some typical supplies intended as components of larger systems are il- lustrated in Figure 1. The earliest power supplies for vacuum tube electronics were rec- tifiers, followed by filtering circuits to create a smooth dc output.

Until quite recently, most power supplies took this same form, usually with the addition of a transformer at the ac in- put to provide the correct output level. This conventional power supply style matured after about , when integrated se- ries regulator circuits were developed and routinely used at the supply output.

A series reg- ulator circuit is a form of amplifier, which provides a very tightly fixed output even from a somewhat noisy rectified signal. The combination of transformer, rectifier, and regulator is referred to as a linear power supply since the output filtering circuit is based on a linear am- plifier the circuit as a whole is still nonlinear.

Classical rectifier power supplies in this form are among the most widely used electronic circuits, and form the power supply for hundreds of millions of small appliances and electronic accessories.

As costs of electronics decline, the power supply becomes a larger fraction of system cost and design effort.

This situation makes new technology developments in power supplies critically important. Late in the s, use of dc sources in aerospace applications led to the. The basic circuit arrangements are much older, and grew out of rectifier applications. Although the basic ideas are old, power semiconductors can be used to make these circuits inexpensive and reliable.

In a typical arrangement, an ac source from a wall outlet is rectified without any transformation; the re- sulting high dc voltage is converted through a dc-dc circuit to the 5 v, 12 v, or other level required by the application.

These switched-mode power supplies are rapidly supplanting lin- ear supplies across the full spectrum of circuit applications. A personal computer often requires three different 5 V supplies, two 12 V supplies, a V supply, a 24 V supply, and perhaps a few more. Only a switched-mode supply can support such complex requirements without high costs. The bulk and weight of linear supplies make them infeasible for hand-held communication devices, calculators, notebook computers, and sim- ilar equipment.

Switched-mode supplies often take advantage of FET semiconductor technology. Trends toward high reliability, low cost, and miniaturization have reached the point at which a 5 V power supply sold today might last , hours more than 50 years! This type of supply brings an interesting, if mundane, dilemma: The ac line cord to plug it in actually takes up more space than the power supply itself.

Innovative concepts such as integrating a power supply within a connection cable will be used in the future. Device technology for supplies is being driven by expanding needs in the automotive industry, the telecommunications industry, and markets for portable equipment. The auto- motive industry uses well-defined voltage levels, but the amount and complexity of elec- tronic hardware in a typical car continue to increase. Power conversion for this industry must be cost effective, yet rugged enough to survive the high vibration and wide temperature range to which a passenger car is exposed.

Global communications is possible only when sophis- ticated equipment can be used almost anywhere in the world. This brings a special challenge, since electrical supplies are neither reliable nor consistent in much of the world. Communications equipment must tolerate these swings, and must also match a wide range of possible backup sources.

Given the enormous size of possible markets for telephones and consumer electronics in developing countries, the need for flexible-source equipment is clear. Portable equipment challenges designers to obtain the best possible performance from small batteries.

Equipment must use as little energy as possible. The low voltages used for portable battery packs, which range from less than 2 V up to only about 10 V, make any conversion circuit difficult. The field of power electronics is relatively new as a distinct discipline, even though the ap- plications and fundamental methods have a long history.

As a special electrical engineering practice, it dates from about the time the SCR was introduced. The term was coined about to describe the subject as a cohesive discipline. Power supplies, either in general, or for specific power needs in computers, electronic in- struments, telecommunications, portable equipment, or other electronic circuits. Power semiconductor devices. Electronic motor drives. Support of energy conversion and control in large power systems. This includes control of power networks, high-voltage dc systems, superconducting magnetic energy storage, alternative energy conversion, and controllers for generators.

Electric transportation and mobile power, including electric cars, railways, aircraft elec- tric power systems, and spacecraft power systems. Computer industry: need for lots of power at a variety of low dc voltages. Backup power is also important. The trend to voltage levels below 5 V will require considerable inno- vation.

Telecommunications industry: needs power for transmission, signal processing, and aux- iliary services. Highly reliable power sources must be distributed throughout a large sys- tem. Rapid communication system growth in developing countries offers vast opportu- nity. There is extraordinary opportunity for portable communications technology, as cellular telephones, pagers, and a variety of personal devices grow in use.

