A forum for the exchange of circuits, systems, and software for real-world signal processing
`
`Volume 40, Number 2, 2006
`
`In This Issue
`Editors’ Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
`Oscar Stirs [The Wit and Wisdom of Dr. Leif—3] . . . . . . . . . . . . . . . . . . 3
`Class D Audio Amplifiers: What, Why, and How . . . . . . . . . . . . . . . . . . . 6
`Power-Supply Management—Principles, Problems, and Parts . . . . . . . . . 13
`Design Your Own VoIP Solution with a Blackfin Processor—
`Add Enhancements Later . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
`Product Introductions and Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
`
`www.analog.com/analogdialogue
`
`Samsung Electronics Co., Ltd.
`Ex. 1062, p. 1
`
`

`

`Editors’ Notes
`ANNIVERSARY
`As faithful readers already know (and are perhaps
`weary of knowing!), Analog Dialogue is
`celebrating our 40th anniversary in print. But there
`is another significant anniversary to celebrate:
`Exactly 20 years ago, in Volume 20, No. 2 (1986),
`we broke with our purely analog past and introduced
`the first Analog Devices digital signal processor
`(DSP), the ADSP-2100. You may be interested in
`recalling the theme of the Editor’s Note welcoming
`our readers to that issue:
`
`ANALOG & DIGITAL
`“Microprocessor?” we hear you ask. “Isn’t
`it a bit unseemly for a nice ‘Analog’ IC
`company to be designing a microprocessor?
`(What could be more digital?)”
`Good question.
`Our objective has always been to design and
`manufacture cost-effective components that are key elements of
`the signal path for processing real-world (i.e., analog) data and
`for which performance is maximized and errors minimized.
`The signal path? Real-world data almost always starts out as
`analog (i.e., parallel, nonnumeric) variables, which are measured
`by sensors that provide analog electrical signals—voltage and
`current. The signals must be accurately and speedily amplified,
`conditioned (almost always in parallel), and converted to digital
`for processing. Once in digital form, they must be processed
`rapidly. Often, they again wind up as analog signals.
`Key elements of the signal path include preamplifiers, analog
`signal processors, data converters to and from digital, and—when
`the signal is in digital form—a digital processor. Inadequacy in
`any one of the key elements—amplifier, analog processor, data
`converter, or microprocessor—can cause poor performance of
`the overall system.
`Obstacles in the signal path include noise, drift, nonlinearity,
`and measurement lag at the analog stages, similar obstacles
`in conversion—and throughput delays in digital processing,
`often because of the lack of parallelism in von Neumann
`architecture.
`Throughout our history, our role in the signal path has been to
`initiate new products (or product lines) when dissatisfied with
`the cost-effectiveness of what’s available (which is often limited
`to user-assembled kludges, when nothing else is available).
`At this point in time, we (and our competitors) have virtually
`eliminated the user-assembled amplifier, signal conditioner,
`and data converter by designing and marketing families of
`cost-effective products.
`We have always been dissatisfied with the cost, power dissipation,
`and slow throughput in the digital domain; this concern led
`to our pioneering development of CMOS multipliers and
`other digital signal-processing ICs (note that because we were
`already familiar with analog multipliers, digital multipliers
`became just another analog signal-processing tool; note also
`our commitment to signal processing—not payroll, desktop
`publishing, or order-handling products). Our dissatisfaction
`with the complexity of systems using Bit-Slice parts led to the
`powerful and compact Wordslice™ microcoded system parts.
`And finally, our dissatisfaction with insufficient throughput in
`DSP processors led to design of the ADSP-2100, which stresses
`the use of that analog characteristic, parallelism, to minimize
`instruction cycles, whether in processing, data transfer, or
`interrupt handling. It’s neat! We invite you to read about it.
