Revise and edit the essay Example | Topics and Well Written Essays - 500 words

Revise and edit the - Essay Example Classes were fun-filled, characterized by â€Å"work and play†. For my colleagues and I, the fun festivity also entailed editing our yearbook pages before the due date for graduation. Every year in college du leman, students set to graduate edit their yearbook pages and keep a copy of the yearbook as a souvenir. The yearbook is meant to record the memories and experiences of the students in their senior year. In the last few months of high school, I was not only happy that I was about to graduate, but also that my grades had significantly improved. The night before graduation, I got to contemplate about the future and what it held for me. When the graduation day finally came, I woke up early in the morning and took a long hot shower to energize me and freshen up. I headed to Theatre du Leman where the graduation was taking place. Graduating students had to stand in lines by alphabetical order, and all the parents were sitting in the salon waiting for us to go on the stage. Bef ore long, graduation started and they started calling the names of the students. When they called my name, I walked in with a proud face and took my Diploma from the General Director of Collage du Leman. I received my certificate from the Director as everybody on the high school honor roll does. When I was receiving my diploma I could see my parents from the middle of the salon looking at me proudly. After I graduated, I went to my country and continued the celebration with my relatives. We went to restaurants and visited places for fun. I was so proud of myself and I felt free to enjoy my time off school work. My father could not hide his joy and he, therefore, allowed me to go on holiday for one month with my friends. He acknowledged my efforts in school and told me that I deserved to have some fun with my friends. So, I went for holiday to Istanbul accompanied by my friends, where we partied and had fun every day. The one month

Case Study Module 3 Example | Topics and Well Written Essays - 1000 words

Module 3 - Case Study Example Dr. MacIntyre finds that the drug Valium in the Avery Clinic was unaccounted. Despite this, her outdated records management system is unable to affirm if the drugs were physically missing. The next problem is the increasing absenteeism of her associate Stephen Saltzman. With Mr. Saltzman not working full time, the sales figures at the Avery clinic are negatively impacted. He is also not available as often as he is expected to be thus disappointing many clients. Mr. Saltzman also seems to have a poor work ethic. Dr.MacIntyre by analyzing the amount spent on tests at the Avery clinic concludes that he may not be taking the time to diagnose properly. These issues point to a bigger problem which is the poor monitoring of the Avery clinic. It is evident from the case that Dr. MacIntyre is closely involved with the Johnsonville clinic where she puts up but not so with the Avery clinic. A new branch or venture always needs close attention to be paid. (Kishel & Kishel, 2005) Leaving the Avery clinic to its own devices seems to cause of all the problems the business is facing. A cause of immediate concern is the few hours been put in Avery and poor work ethic by Mr. Saltzman at Avery. This is because the two directly influence income and customer satisfaction. The hours Mr. Saltzman is not attending to clients are all hours not spent billing. Not taking enough time to diagnose animals is poor service delivery and leads to unhappy clients. Neglecting client’s needs ruins the reputation of the business. (Scott, 1991) As a result of the problems mentioned above, other areas of the business suffer. Profitability has gone down in the Avery clinic because as a direct result of the absenteeism of Stephen Saltzman. It has gone down in Johnsonville as Dr. MacIntyre had to reduce her hours of working to travel to and from Avery to assist with the workload there. Strategic direction for the company also suffers as the lack of sufficient

Hamlets Contradicting Traits Essay Example for Free

Hamlets Contradicting Traits Essay William Shakespeare created many complex characters in his play Hamlet. One of these complex characters being the protagonist, Prince Hamlet. Hamlet has many contradictory traits, two of them being that Hamlet sometimes thinks rationally, and that being overcome by the command left by the ghost of his belligerent father, King Hamlet, he tends to make irrational decisions. When Hamlet is first introduced to the ghost’s commands in scene one, act 5, they begin to consume him with thoughts of vengeance, to murder Claudius, his father’s murderer. Throughout the play, Hamlet acts in such a way to provide evidence supporting both traits. Conflicted by these two opposing traits, Prince Hamlet has a war of two spirits in his mind, deciding which side is right. During the length of the play, Hamlet frequently argues with himself. Many of his soliloquies are debates between Hamlet and the warring side of his mind that believes he should listen to the vengeful plan of his father’s ghost. At the beginning of the play, Hamlet, the Prince of Denmark, is a rational scholar from Wittenberg. When he returns from Wittenberg, his mother, Queen Gertrude confronts him concerning his melancholy. He replies â€Å"Seems, madam? Nay it is. I know not ‘seems’† (1. 2. 