Aerospace industry: lightweight converters for aircraft energy needs and for spacecraft electric power processing. Reliability requirements are extreme. Conversion from solar power and other alternative energy sources. The all-electric aircraft is a recent develop- ment driven partly by advances in power electronics. Electronic equipment industry: power supplies for instruments, consumer electronics, portable and remote measurement devices, and many other products.

Many of these rep- resent major growth areas in power electronics. For example, power electronic ballasts for high-efficiency fluorescent lighting are being manufactured in high volumes.

Zndustriul controls: motor and motion control applications. Power sensing and measure- ment. Advanced power-electronic ac motor controls are now available commercially. They can be expected to supplant almost all existing dc motor systems over the next two decades. Automobile industry: electric actuators and energy control. Electric traction systems. Air pollution concerns are forcing the issue of electric cars.

Electric power industry: emergency backup power supplies. Alternative energy source conversion. HVDC transmission. Power supply quality, and direct electronic control of utility grids.

It is possible to move more energy through existing connections if power electronic controls are added. Devices suitable for the power grid are eagerly anticipated. These examples span nearly the full range of both light and heavy industry. Power electronics today influences the design of everything from office equipment and home appliances to high-speed transportation and satellites.

Much of this historical discussion has described the special semiconductors used for power conversion circuits. The special energy processing applications addressed by power elec- tronics have also been described. Not long ago, the devices were in many ways the limiting factors in converter design. The fast pace of change in devices has brought about entire new families of power electronic applications, and devices are less and less constraining.

The im- portant classes of power electronic components routinely reach power handling levels at least equal to a household appliance load, to a small industrial process, or to most elements of an automobile.

Many alternatives are often available. This is no longer the case. This trend will continue into applications such as those suggested by Figure 1. The figure shows an industrial robot, a portable telephone, a powerful portable computer, an electric car, and a utility plant. The chronology is summarized in Table 1. Among the key opportunities in the next few years are:. Electronic ac motor drives. These offer a revolution in energy conservation and industrial processes.

It is becoming possible to use sophisticated controls for refrigerators, fans, con- veyers, and even washing machine motors. Energy usage can be reduced considerably in many cases. Electric transportation. Power electronics is the cornerstone of modern initiatives for elec- tric, hybrid, and alternative vehicles. Battery energy can be conserved well enough for practical cars to reach about km of range with conventional batteries. Novel ideas and innovations are needed for the best designs.

Electrical systems for high-efficiency lighting and appliances. Modern fluorescent lights are many times more efficient than incandescent bulbs. They require high-frequency power electronics for optimum operation.

Similar new developments extend to appliances such as microwave ovens and other major energy consumers. Power supplies for telecommunications. There are billions of people without telephones or other means of outside communication. Many developing countries do not plan to build expensive hardwired networks. Satellite links, wireless communications, and other new technologies must be integrated with existing equipment. Each different application has unique power supply needs.

Power supplies in battery-based portable products. Energy conservation is crucial in bat- tery systems. Converters for applications below 5 V are a special challenge. Power electronic applications in electric utility networks. It is possible to extend conver- sion advantages to extreme energy levels. Systems with fast control of all energy flows can be imagined.

This gives a tremendous range of opportunities for lower cost electric- ity distribution. Novel power electronic methods are being applied to audio amplifiers, cellular telephones, and microprocessors.

The list is long, and there is need for skilled engineers who can apply the methods in unconventional ways. Dates Device or Technology Conversion Technologies s Transformer, M-G sets Electromechanical units for ac-dc conversion, voltage level shifting for ac.

Electronic circuits for ac-dc and dc-ac conversion. Basic techniques worked out for ac-ac conversion. Further advances in electronic conversion. Growing need for small power supplies for electronic gear. These quickly replaced gas tubes, and rectifiers SCRs made controllable ac-dc converters practical and cheap.

The influence of device properties on transistors power electronics begins to wane. Rapid expansion of mru-kets for miniature power supplies. Emphasis on the best alternative for a given application. The function of a power conversion circuit is to control the energy flow between a given electrical source and a given load, as depicted in Figure 1. A converter must manipulate flow, but should not consume energy.

The reason is simple. Since a power converter appears between a source and a load, any energy used within the converter is lost to the overall sys- tem. This is the first and primary design objective in power electronics:. We seek lossless processes to implement converters. A power converter connected between a source and a load also affects system relia- bility. If the energy source is perfectly reliable it is on all the time , then a failure in the converter affects the user the load just as if the energy source fails.