`
`Dan Sheingold [dan.sheingold@analog.com]
`
`RANDOM THOUGHTS ON THIS ISSUE
`Dr. Leif’s World—And Ours
`In this issue, enjoy Oscar Stirs, part three of
`Niku’s quest to understand the start-up phase
`of an ideal oscillator. In Dr. Leif’s world, the
`effects of global warming have already been felt,
`yet there is hope for the future. Is our outlook
`as bright, or will some of the cataclysmic events
`experienced in Niku’s lifetime become reality
`in ours? Everyone should see the intentionally
`biased movie, An Inconvenient Truth, regardless of their current views
`on global warming. At the very least it will make them wonder about
`how robust or fragile our environment is and question what they read
`in the popular press. Some may be motivated to act by reducing their
`own impact on our ecosystem or becoming advocates for change. For
`more information, and some simple suggestions for becoming carbon
`neutral, visit http://yosemite.epa.gov/oar/globalwarming.nsf.
`VoIP—Pro and Con
`After using VoIP for about two years, I finally cut my personal ties
`with Ma Bell. For less than 20 dollars a month I got everything that
`was previously provided by my land line, plus a lot more. Some of the
`cool features include voice mail messages sent via email, allowing me
`to access them from any PC, and the ability to reject anonymous calls
`without being forced to jump up and check the caller ID. In addition,
`I can make unlimited calls to the US and Canada, and limited free
`international calls. So, what’s the downside? Well, even with 8 Mbps
`Internet access and 92% quality of service (QoS), the voice quality,
`noise level, and echo rejection are not as good as with the wired phone.
`Also, a call is occasionally dropped, something I never experienced with
`the land line. Furthermore, I’d lose my VoIP connection in the event
`of a power failure, in contrast to the always-up reliability of the plain
`old telephone system (POTS). With a cell phone as a backup, though,
`VoIP is a smart choice. In this issue, read about implementing VoIP on
`a Blackfin processor.
`Power-Supply Management
`With today’s portable devices and green appliances, power consumption
`must be kept to a minimum, yet complex consumer electronics
`equipment often requires multiple power supplies for the analog
`circuitry, memory, microprocessors, DSPs, and ASICs. These supplies
`must be turned on and off in sequence to avoid damage to their
`associated components, with timeouts occurring in the event of a system
`fault. All of this increases the importance of integrated power-supply
`management. In this issue, learn the basics of the problem and of the
`available solutions.
`Class D Amplifiers
`Class D amplifiers provide the advantages of higher efficiency,
`smaller size, and lower cost, while still achieving low distortion,
`wide dynamic range, and clickless muting. Recently, everyone seems
`to be writing about Class D. After reading the article in this issue,
`you may also be interested in reading “How Class D Amplifiers
`Work” by Jun Honda and Jonathan Adams, “Design and Analysis
`of a Basic Class D Amplifier” by Chi Ho Li, and “Class D in Audio
`Hubs Extends Battery Life” by Robert Hatfield. All can be found
`at http://www.audiodesignline.com.
`Scott Wayne [scott.wayne@analog.com]
`
`dialogue.editor@analog.com
`www.analog.com/analogdialogue
`Analog Dialogue is the free technical magazine of Analog Devices, Inc., published
`continuously for 40 years—starting in 1967. It discusses products, applications,
`technology, and techniques for analog, digital, and mixed-signal processing. It is
`currently published in two editions—online, monthly at the above URL, and quarterly
`in print, as periodic retrospective collections of articles that have appeared online. In
`addition to technical articles, the online edition has timely announcements, linking to
`data sheets of newly released and pre-release products, and “Potpourri”—a universe
`of links to important and rapidly proliferating sources of relevant information
`and activity on the Analog Devices website and elsewhere. The Analog Dialogue
`site is, in effect, a “high-pass-filtered” point of entry to the www.analog.com
`site—the virtual world of Analog Devices. In addition to all its current information,
`the Analog Dialogue site has archives with all recent editions, starting from Volume
`17, Number 1 (1983), plus three special anniversary issues, containing useful articles
`extracted from earlier editions, going all the way back to Volume 1, Number 1.