76) He is very straightforward with her and speaks in a sensible and rational manner. This conversation happened before Hamlet encountered the ghost; therefor the militant and vengeful spirit has not yet influenced him. When Hamlet is preparing to rig the play to gage a reaction from Claudius to prove he is guilty of murdering his father, he is thinking rationally. Ill have these players/Play something like the murder of my father/Before mine uncle: Ill observe his looks; /Ill tent him to the quick: if he but blench, /I know my course. † (2. 2. 601-605) it takes and intelligent, sensible, and rational person to develop such a precise and functioning plan, therefor proving Hamlet is able to think rationally. Once Hamlet has met and been influenced to his father’s ghost, he becomes consumed with the thought of avenging his father. Hamlet is not a violent person; therefor the thought of murdering Claudius causes a lot of internal conflict for Hamlet. As Hamlet and Laertes fight in Ophelia’s grave, Hamlet says to Laertes â€Å"For, though I am not splenitive and rash, /Yet have I something in me dangerous, /Which let thy wiseness fear† (5. 1. 265-267). This quote proves that Hamlet is aware that though he is not generally a violent person, he now possesses something dangerous in him due to his dead father’s command. Later, Hamlet claims to Laertes that he is mad. â€Å"Roughly awake, I here proclaim was madness. /†¦ Who does it, then? His madness: ift be so, /Hamlet is of the faction that is wrongd; /His madness is poor Hamlets enemy† (5. . 224-233) according to Hamlet it was not him who killed Polonius it was his madness. Again, Hamlet is aware that avenging his father has driven him to be something he is not, and to do irrational things such as murdering Polonius. Hamlet had stabbed Polonius through a curtain simply because there was a slight chance it would have been Claudius hiding. Before chec king, he quickly stabbed Polonius, this is completely irrational and risky on Hamlet’s part. This dramatic turn of events caused negative repercussions towards Hamlet. By killing Polonius, Hamlet pushed Laertes to decide to avenge his own father and in the end, he murders Hamlet. The overwhelming urge to avenge his father caused Hamlet to act without thinking, putting Hamlet in a dangerous situation. Due to Hamlet’s strongly contradicting traits, he frequently argues with himself, usually in his soliloquies. Hamlet’s soliloquy â€Å"To be or not to be† is a literal debate between scholarly, rational Hamlet and Prince Hamlet as the soldier-son, seeking revenge for his pugnacious father. In this soliloquy, Hamlet questions his motives and morals. To be, or not to be: that is the question:/Whether tis nobler in the mind to suffer/The slings and arrows of outrageous fortune, /Or to take arms against a sea of troubles, /And by opposing end them? † (3. 1. 56-60) he is debating with himself on whether or not it is worth it to avenge his father. This way of making a decision is a rational and logical thought process in which Hamlet is evaluating all of his options and their repercussions. However, had Hamlet not had irrational thoughts to begin with, he would not have to go through with this process. Eventually Hamlet`s irrational urge to avenge his father consumes him. Most of his rationality has vanished and all of his thoughts concern revenge, or are not fully thought through. In his â€Å"My thoughts be bloody†¦Ã¢â‚¬  soliloquy, the irrational part of Hamlet`s divided soul is convincing him that if he does not avenge his father essentially he has no purpose â€Å"What is a man,/If his chief good and market of his time /Be but to sleep and feed? a beast, no more† (4. 4. 36-38) Hamlet says if he has no purpose, he is nothing. At the end of the soliloquy Hamlet decides â€Å"My thoughts be bloody, or be nothing worth! (4. 4. 68) this is him saying that if his thoughts are not concerning violent actions towards Claudius, they are worthless. These thoughts are completely irrational, and the benefits and downfalls of this decision have not been taken into consideration. Later when Hamlet is asked whether he would prefer to battle Laertes now, or give himself some tim e to prepare, he quickly responds that he will fight him now, leading to Hamlet’s death. Again, Hamlet has irrationally made a decision without considering each side of the argument. The command left by the ghost of his father has completely overcome his mind leaving him not thinking logically or rationally as he was at the beginning of the play. Hamlet is an irrational rationalist. Before the ghost confronts him, Hamlet is a rational scholar from Wittenberg, however afterwards, the ghost’s vengeful thoughts consumes him, giving Hamlet an irrational and violent mindset. During the play, these two combative traits are warring in his mind, and expressed through soliloquies. Many of Hamlet’s soliloquies are debates between these two opposing traits. Eventually, the vengeful thoughts consume Hamlet and he becomes highly irrational. He does not plan or think anything through as he did at the beginning of the play. Hamlet’s irrationality is potentially the cause of his madness, and death. Had Hamlet not been so irrational whilst making decisions and allowing the vengeful thoughts left by his father to consume him, Claudius would not be seeking to murder him. Though Hamlet is genuinely a rationalist, his need to avenge his father’s death consumes him, causing him to make irrational and illogical decisions.