An unreliable power converter creates an unreliable system. Reliability requirements are extreme in many appli- cations. To put this in perspective, consider that a typical U. Energy is available A converter must be better than this to avoid degrading a system. As high efficiency becomes more routine, this second reliability objective grows in importance:. Reliability is often a more difficult objective than efficiency. Imagine just trying to prove that a circuit will not fail over decades of use.

Spectacular failures are a traditional property of power supplies, and other equipment is often damaged in the process.

As simple a circuit element as a light switch like the one in Figure 1. Ideally, when a. The de-. The switch controls energy flow with. Electrical Figure 1. Reliability is high, too. Household light switches perform over decades of use and perhaps , operations. Of course, a mechanical light switch does not meet all the prac- tical needs. A switch in a power supply often functions ,times each second. Even the best mechanical switch will not last beyond a few million cycles.

A circuit built from ideal switches will be lossless. The advantages of switching cir- cuits are so significant that many people equate power electronics with the study of switch- ing power converters.

Other lossless elements such as capacitors, inductors, and conventional transformers, might also be useful for conversion. The complete concept is shown in Figure 1. Such a system consists of an energy source, an electrical load, a power electronic circuit, and control functions. The power electronic cir- cuit contains switches, lossless energy storage elements, and magnetic transformers. The con- trols take information from the source, load, and designer, then determine how the switches operate to achieve the desired conversion.

Usually, the controls are built up with conven- tional low-power analog and digital electronics. It is well established in military electronics that the more parts there are in a system, the more likely it is to fail. As we shall see, power electronic circuits tend to have few parts, es- pecially in the main energy flow paths.

The necessary operations must be carried out through shrewd use of those parts. Often, this means that sophisticated control strategies are applied to seemingly simple conversion circuits.

One way to avoid the reliability-complexity tradeoff is to use highly integrated com- ponents. A high-end microprocessor, for example, contains more than a million parts. Since all interconnections and signals flow within a single chip, the reliability is nearly that of a single part. An important parallel trend in power electronic devices is the integrated mod- ule.

Manufacturers seek ways to package several switching devices, their interconnections,. Control circuits for converters are also inte- grated as much as possible to keep reliability high. In a power electronic system, several electrical quantities are of special interest. Efficiency has already been identified. Maximum values of currents and voltages will be needed to de- termine the necessary device ratings. Energy flow is the underlying objective, and power and energy levels in each part of the system are very important.

We are most interested in en- ergy flow over reasonable lengths of time. The power electronic circuit must work to alter the flow from source to load. The average energy flow rate, or average power, is therefore of particular interest. Some important quantities:. This represents useful energy flow over time. These determine device ratings. These represent the dc values in a circuit. These represent power in resistors, and often determine the losses in a converter.

Power electronic circuits often have clear graphical properties. Switches are not quite ideal, and some residual power will be lost in them.

All these quantities are crucial to a basic understanding of power electronics and the circuits studied in it. Notation for average and RMS values of some periodic function v t will be given as. It contains an ac source, a switch, and a resistive load. It is therefore a simple but complete power electronic system. Just to get an idea of how power conversion might take place, let us assign some kind of control to the switch. The input and output voltage waveforms are shown in Figure 1.

The output has a nonzero aver- age value given by. Vpeak COS 6 do -k ;1: 0 do 1. Vpeak - -- - 0. Confirm this RMS value as an exercise. The output has some dc voltage content. The circuit can be thought of as an ac-dc converter. The circuit in Example 1. A diode can be substituted for the switch. The example shows that a simple switching circuit can perform power conversion functions.

But, notice that a diode is not, in general, the same as the switch. A diode places restrictions on the current direction, while a true switch would not. Consider a second half-wave circuit, now with a series L-R load, shown in Figure 1. This circuit operates much differently than the half-wave rectifier with resistive load. Remember that a diode will be on if forward biased, and off if reverse biased. Notation Description Instantaneous values of voltage.

Given in lower-case notation. Time is usually shown explicitly. Bracket notation for average or dc quantities. Averages are defined over some time period T in integral form.

Upper-case form. Used for explicit dc source values. Also used as an alternative notation for averages, especially for average power. The true root mean square value associated with a given time function. RMS quantities are defined over a time pe- riod T in integral form. In conventional power systems practice, a given voltage or current is an RMS value unless explicitly stated otherwise. Moving-average quantities. A simple alternative P r will usually be used to indicate the moving average of power.