`If you wish to subscribe to—or receive copies of—the print edition, please go to
`www.analog.com/analogdialogue and click on <subscribe>. Your comments
`are always welcome; please send messages to dialogue.editor@analog.com
`or to these individuals: Dan Sheingold, Editor [dan.sheingold@analog.com]
`or Scott Wayne, Managing Editor and Publisher [scott.wayne@analog.com].
`
`ISSN 0161-3626 ©Analog Devices, Inc. 2006
`
`Samsung Electronics Co., Ltd.
`Ex. 1062, p. 2
`
`

`

`OSCAR STIRS
`[The Wit and Wisdom of Dr. Leif—3]
`By Barrie Gilbert [barrie.gilbert@analog.com]
`Back in her small apartment, Niku tossed two units of MycoPro
`into the hyperphase and settled to watching the top stories on the
`TransGlobal Network (TGN, Channel 28.20.20). She was feeling
`upbeat. After weeks of orientation at ADI, she’d just been given
`her first real assignment as a Product Originator. From the initial
`discussions, it didn’t appear that her contributions to this mixed-
`signal ASIC, a new type of monitor of deep-ocean conditions for
`the International Oceanic Authority, would require much in the
`way of “original” design; but she was excited at the prospect of
`finally doing something productive, working under the guidance
`of her team leader, Jeff Rawlings, another protégé of Dr. Leif.
`
`It was Leif who first alerted him to Niku’s peculiarly dogged
`interest in some little-studied subtleties of HF oscillators. Until
`recently, Jeff had been too preoccupied to ask about this work.
`But when the opportunity arose, she enthusiastically shared her
`notes of the step-by-step questioning she’d applied to the start-
`up behavior of the basic two-transistor differential topology she
`was exploring. He was immediately impressed by her diligence in
`this self-appointed enterprise, and encouraged her to present a
`summary of her work at “Daedalus Days,” the series of meetings
`that Dr. Leif had instituted, years ago, and had named after the
`mythical Greek inventor. After that chat, Jeff was even more certain
`that her penetrating curiosity and insatiable appetite for pursuing
`basic insights would be valuable assets for their new project. Asking
`questions is the beginning of wisdom.
`
`The majority of the other team members were Fusers. While they
`were experienced and efficient, and the older ones were broadly
`informed about the IC business, their satisfaction came largely
`from providing a quick solution to a field application, using the
`large library of precharacterized, time-proven cells. Most of the
`Fusers had scant interest in topological exploration, save for one
`of them: Mauricio Pegna, hired several months before Niku. Rico
`showed great promise as an eager treasure seeker in the vast and
`rich forests of analog cell invention, and was clearly destined for
`an early promotion. A remote relative, Guido Pegna, once taught
`physics at the University of Caligari in Sardinia. Prof. Pegna,
`an exceptional teacher, offered a boldly different perspective on
`science—one that was, he said, “less worrying, less dramatic,
`more fun, more human, more delightful.” Among his legacies was
`a fascinating site on the old Internet: www.pegna.com.
`
`While picking away at her nutritional but totally uninspiring
`dinner, Niku watched the latest reports of the disappearing polar
`ice. The erosion of habitat for polar bears in the Arctic, and the
`confusing loss of landmarks for penguins and other migratory birds
`in Antarctica, who for eons had regarded these stable regions as
`their home and birthright, was troubling enough. But disruptions
`of that sort were eclipsed by the sheer magnitude of the threat to
`human life and property posed by the ever-rising sea level.
`
`As a kid, during the overture to the 21st century, Niku had heard
`plenty of talking heads indulging in endless exchanges of blame:
`across national borders, between political parties, and between
`various agencies charged with caring for the environment. But little
`was done to reverse these trends. For all the bickering, pollutants
`and greenhouse gases were still on the rise as late as 2016. Now,
`in the mid ’20s, at least they were stable, but at levels far too high
`for complacency. Only when low-lying coastal regions began to be
`inundated did world governments finally grasp the ominous reality
`of the science. After years of glory, the older areas of Venice were
`the first to succumb, and were soon abandoned.