Theories in the marketing communication framework

Theories in the marketing communication framework According to Kotler (2003, p.563) A way of looking at the whole marketing process from the viewpoint of customer Fundamentally, marketing communication is the essential process to convey the message between corporations and consumers which is to make the target audience trust the brand and marketer Burnett (1993). It has the different methods to reach the audience but the main aim is to build the medium which can inform and persuade the consumers. Also, marketing communication is the method to establish the invisible relationship between firm and customers. To ensure the audience correctly received the message is primary step. By using marketing communication, consumers can understand about firms, products and brands (Kotler and Keller, 2006). One fact which needs to be noted is that the difference between advertising, marketing communication and promotion. It has been claimed that advertising is part of marketing mix which is wider and complex than advertising. However, it is hard t o distinguish the slight difference between. Therefore, they mean the same meaning in this report. Traditionally, there are several elements in the marketing communication which includes advertising, sales promotion, sponsorship, public relations, direct marketing, and personal selling (Pickton and Broderick, 2005). Even though there has been divided into several elements to distinguish the difference. There is still some room which is overlapped. Hence, it shows the importance of integrated marketing communication. Moreover, it has been claimed that there are some tools which also can be in the marketing communication mix such as packaging, word of mouth, point of sales, E-marketing and exhibitions. It has been stated that there are two categories, namely, above the line and below the line. Above-the-line include advertising which needs to pay the space for promotion such as TV commercial, radio or newspaper and magazine of press. Below the line consist of sales promotion and publi c relations (Smith and Taylor, 2004). The main reason to choose integrated marketing mix is that the message and information can extensively reach the target audience by all channels as well as more suitable and effective methods to achieve marketing communication objectives. By multi-channels promotion, it increase the awareness of brand and comprehend the message. After this, the purchase action could be expected happen by consumers Patrick et al., 2004, Smith and Taylor, 2004) Hence, each marketing communication mix element has the particular function to promote the brand in marketing campaigns. Nowadays, TV commercial, sponsorship, sales promotion are popular and essential marketing communication tools to be used in beer promotion campaign. Also, it has been found that words of mouth play the major role to influence the some beer customer. These marketing communication mix elements will the discussed as below. In beer promotion campaign, Advertising: Advertising is the primary element in the marketing communication mix. It is common to find that majority of audiences consider advertising equal to promotion. According to Kotler and Keller (2006) Any paid form of non-personal presentation and promotion of idea, goods or services by an identified sponsor. It is a general definition of advertising but shows the key point of characteristic which are the promotion for product or service by a sponsor. It has also been admitted that advertising is suitable to build the long term brand image and create the initial awareness. It is controversial issue to distinguish which element is the most influential one in the marketing mix. However, it still needs to be admitted that advertising take the majority part of promotion budget in the campaign regularly as well as widely reach the mass target audience. Furthermore, TV advertising would is arranged the most money because it costs more than other categories like press or radio. In other words, although advertising takes most spend of promotion, it is still the low cost for each unit person (Kotler and Armstrong, 2006). Therefore, from firms perspective, advertising seems to be the economical methods to reach most consumers (Pickton and Broderick, 2005). Moreover, advertising can play the major role to supplement the rest of tools which efficiently enhance the awareness of campaign and increase sales. For example, it is evidential that most sales promotion messages are conveyed by advertising to reach most audiences. In addition, public relations event such as event sponsorship needs the advertising support to announce the information which also can enhance the awareness (Burnett, 1992). However, there are some limitations of advertising which have been argued. Firstly, it is hard to prove that audience would purchase the products after receiving the commercial message. In other words, the sequenced process needs to be demonstrated more evidences. (Pickton and Broderick, 2005). Also, there are several vital cause which can influence the purchasing such as reasonable price, convenient location and quality product (Burnett, 1992). Therefore, advertising can be the influential facts to brand awareness and attitude. Even the direct effect for stimulating purchasing needs to be considered the relationship, it still can be the functional tools in marketing communications. Sponsorship: Sponsorship is in the sub-category of public relations which is to build a relationship and corporation image (Kotler and Armstrong, 2006). The definition of sponsorship is that the firms invest the money or in kind to expect the potential revenue to achieve the marketing objectives (Meenaghan, 1991; Berrett, 1993). In recent years, sponsorship has been popular and divided from public relations to be an independent tool in the marketing communication mix which show that the use of sponsorship is increasing and more different types of sponsorship are developing (Pickton and Broderick, 2005). Although most of firms keep a limited budget for sponsorship, in some sponsored activities the cost is still a great deal of money such as Carling sponsor as a title to Carling cup. Moreover, the world cup and Olympic both are the popular event which have attracted many aggressive sponsor to invest in it. It has been claimed that sport, arts, education and broadcast are the most popular categories for sponsorship (Smith and Taylor, 2004). It has been claimed that audiences can be aware of the sponsor brand and evoke the brand in the purchasing occasion which increase the brand recall and add the brand into the considered brand portfolio. The brand awareness would be higher than advertising promotion and get more involvement. Moreover, sponsor would evaluate the applicability of event which can be expected to convey the positive emotion and attitude to audiences. Therefore, sponsor expects to link the positive to their brand. In the sport, audiences also can be persuaded with the sport stars endorsement which can enhance the purchasing possibility (De Pelsmacker et al, 2004). It can be concluded that perfect sponsorship could to