Complex phasor quantity, with magnitude given in RMS units. Small-signal perturbation or ripple. A small change around a constant level. Whenever the diode is on, the circuit is the ac source with R-L load Figure 1.

Let the ac voltage be V,-, cos wt. Let us assume that the diode is initially off this assumption is arbitrary, and we will check it out as the example is solved.

The diode will become forward-biased when vac becomes positive. The diode will turn on when the input voltage makes a zero-crossing in the positive direction. The differential equa- tion can be solved in the conventional way3 to give. What about diode turn-off? One first guess might be that the diode turns off when the voltage becomes negative, but this is not correct.

We notice from the solution that the current is not zero when the voltage first becomes negative Check this! If the switch attempts to turn off, it must drop the inductor current to zero instantly. What really happens is that the falling current allows the inductor to maintain forward bias on the diode. The diode will turn off only when the current reaches zero.

A diode has very definite properties that determine the circuit action, and both the voltage and current are relevant. We have considered the diode in these two example circuits so far.

While the device acts as a switch, we do not have any control over its behavior. Let us consider a different way to operate the switch in the first example circuit. The input and output voltage wave-. Appendix C provides a list of computer code necessary for many equations in the text, including the one here. The output average value is given by. In the Example 1. The circuit still performs rectification, but some more general switch will be needed to permit the necessary control.

The rectifier example shows how a switch can be used to ob- tain a conversion function. From the examples, rectifier operation can be adjusted by ma- nipulating switch timing or the load properties. The dc output depends on when the switch is turned on or off.

However, the output was not a clean dc waveform. We need filtering to recover the dc value. Any type of low-pass filter could, in principle, allow recovery of the dc output.

Filters are one way in which energy storage elements are applied in power elec- tronics. Storage elements also appear at intermediate points in many power converters. An ex- ample appears in Figure 1. In this circuit, the left switch is turned on to store energy in the inductor.

The right switch sends energy from the inductor into the load. The inductor mediates energy transfer through the system, and adds flexibility to the converter. Let us consider a possible way of operating this circuit. What does the circuit do if each switch operates half the time?

The inductor and capacitor have large values. When the left switch is on, the source voltage V,, appears across the inductor. When the right switch is on, the output voltage V,,, appears across the inductor. If this circuit is to be a useful converter, we want the inductor to receive energy from the source and deliver it to the load without loss. Over time. The power into the inductor therefore must equal the power out, at least over some reasonable period of time.

The average power in should equal the average power out of the inductor. Let us denote the inductor current as i. The input is a constant voltage source. Assuming that the inductor current is also constant, since L is large, the average power into L is. The average power out is? Again, if this circuit is to be useful as a converter, the net energy flow should be from the source to the load over time.

The circuit of Figure 1. The output voltage magnitude is the same as that of the input, but the output polarity is negative with respect to the reference node. The circuit is often used to generate a negative supply for analog circuits from a single positive input level. If the inductor in the polarity reversal circuit is moved instead to the input, a step-up function is obtained.

Con- sider the circuit of Figure 1. Each switch is on during half of each cycle. Determine the relationship between V,, and V,,,. The inductor's energy should not build up when the circuit is operating normally as a converter. A power balance calculation can be used to relate the input and output voltages. Again let i be the inductor current. When the left switch is on, power is injected into the in- ductor.

Its average value is. Power leaves the inductor when the right switch is on. Again we need to be careful of polarities, and remember that the current should be set negative to represent output power. The result is. Many seasoned engineers find the dc-dc step-up function of Figure 1.

Yet Figure 1. Others including circuits related to Figure 1. The circuits of the examples have few components. A commercial step-up circuit is shown in Figure 1. The left switch is implemented as four power MOSFETs metal- oxide-semiconductorfield effect transistor in parallel, while the right switch is a diode.

This circuit actually takes in an ac supply, then rectifies it and boosts up the result. It can supply up to W at V dc from a V ac source. There are extra components for control functions, but the power electronics are very much those of Figure 1. Another commer- cial circuit is shown in Figure 1. Although it is far more complicated than the preceding examples, its power electronic heart is the polarity reversal circuit.

The history of power electronics has tended to flow like these examples: a circuit with a particular conversion function is discovered, analyzed, and applied. As the circuit moves from a simple laboratory test to a complete commercial product, control and protection func- tions are added. The power portion of the circuit remains close to the original idea.