`
`These shocking events were followed by the asteroid strike in
`August of 2017. Fortunately for humanity, after a terrifyingly
`blazing journey on an uncertain and wobbly trajectory, it had
`burned itself down to the size of a one-seat commutobile when it
`hit a remote region of Antarctica at a fairly steep angle. The heat
`equivalent of its massive kinetic energy had greatly accelerated
`the melting of the ice and the rising sea levels. That event led to
`the formation of the Coalition of Terrestrial Governments, and
`galvanized its member-nations into drafting laws which earlier
`would have been regarded as quite untenable. Several smaller
`nations declared martial law, strictly rationed supplies, and then
`applied repressive penalties for any kind of wastage. There were
`sporadic demonstrations, but they soon fizzled out.
`Now, only eight years later, the outrage and tensions had eased,
`in a seemingly miraculous—certainly astonishing—reversal of
`history. The disparate and entrenched ideological stances of the
`leading nations were dissolving into acts of genuine cooperation.
`The first fragile signs of a shift in attitude toward the arbitrariness
`and irrationality of nationalism were becoming evident. Another
`big shake-up: In 2018, NASA, ESA, and other space agencies
`were obliged to accept a new charter: to put space exploration on
`hold, until Earth, this most important and precious of planets,
`was clearly on its way to recovering from the ravages and excesses
`of more than a century of unmitigated abuse.
`Understandably, most scientists and engineers in these agencies,
`and many academicians, were violently opposed to this directive;
`but the dire urgency of the prevailing circumstances soon forced
`them to come around. These reorganized agencies, and new ones
`such as the IOA, had, for about seven years now, applied their best
`minds to Project Milton—“Restoring Our Common Habitat and
`Heritage.” The notion of freedom had taken on a new, more vital
`and self-disciplined meaning, and not a decade too soon.
`Removing the visionizer headband, and putting aside her food
`tray, Niku settled down for the evening. Saying RAISE! to the
`SyntheDown pillow unit, it fine-tuned the personalized presets
`interactively to conform even more comfortably to her contours.
`She reached for the thin blue Actablet, which kept the details of
`her studies. Propping it up on her raised knees, it came alive at her
`touch. She struggled to refocus her mind for the evening’s work:
`to be well prepared for next week’s Daedalus Day presentation,
`she needed to get these notes, and the many results, into some
`semblance of order.
`But almost immediately, Marcoloonie, her lithe and intelligent
`Abyssinian kitten, was vying for attention. Plunking himself
`on her chest, with no room for negotiation, he offered his wide
`eyes in place of the screen—an old trick of cats. Succumbing
`to the hypnosis, she planted her hands on his warm fur. Nose
`to nose, they shared air, and her racing mind dropped down to
`first gear. Half-waking sometime later, she found Marco asleep,
`curled in a contented ball at her feet. She sighed LOWER! to
`the pillow unit.
`* * *
`At mid-morning, Dr. Leif encountered her in the hall. “Hi, Niku!
`How are you? Y’know, I’ve been meaning for some time to ask
`you about the rest of your oscillator story. Do you have time for a
`good cup of coffee over at GalaxyBux?”
`“Sure, Dr. Leif. I’ve been trying to put my notes into a logical
`order for the Daedelus talk next week, but so far I haven’t made
`much progress. A chat with you would help a lot. Let me just pop
`back to the lab for my Actablet.”
`As they arrived at the coffee shop, the Greeter did its usual thing,
`except that now it also recognized Niku: “Good morning, Dr. Leif,
`Dr. Yeng. I trust your day is going well. We have a great special
`
`Analog Dialogue Volume 40 Number 2
`
`3
`
`Samsung Electronics Co., Ltd.