increase the positive attitude to sponsor and sponsored activities both. However, there are some potential risks of sponsorship which need to be noted. For example, the negative facts influence the sponsored entities which impact the sponsors directly or indirectly. It often happens in sport sponsorship like the sponsored teams or players do not play well in the match. It can be found that Carling and Guinness sponsor the different sport league not particular teams or player that would be a considered sponsorship strategies. In addition, overlapped sponsorship shows the extreme commercial image which could make audiences ignore the message (Pickton and Broderick, 2005). Hence, even sponsorship cost generally would be lower than advertising, it still need to be consider punctiliously. Ensuring the sponsored objective will be achieved and can be suitable to marketing communication objective. Also, budget and effectiveness measurement have to be planned in the process. After these, to integrate sponsorship into other communication mix element will reinforce the promotion campaign effectiveness (De Pelsmacker et al, 2004). Sales Promotion: Sale promotion is a short-term promotion to stimulate the consumer buying behaviour (Kotler and Armstrong, 2006). The function of sales promotion is not similar with other elements which to increase the long term relationship with consumers. It focuses to increase the sales immediately. There are two ways to achieve the sales. One of these is to encourage the current customers purchasing more products or another one is to attract the new customers attention to purchase. Therefore, it can be concluded that the features of sales promotion is to use simulative offers encourage the customers buy product in the limited time. Also, the measurement of sales promotion is easier to conduct than other communication mix tools (De Pelsmacker et al, 2004). Many tools can be used in the sales promotion such as couponing, sampling, premiums, contest and money-off. Those of instruments are planned to be used in different categories of products. Also, there are some particular sales promotion tools f or trade like point -of tail materials and merchandising. One fact which it needs to note is that sales promotion would be often implemented with advertising which can enhance the effectiveness of campaign. By using sales promotion information in advertising, it would be effective to encourage from awareness to purchase (Pickton and Broderick, 2005). Even though sales promotion has been admitted to increase short-term sales influentially, the long-term effect to the brand and sales also needs to be considered. It has been stated that consumers would be used to the price reduce and disregard the quality of products. Moreover, sales promotion would offer a reference price in their mind which makes them more sensitive to the price. Therefore, sales promotion would need more striking price promotion to attract the consumer in the future (De Pelsmacker et al, 2004). In beer industry, sales promotion is often used to compete with other brewers in special period like world cup or Xmas. The re also has some regular sales promotion which tried to be incentive for consumers. In recession, sales promotion are increasingly important to the total sale and integrate more communication mix elements to boost the sales. Hence, it can be expected that more sales promotion would be emphasized in the future. Words of mouth: Word of mouths is a strong medium for marketing communication. It is difficult to contend with friends recommendation by advertising or other communication mix elements. Also, it has been claimed that consumers are more likely to change their brand preference by advice than promotion mix. Thus, by people communication, experience, reputation and recommendation can be conveyed and believed effectively. Moreover, mass media has been claimed that it is not efficient to reach the besieged audience. Words of mouth can be the tool to break the barrier (Smith and Taylor, 2004). With the development of internet, the communication channel is convenient and the information is overload. The experience and feeling can be spread extremely fast which is not like other communication mix elements that could not be measured and control simply by promoters (Berrett, 1993). Even it is complicated to control words of mouth and ensure the content of communication to the brands or products, the impressive communication mix campaign could be the topic to be discussed and increase the positive attitude (Smith and Taylor, 2004). Therefore, words of mouth would be the most influential and uncontrollable part of marketing communication mix. Hierarchy of effect models: One of the prime theories in the marketing communication framework is hierarchy of effect model which logically explains the sequential tasks of marketing message influence. On other words, it affects the consumers awareness to purchase action which is assumed that the relative step would ideally push through to next process. First process is cognitive part which means consumers have received the message and like to awareness. Second process is affective part that shows the attitude and reaction to the promotion messages have been generate in the step. The final process is behaviour part which is the actual purchase to the promoted brand (De Pelsmacker et al, 2004). According to these three main processes, many different models have been created and AIDA is one of the models and often to be referred. AIDA: AIDA model is the fundamental theory in the hierarchy of effect model. It was created by Elmo Lewis who claimed that the influential process of marketing communication can be divided into four steps: Awareness, Interest, Desire and Action. It used to be used for sales training. However, it has been the most influential theory to explain marketing communication work nowadays. The model is explained that the process how to shift consumers from the beginning of unawareness to perceived the message and shows the reaction to action (Pickton and Broderick, 2005). Firstly, awareness is that the audiences have noticed and been aware of the promotion. Then, the audiences understand and believe the messages as well as feel interested to the advertising or brands. Following this, the message arouse consumer desire to look for this advertised product or brand. Finally, consumers do the action to purchase. In addition, it has been claimed that each marketing communication mix element can be influ ential to particular step in AIDA model. Firstly, Advertising and public are suitable to build awareness to make consumers know the brand as well as feel interested for the product. However, advertising are not effective to increase the immediate purchase. Meenaghan, T. (1991) The role of sponsorship in the marketing communications mix, International Journal of Advertising, 10 (1) pp.35-47 Berrett, T (1993) The sponsorship of amateur sport-government, national sport organization and corporate perspectives, Society and leisure, 16(2), 323 346. De Pelsmacker et al, (2004) Marketing Communications: A European Perspective, 2nd ed. Essex: Pearson Prentice Hall.