The nat- ural question arises as to whether a systematic approach to conversion is possible. Can we start with a desired function and design an appropriate converter? Are there underlying prin- ciples that apply to design and analysis? Where do all these control functions come from and what do they try to accomplish?

How do the circuits work? In this text, we will begin to see how the various aspects of energy flow manipulation, sensing and control, the energy source, and the load fit together in a complete design. The goal is a systematic treatment of power electronics. Keep in mind that while many of the circuits look deceptively simple, all are nonlinear systems with unusual behavior. RECAP Definition: Power electronics involves the study of electronic circuits intended to con- trol the flow of electrical energy.

These circuits handle power flow at levels much higher than the individual device ratings. Energy conversion is our business because people use light, mechanical work, information, heat, and other tangible results of energy-not electricity. In most electronics, devices are limited by their ability to dissipate lost energy. In power electronics, we are interested in how much energy flow a device can manipulate, and intend to keep the dissipation as low as possible.

Power handling ratings the product of ratings for voltage and current are larger than power dissipation ratings by more than a factor of for many devices. Voltage level and frequency conversion are the most common needs for electrical en- ergy conversion. All major industries use power converters. Significant growth is expected in ac drives, electric transportation, portable power, telecommunications applications, and utility applications over the next few years.

A power converter is positioned between a source and a load. Very high reliability is also important. The switch is a familiar lossless de- vice that can manipulate energy flow. Many circuits can be analyzed through energy con- servation considerations. Functions such as dc voltage conversion can be created with switch networks. I 1 Definition: A power electronic system consists of an electrical source and load, a power electronic circuit containing switches and energy storage, and control functions.

The power electronic circuit portion often has relatively few parts, and most of the components in a commercial system pelLf0l-m control functions. From R. Patel, D. Reilly, and R. Lexington, MA: Unitrode, Reprinted with permission of Unitrode Corporation. Power electronics today is evolving from a device-driven field to an applications-driven field.

Not long ago, the possible conversion functions were limited by the types of switch tech- nologies. Today, new applications such as ac motor controllers can be built with several types of devices. In the future, application requirements will not be limited by device capabilities. List five products that you own which require electrical energy conversion. Try to list the motors and their functions in a typical household e.

List some possible applications of rectifiers. Which of these could benefit from the ability to ad- just the dc output level with a controlled rectifier? Consider the circuit of Example 1. The switch will turn off one-half cycle later. What is the output average voltage as a function of k? In the polarity reversal circuit of Example 1. Again, the input and out- put power must match.

The step-up converter of Example 1. What is the ratio V,,JV,, in this case? The circuit in Figure 1. What is the ratio VouJVin? See Example 1. The converter will be damaged whenever the power dissipated inside it exceeds 6 W. If the converter is intended to op- erate for output loads between 20 W and some maximum limit, what is the upper limit of output power which can safely be supplied?

A designer constructs the converter of Problem 1. The purchaser finds that the efficiency is slightly worse than expected: It is What power limit will the purchaser encounter? The customers of a certain electric utility company use energy at a combined rate of 10 GW. A small company has developed a new switching power converter for sup- plying energy to fluorescent lights. If every utility customer installed the new converters, how much money would be saved in energy costs each year?

Power balance can be a delicate thing. The field is growing rapidly because electrical devices need electronic circuits to process their energy.

Elements of Power Electronics, the first undergraduate book to discuss this subject in a conceptual framework, provides comprehensive coverage of power electronics at a level suitable for undergraduate student engineers, students in advanced degree programs, and novices in the field.

It aims to establish a fundamental engineering basis for power electronics analysis, design, and implementation, offering broad and in-depth coverage of basic material. The texts unifying framework includes the physical implications of circuit laws, switching circuit analysis, and the basis for converter operation and control.

Dc-dc, ac-dc, dc-ac, and ac-ac conversion tasks are examined and principles of resonant converters and discontinuous converters are discussed. Models for real devices and components are developed in depth, including models for real capacitors, inductors, wire connections, and power semiconductors.

Magnetic device design is introduced, and thermal management and drivers for power semiconductors are addressed. Control system aspects of converters are discussed, and both small-signal and geometric controls are explored. Many examples show ways to use modern computer tools such as Mathcad, Matlab, and Mathematica to aid in the analysis and design of conversion circuits. Featuring a fundamental approach to power electronics coupled with extensive discussion of design and implementation issues, Elements of Power Electronics serves as an ideal text for courses in power electronics and as a helpful guide for engineers new to the field.

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