`Ex. 1062, p. 3
`
`

`

`this morning. It’s …” They didn’t wait to hear about the day’s
`special, nor the ad that was sure to follow. Finding a table for four,
`Niku sat beside her mentor, to more easily share the screen of her
`’tablet. With coffee ordered, a touch brought up the usual gallery
`of icons. She selected one labeled Oscar.
`“Oscar?” quizzed the amused senior. “Why Oscar?”
`“Oh, I’ve become quite fond of this little circuit, so I gave him a
`name. Actually, the title I’ll use for the talk is “Oscar Awakes,”
`to emphasize that it’s about the brief start-up phase, and how it’s
`dominated by circuit noise in a well-designed and well-balanced
`circuit. But I’m afraid I got sidetracked into other issues.”
`“Ah ha. I see. So, where did we leave off?”
`“Well, if you remember, I was taking each step cautiously, and the
`last time we talked I’d gotten as far as showing that when a fast step
`of current, I, is applied to a parallel LC tank, the circuit behaves as
`a pure resistance of √(L/C), resulting in a voltage, V = I√(L/C),
`which persists as the nondecaying amplitude of a sinusoid,
`while the magnetic and dielectric energies oscillate between LI 2
`and CV 2. Of course, that never happens in a real circuit, mostly
`because of the finite series resistance of the inductor. But even if
`the elements were ‘perfect,’ some of the stored energy must be lost
`by radiation—mostly from the inductor, whose magnetic field, in
`the case of an open coil, generates an EM wave.”
`“Did you try calculating the radiation loss from first principles?”
`“Hmm … I haven’t given it any thought and I’m not sure I could.
`I’m trying to stay focused on the issue of the noise-excited start-
`up trajectory. I mean … there are so many other basic questions
`you could investigate. For example, intuition tells me that there’s
`a dual—the series-connected LC tank, driven by an ideal voltage
`source. A fast step of V would then set up a circulating current of
`V/ √(L/C). Thinking about the Fundaments—if I may adopt your
`valuable idea—it couldn’t be anything else, since L and C must
`determine the impedance, and, from a dimensional perspective,
`these have to be combined as √(L/C). I don’t think one needs to
`demonstrate that by separate simulations.”
`The coffee arrived. “Your intuitions serve you well, Niku. These
`kinds of nonmathematical analysis provide just one example of what
`I call the What Must Be philosophy. Understanding of crucial
`aspects of circuit design or behavior can often be gained simply
`by listing the known variables, then asking how the dimensional
`constraints can be satisfied. In the case of little Oscar’s parallel-
`tuned tank, you knew there has to be a voltage, V, caused by the
`applied current, I, which demands a relationship via impedance,
`because V = IZ. So there’s one What Must Be factor, right away.
`“Then, when GE8E later showed you that the amplitude of the
`resulting sinusoid didn’t change over time, it confirmed your
`intuition that ‘Z’ has to be a simple resistance. You realized that
`there’s only one way of getting something with the dimension
`of resistance out of an L and a C, and that’s from their ratio
`L/C—although this is actually R2. After all, there is only one
`other simple dimensionally correct way of combining L and
`C—as the product, LC. This probably led you to think of two
`standard forms: √(L/C), which has the dimension of resistance;
`and √(LC), which has the dimension of time—or 1/√(LC), which
`has the dimension of angular frequency. One can easily arrive at
`these basic forms from first principles, considering the inherent
`dimensions of inductance and capacitance. This concern for what
`has to be included and what can be excluded without significant loss is
`philosophically related to the Principle of Occam’s Razor.”
`“Mmm ...?” said Niku, sipping the dark brew. “Who is Occam,
`and what do his shaving habits have to do with a principle?”
`“William of Ockham was a 14th-century … No, that can wait.