Impact of War in Tim OBriens The Things They Carried :: Things They Carried Essays

Impact of War in Tim O'Brien's The Things They Carried      For young people, the Vietnam War is a thing of the past and they can only learn about it from second hand sources. In Tim O'brien's The Things They Carried, it becomes very apparent that the Vietnam conflict has proved to be one that many of the participants have not been able move away from, while getting on with their lives. O ²brien shows that the conflict takes on a parasitic form that eats away on its victims for the rest of their lives.      A parasite is defined as an organism that grows, feeds, and is sheltered on or in a different organism while harming its host. The war in this case takes the place of the organism, and the host becomes the soldiers. There are several examples of the parasitic nature of war through out the book. In one particular section, Tim O'Brien returns to Vietnam with his daughter. Twenty years had gone by, but it seems as though all of his thoughts are geared back to the time he had spent in the jungle so long before.   The two of them travel all over the country, but before their departure, he returns to the field where he feels he lost everything.   On this list he includes his honor, his best friend, and all faith in himself. For O'Brien, evidence of the parasite is not solely in his return Vietnam, but rather a constant personal preoccupation that seems to flow through the collection of stories. O'Brien shows how the memories of the war take on a parasitic form, and uses himself as an example.      In the chapter  ³Speaking of Courage ², O'Brien introduces a character by the name of Norman Bowker. In the story Norman finds him self home after serving his time in Vietnam. Even though he is back in his home town, things do not seem the same to him. The was seems to have put a new spin on his life. Most of the story he spends driving in circles while thinking about the war and his lack of place in his old society. The war becomes his whole life, and he feels as though he is to far distant from the town people for them to understand. The reader then finds out that Bowker

Albert Einstein :: essays research papers

Albert Einstein Albert Einstein was born on March 14,1879 in Ulm, Wurttemberg, Germany.He died April 18 1955 in Princeton,NJ.When Einstein was five years old his father showed him a compass.He was very impressed by the behavior of the needle of the compass,which kept pointing in the same direction no matter which way the compass was turned.He later said he felt that "Something deeply hidden had to be behind things". After public school in Munich and in Aarau,Switzerland,Einstein studied mathematics and physics at the Swiss Polytechnic Institute in Zurich.He graduated in 1900.From 1902 to 1909 he worked as an examiner at the Swiss Patent office in Bern.This job as patent examiner gave him a lot of free time,which he spent doing scientific investigations.He became a Swiss citizen in 1905.Einstein liked music also.He listened to classical music and played the violin.He supported zionism and was asked to be the president of Israel when president Chain Weizmann died in 1952.He decided not to except,saying that he wasn't right for that position.Einstein was never concerned about money.Publishers from all parts of the world offered him huge amounts of money for an autobiography.He never accepted any of their offers.Einstein was married twice.He was seperated from his first wife after he arrived in Berlin.During World War I he married his first cousin,Elsa.She shared his life with him until she died in Princeton in 1936.He had two sons from his first marriage.He also had two stepdaughters from his second marriage.In 1933 while Einstein was visiting England and the United States the Nazi government of Germany took his property and deprived him of his positions and his citizenship.Even before this happened he had been asked to direct the school of mathematics in the Institute for Advanced Study in Princeton,New Jersey.He accepted this position and he directed the school for the rest of his life.Einstein became an American citizen in 1940.After he took the job he moved into a two-story house at 112 Mercer St. in Princeton.He lived and worked there until he died. Albert Einstein is best known for his theory of relativity,which he first advanced in 1905 when he was 26 years old.Einsteins theory revolutionized scientific thought with new conceptions of time,space,mass,motion,and gravitation.Einstein laid the basis for splitting the atom by treating mass and energy as exchangable and not distinct.Einsteins famous equation E=mc2 {energy equals mass times the velocity of light squarred} became a important foundation in the development of atomic energy.Einstein arrived at his theory by means of highly involved mathematical calculations and equations.Einsteins theories were used in making the atomic bomb.He helped in it's making in another way also.

Harmonic Elimination

336 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 1, JANUARY 2007 Modulation-Based Harmonic Elimination Jason R. Wells, Member, IEEE, Xin Geng, Student Member, IEEE, Patrick L. Chapman, Senior Member, IEEE, Philip T. Krein, Fellow, IEEE, and Brett M. Nee, Student Member, IEEE Abstract—A modulation-based method for generating pulse waveforms with selective harmonic elimination is proposed. Harmonic elimination, traditionally digital, is shown to be achievable by comparison of a sine wave with modi? d triangle carrier. The method can be used to calculate easily and quickly the desired waveform without solution of coupled transcendental equations. Index Terms—Pulsewidth modulation (PWM), selective harmonic elimination (SHE). I. INTRODUCTION S ELECTIVE harmonic elimination (SHE) is a long-established method of generating pulsewidth modulation (PWM) with low baseband distortion [1]–[6]. Originally, it was useful mainly for inverters with naturally low switching frequency due to high power level or slow switching devices.Conventional sine-triangle PWM essentially eliminates baseband harmonics for frequency ratios of about 10:1 or greater [7], so it is arguable that SHE is unnecessary. However, recently SHE has received new attention for several reasons. First, digital implementation has become common. Second, it has been shown that there are many solutions to the SHE problem that were previously unknown [8]. Each solution has different frequency content above the baseband, which provides options for ? attening the high-frequency spectrum for noise suppression or optimizing ef? iency. Third, some applications, despite the availability of high-speed switches, have low switching-to-fundamental ratios. One example is high-speed motor drives, useful for reducing mass in applications like electric vehicles [9]. SHE is normally a two-step digital process. First, the switching angles are calculated of? ine, for several depths of modulation, by sol ving many nonlinear equations simultaneously. Second, these angles are stored in a look-up table to be read in real time. Much prior work has focused on the ? st step because of its computational dif? culty. One possibility is to replace the Fourier series formulation with another orthonormal set based on Walsh functions [10]–[12]. The resulting equations are more tractable due to the similarities between the rectangular Walsh function and the desired waveform. Another orthonormal set approach based on block-pulse functions is presented in [13]. In [14]–[20], it is observed that Manuscript received August 2, 2006; revised September 11, 2006.This work was supported by the Grainger Center for Electric Machines and Electromechanics, the Motorola Center for Communication, the National Science Foundation under Contract NSF 02-24829, the Electric Power Networks Ef? ciency, and the Security (EPNES) Program in cooperation with the Of? ce of Naval Research. Recommended for publ ication by Associate Editor J. Espinoza. J. R. Wells is with P. C. Krause and Associates, Hentschel Center, West Lafayette, IN 47906 USA. X. Geng, P. L. Chapman, P. T. Krein, and B. M.Nee are with the Grainger Center for Electric Machines and Electromechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (e-mail: [email  protected] edu). Digital Object Identi? er 10. 1109/TPEL. 2006. 888910 the switching angles obtained traditionally can be represented as regular-sampled PWM where two phase-shifted modulating waves and a â€Å"pulse position modulation† technique achieve near-ideal elimination. Another approximate method is posed by [21] where mirror surplus harmonics are used. This involves solving multilevel elimination by considering reduced harmonic elimination waveforms in each switching level.In [22], a general-harmonic-families elimination concept simpli? es a transcendental system to an algebraic functional problem by zeroing entire harmonic fami lies. Faster and more complete methods have also been researched. In [23], an optimal PWM problem is solved by converting to a single univariate polynomial using Newton identities, Pade approximation theory, and symmetric function properties, which . If a few can be solved with algorithms that scale as O solutions are desired, prediction of initial guess values allows rapid convergence of Newton iteration [24].Genetic algorithms can be used to speed the solution [25], [26]. An approach that guarantees all solutions ? t a narrowly posed SHE problem transforms to a multivariate polynomial system [27]–[30] through trigonometric identities [31] and solves with resultant polynomial theory. Another approach [32]–[34] that obtains all solutions to a narrowly-posed problem uses homotopy and continuation theory. Reference [35] points out the exponentially growing nature of the problem and proposes the â€Å"simulated annealing† method as a way to rapidly design the wavef orm for optimizing distortion and switching loss.Another optimization-based approach is given in [36] and [37], where harmonics are minimized through an objective function to obtain good overall harmonic performance. There have been several multilevel and approximate real-time methods proposed; these are beyond the scope here but discussed brie? y in [38]. This manuscript proposes an alternative real-time SHE method based on modulation. A modi? ed triangle carrier is identi? ed