`
`Roughly speaking, he conjectured that when faced with two or
`more ways to explain some phenomenon, the most simple is usually
`the right one: the razor will pare away the rest. In the same spirit,
`faced with several ways to configure a basic circuit, in meeting
`some performance challenge, it often pays to use the simplest
`possible form. Of course, you can’t create new circuit forms, from
`scratch, in this way, only choose from pre-existing possibilities.
`The origination of topology is a daunting aspect of analog design,
`and the chief reason why many find it Difficult.
`
`“Still, Occam’s Razor can nicely complement the philosophy of
`intuitive design, the most important aspect of which is the habit of
`ceaselessly asking What If? How About? Why Is That? What Must
`Be?—that kind of question—before plunging into a detailed and
`time-consuming analysis that may turn out to be irrelevant or fail
`to contribute any useful insights.
`
`“A simulator is an indispensable partner in telling you what will
`happen— with high numerical accuracy—if that is all you need
`to know. But after seeing what happens, your eyes are invariably
`opened to insights; and these lead to even more deeply probing
`questions, as you’re demonstrating. Sometime, I’d like to share
`some personal case histories of What Must Be reasoning. Many of
`them rely on elegance-driven heuristics like Occam’s Razor. But
`I’m anxious to hear about Oscar. What did you do next?”
`
`“Well, this actually wasn’t the next thing I looked at, during my
`early studies; but I was curious and went back later to explore it. In
`fact, Dr. Leif, that’s my dilemma. I don’t know whether to include
`such details in my talk or not, because they are merely tangential
`to the original topic. But I will tell you about this one.
`“I was curious about the effect of the rise time, tR, of the current
`step. Only a pulse having a rise time of zero would generate the full
`I √(L/C), so I wanted to discover the relationship between the rise
`time and the resulting amplitude of the tank voltage. What rise
`time would cause it to be reduced by, say, 10%? What if it’s equal
`to a significant fraction of the period, up to or even beyond the
`full period? One thing was certain: for very slow rise times—when
`tR is hundreds of times √(LC)—practically all of the current must
`flow in the inductor, generating a small voltage LdI/dt.”
`
`“Niku,” interrupted Dr. Leif, touching her lightly on the wrist.
`“Y’know, these questions aren’t all that far off the beaten track.
`After all, in a practical oscillator, the currents coming from the
`driving circuit will have finite rise times, and you might have
`uncovered an ‘incidental’ fact that would alter the direction of
`your studies—perhaps radically. The trick is knowing when to
`stop chasing every side thought. You can never suppress them.
`Even if one’s thinking is clear and controlled, the mind will be
`nonetheless seething with questions continuously generated by
`our innate propensity for confabulation. Look, you have hardly
`touched your coffee. Please, take a moment to enjoy it.”
`
`But Niku rattled on as the coffee contributed to cosmic entropy.
`“Yes, I really do find it difficult to cope with all the questions
`and ideas for new experiments that keep coming to mind! The
`question about the importance of the rise time led me to worry
`about the effect of the detailed wave-shape of the current step,
`since this obviously determines the frequency-domain spectrum
`of the voltage. How would my ideal, infinite-Q tank be affected
`by this? GE8E provides a rich assortment of forms, including
`the simple ramp [the PULSE source in SPICE—Ed.] and the
`raised-cosine form, both of which occupy a finite time; and it
`provides the Gaussian form, which must be truncated before
`t = 0, for any finite delay—though, it’s only 0.148 ppm of the
`final value at a time four times earlier than that needed to get
`10% up the edge.
`
`4
`
`Analog Dialogue Volume 40 Number 2
`
`Samsung Electronics Co., Ltd.
`Ex. 1062, p. 4
`
`

`

`On the other hand, the measured peak voltage of 14.235… V is
`exactly twice my erroneously predicted value, which happens to
`be exactly (1/p) × 44.72… V—isn’t that intriguing! So until I
`have all my facts together, I won’t touch on this in my talk.”