that is compared to an ordinary sine wave. In place of the conventional of? ine solution of switching angles, the process simpli? s to generation and comparison of the carrier and sine modulation, which can be done in minimal time without convergence or precision concerns. The method does not require an initial guess. In contrast to other SHE methods, the method does not restrict the switching frequency to an integer multiple of the fundamental. The underlying idea was proposed in [39] but has been re? ned he re to identify speci? c carrier requirements that exactly eliminate harmonics and improve performance in deeper modulation. The method involves a function of modulation depth that is derived from simulation and curve ? ting. In this respect, it has some similarity to [15] and [16], in which approximate switching angles are calculated and ? tted to simple functions for cases of both low-( 0. 8 p. u. ) and high-modulation depth. It is interesting that the proposed approach connects modulation to a harmonic elimination process. Carrier waveform mod- 0885-8993/$25. 00  © 2007 IEEE IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 1, JANUARY 2007 337 Fig. 1. Direct calculation of the phase modulation function at various modulation depths with ? rst through 109th harmonics controlled.Fig. 2. Direct calculation of the phase modulation function at various modulation depths with ? rst through 177th harmonics controlled. i? cation is common in other PWM work, as in switching frequency ra ndomization intended to reduce high-frequency components. A detailed review is outside the scope, but one discussion is given in [40]. The proposed technique is not a variation of random-frequency carriers. Instead, the carrier waveform is modi? ed in a speci? c and deterministic way to bring about a certain effect. The proposed method is readily implemented in real time.The switching signals themselves can be generated by analog comparison, while the modi? ed carrier is generated with fast digital calculation and digital-to-analog conversion. Hardware demonstration is provided here. An approximate, low-cost implementation based on present-day hardware is given in [41], but further re? nement is needed for precise elimination. II. SIGNAL DEFINITIONS AND SIMULATED RESULTS Consider a quasi-triangular waveform to be used as the carrier signal in a PWM implementation. In principle, the frequency and phase can be modulated.To represent this, consider a triangular carrier function written as (1) where is the base switching frequency, is a phase-mod0, (1) reulation signal, and is a static phase shift. For duces to an ordinary triangle wave based on conventional quadrant de? nitions of the inverse cosine function. The modulating where signal will be represented as is the depth of modulation. The pulsewidth-modulated signal, , is 1 if and 1, otherwise. 2 In [39], a phase modulation function is considered, where is the desired output fundamental fre, but dequency. This was shown to approach SHE at low 0. . To determine a better phase-modulagrades above tion function, the pattern of switching angles that occurs was investigated. Fig. 1 shows the phase modulation values needed for various with harmonics 1–109 conversus angle trolled. Fig. 2 shows the same with harmonics 1–177 controlled. Many other sets of controlled harmonics were tested with similar results. The pattern looks much like a shockwave pattern that can be modeled with the Bessel–Fubini e quation from nonlinear acoustics [42] (2) where is a Bessel function of the ? rst kind. The natural is in? ity in principle, but for calculation purposes number 15 or higher is usually suf? cient, as discussed below. The and have been determined by curve functions ? tting as (3) 1. and (4), shown at the bottom of the page, where 0 Fig. 3 shows a closeup view of a PWM waveform generated as in (2). Nineteen harmonics are with a carrier that uses 0. 95. The waveform is compared controlled with a (high) to one generated with conventional elimination by numerical solution of nonlinear equations. As can be seen, the switching edges match well. Fig. 4 shows a full-period time waveform and a magnitude 11.With spectrum [fast Fourier transform (FFT)] for this switching frequency ratio, the method eliminates harmonics two through ten (even harmonics are zero by symmetry). The 2 and the modulation depth carrier phase shift is set to 1. The spectrum con? rms the desired elimination. is 0. This v alue Fig. 5 shows the same study except with also achieves satisfactory baseband performance, but with a different pulse pattern. The pattern provides slight differences in higher-order harmonics. For example, the 11th and 13th harto . monics vary 2%–3% in magnitude as is varied from (4) 338IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 1, JANUARY 2007 Fig. 3. Conventional harmonic elimination waveform and proposed PWM 0. 95, harmonics controlled through the 19th). waveform (m = Fig. 5. Pulse waveform p, message signal m, and magnitude of pulse waveform 1, and ‘ 0. spectrum for ! =! 11, m = = = Fig. 4. Pulse waveform p, message signal m, and magnitude of pulse waveform spectrum for ! =! 11, m 1, and ‘ =2. = = = In these cases, all baseband harmonics are eliminated. In three-phase systems, triplen harmonics may cancel in the currents automatically if neutral current does not ? w. Therefore it is not always necessary to eliminate them by design in the SHE pro cess. Modulation-based harmonic elimination excluding triplen harmonics is similar in many respects to the case here. However, the phase-modulation functions resemble piecewise polynomials rather than the shockwave form of Figs. 1 and 2. This is discussed in detail in [38]. The speed of calculating these waveforms is dictated by , the number of terms to keep in the series (2), and , the number of discrete points used to approximate the waveforms. A personal computer (1. 86-GHz Intel M Processor with 1. -GB RAM) running MATLAB on Windows XP was used to carry out the calculations. First, a modi? ed triangle wave was ap100 000 points per cycle, the modulation proximated with 1, and a frequency ratio of 19 was used. depth was set to was varied from ? ve to 35. Over this range, the The number quality of solution was acceptable and the average calculation time varied from 0. 327 to 0. 915 s. Next, the same conditions 35 and was varied from 10 000 were used with except to 200 000. The aver age calculation time varied almost linearly from 0. 149 to 1. 78 s with no signi? cant difference in the resulting spectrum.Finally, with held constant at 100 000, the frequency ratio was varied from seven to 51. The average calculation time was consistently near 0. 92 s. This is expected since the number of harmonics eliminated has no scaling effect in (2). However, for larger frequency ratios, larger may be needed for precision. In summary, it is recommended that be set to at least 1,000 the frequency ratio and set to at least 15. In any case, with present-day personal computers the solution can be calculated in less than 1 s (typically) without iteration, divergence, or need for an initial estimate, and reduced versions can be computed in less than 200 ms.Notice that this time interval need not cause trouble with real-time implementations. The carrier only needs to be recomputed with the modulation signal changes. In applications such as uninterruptible supplies, this is infreque nt. In motor-drive applications, a response time of 200 ms to a command change may be acceptable as is. Alternatively, a look-up table can store some of the relevant terms to speed up the process dramatically. Dedicated DSP Please de? ne DSPalgorithms will be much faster than PC computations based on MATLAB. III. EXPERIMENTAL EXAMPLES To show that the proposed technique satisfactorily eliminates harmonics, the modi? d carrier was programmed into a function generator. The output provided a carrier signal in a conventional sine-triangle process. Three examples are shown below to reveal a range of interesting conditions. Fig. 6 shows the resulting waveforms for a high-depth case 0, and 0. 95. The with nineteen harmonics eliminated, and are shown at frequency ratio is 21:1. The signals the top, followed by the PWM waveform and the FFT spectrum. From the spectrum it can be seen that the desired harmonic-free baseband spectrum is achieved. In the next example, the phase 2.The unexpected r esult was that the spectrum shift is was insensitive to , as shown in comparison to Fig. 7. The desired spectrum occurs despite the difference in carriers. The resulting PWM waveforms at various values of may not offer obvious advantages, but it is noteworthy that they are not the same as conventionally computed SHE waveforms and would not be achievable with conventional SHE solution techniques. As another example, it is shown that the carrier base fre, need not be an odd multiple of . In Fig. 8, the frequency, IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 1, JANUARY 2007 339 Fig. . Experimental modulation-based SHE with ! ‘ 0. = =! = 21, m = 0. 95, Fig. 9. Experimental modulation-based SHE with ! ‘ 0. = =! = 13. 5, m = 0. 95, Fig. 7. Experimental modulation-based SHE with ! ‘ =2. = =! = 21, m = 0. 95, Fig. 10. Experimental modulation-based SHE with ! ‘ 0. = =! = 50, m = 0. 95, The last example, shown in Fig. 10, applies to a case where a high number of harmonics is eliminated (50 1 ratio) effectively, which is much higher than typically are reported in the literature. IV. CONCLUSION A method for calculating and implementing SHE switching angles was proposed and demonstrated.The method is based on modulation rather than solution of nonlinear equations or numerical optimization. The approach is based on a modi? ed carrier waveform that can be calculated based on concise functions requiring only depth of modulation as input. It rapidly calculates the desired switching waveforms while avoiding iteration and initial estimates. Calculation time is insensitive to the switching frequency ratio so elimination of many harmonics is straightforward. It is conceivable the technique could be realized with low-cost microcontrollers for real-time implementation.Once the carrier is computed, a conventional carrier-modulator comparison process produces switching instants in real time. REFERENCES [1] F. G. Turnbull, â€Å"Selected harmonic reduc tion in static dc-ac inverters,† IEEE Trans. Commun. Electron. , vol. CE-83, pp. 374–378, Jul. 1964. Fig. 8. Experimental modulation-based SHE with ‘ 0. = ! =! = 20, m = 1. 0, quency ratio is adjusted to be 20:1, with 0, and now 1. 0. The same nineteen harmonics are eliminated, but now the switching frequency is 5% lower. 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