`
`“Well, yes; but it would be more intriguing if the factor weren’t
`(1/p) but, say, exactly (1/7), because then you’d need a theory to
`explain where this new number comes from! Anyway, now that
`GE8E has shown you the error of your ways, I agree it wouldn’t
`be wise to introduce this matter, unless you know what’s going
`on,” said Leif, his eyes twinkling. “I understand why you’d feel
`uncomfortable about not being able to get to the bottom of all
`these details. Still, at this point, I’m going to let you—how does
`it go?—stew in your own juices for a while!
`
`“However, I will mention that this is one of those times when
`you will need to dust off your Laplace transforms, and use
`paper and pencil to find out Why Is That? Though simulators
`are excellent tools, and fine for showing what happens, they
`haven’t a clue as to why. They aren’t aware, as we are, of the
`Fundaments, and in spite of decades of promises from the AI
`folks, GE8E still can’t emulate creativity in any useful way.
`That’s why we hire people like you, Niku, and why we use the
`job description Originator. But I have a question for you to mull
`over: Do you recognize the functional shape of your plot of PSS
`amplitude vs. rise time?”
`
`“Well, it looks like the absolute-sine-x-over-x form,” Niku said,
`“but I don’t know why. I suppose if I could trust Occam’s Razor,
`that simple answer would probably be the right one.”
`
`“Mmm. It’s not really a job for Occam, since you have only
`one suggestion! But it’s a smart guess. Still, why would it
`have that form, and what causes all those nulls? Every effect
`has a cause.”
`
`His wink was the only encouragement she needed to strengthen
`her resolve to understand this by Daedalus Day. “Maybe I
`will include these analyses, after all,” she beamed, confident
`of her practiced ability to wield the Laplacian sword. As they
`left, her coffee continued its spiraling descent to ambient.
`Walking back to the lab, under a yellowish sky, Niku said,
`“By the way, you still haven’t told me what the Fourth Dee
`of analog design is.”
`
`“Ah, but I did,” said Dr. Leif, “only a few moments ago.”
`
`Barrie Gilbert, the first-appointed ADI
`Fellow, has “spent a lifetime in pursuit
`of analog excellence.” Barrie was born
`in Bournemouth, England, in 1937.
`Before joining ADI, he worked with
`first-generation transistors at SRDE in
`1954. At Mullard, Ltd. in the late ’50s,
`he pioneered transistorized sampling
`oscilloscopes, and in 1964 became a
`leading ’scope designer at Tektronix. He
`spent two years as a group leader at Plessey Research Labs before
`joining Analog Devices in 1972, where he is now director of the
`Northwest Labs in Beaverton, Oregon. Barrie is a Life Fellow
`of the IEEE and has received numerous service awards. He has
`about 70 issued patents, has authored some 50 papers, is a reviewer
`for several professional journals, and is a co-author or co-editor
`of five books. In 1997, he was awarded an honorary doctorate of
`engineering from Oregon State University.
`
`“Anyway, I thought it might be useful to explore these effects for
`an isolated tank, using a 20-nH inductor shunted by a 10-pF cap,
`which resonates at 355.88… MHz, this time using a single unit
`step of 1 A. As expected, the tank voltage for an extremely slow
`ramp is dI(t)/dt times the inductance. But I didn’t expect this …”
`Turning the screen of her Actablet to a better angle for Leif, she
`showed him the first of two sets of plots.
`44.72V
`
`I(t)
`
`C
`10pF
`
`L
`20nH
`
`PEAK AMPLITUDE OF THE OSCILLATION
`DURING THE RISING INVERVAL
`
`SUSTAINED AMPLITUDE OF THE
`OSCILLATION DURING THE RISING INVERVAL
`
`~9.7V
`
`40V
`
`30V
`
`20V
`
`10V
`
`AMPLITUDE OF OSCILLATION
`
`5
`
`0
`
`0
`
`4
`3
`2
`1
`RISE TIME, NORMALIZED TO ONE PERIOD OF THE TANK
`Figure 1.
`“Let’s see,” he pondered. “The horizontal axis (Figure 1) shows
`the number of periods of the tank over which the current linearly
`rises to 1 A; and vertically, you’re showing the peak amplitude of
`the oscillation both during and after the rising edge, right?” Niku
`nodded. “And I see that for fast-rising pulses, the stable periodic-
`steady-state amplitude of the sine wave is 44.72… V, which is
`consistent with your √(L/C) value of 44.72… V. Then, as the rise
`time increases, the PSS amplitude steadily falls, becoming zero
`when it’s exactly equal to one whole period of the tank. For slower
`rise times, it rises back up, to roughly 9.7 V, falling back to zero
`whenever the rise time is an integer number of periods. And your
`second set (Figure 2) shows the actual time-domain voltages for
`several rise times up to one full period. Okay. Now, what did you
`expect would happen?” Leif asked mischievously.
`
`1A
`
`I(t)
`
`0
`
`40V
`20V
`0
`–20V
`–40V
`15V
`
`10V
`
`5V
`
`0
`
`+44.72V
`
`+14.235V
`
`+14.235V
`
`RISE TIME = ONE PERIOD
`
`–44.72V
`
`EXPANDED PLOT
`OF THE CASE
`WHERE tr IS
`EXACTLY ONE
`PERIOD
`
`3.6
`
`4.0
`
`4.4
`
`4.8
`
`0
`
`0.4
`
`0.8
`
`1.2
`
`1.6
`
`2.0
`2.4
`2.8
`3.2
`REAL TIME (ns)
`Figure 2.
`“Well, until I saw this, I expected the amplitude to simply keep
`on falling as tR increased. I assumed that, for a rise time as long
`as one tank period, it would be already slow enough to approach
`the point where the voltage would be just LdI/dt, and that a 1-A
`step with a rise rate of 355.88127 A/ms, when multiplied by the
`inductance of 20 nH, would make a rectangular voltage pulse of
`7.117625 V. But the actual waveform seems to be a raised sine.
`Then I realized that if a step of voltage did appear, immediately,
`at the foot of the current ramp, there’d be a very large capacitor
`current, so my ‘simple’ expectation was just a bit too simplistic!
`
`Analog Dialogue Volume 40 Number 2
`
`
`
`Samsung Electronics Co., Ltd.
`Ex. 1062, p. 5
`
`

`

`Class D Audio Amplifiers:
`What, Why, and How
`
`By Eric Gaalaas [eric.gaalaas@analog.com]
`
`Class D amplifiers, first proposed in 1958, have become
`increasingly popular in recent years. What are Class D amplifiers?
`How do they compare with other kinds of amplifiers? Why is
`Class D of interest for audio? What is needed to make a “good”
`audio Class D amplifier? What are the features of ADI’s Class D
`amplifier products? Find the answers to all these questions in the
`following pages.
`
`Audio Amplifier Background
`The goal of audio amplifiers is to reproduce input audio signals
`at sound-producing output elements, with desired volume and
`power levels—faithfully, efficiently, and at low distortion. Audio
`frequencies range from about 20 Hz to 20 kHz, so the amplifier
`must have good frequency response over this range (less when
`driving a band-limited speaker, such as a woofer or a tweeter).
`Power capabilities vary widely depending on the application,
`from milliwatts in headphones, to a few watts in TV or PC audio,
`to tens of watts for “mini” home stereos and automotive audio,
`to hundreds of watts and beyond for more powerful home and
`commercial sound systems—and to fill theaters or auditoriums
`with sound.
`A straightforward analog implementation of an audio amplifier
`uses transistors in linear mode to create an output voltage that
`is a scaled copy of the input voltage. The forward voltage gain
`is usually high (at least 40 dB). If the forward gain is part of a
`feedback loop, the overall loop gain will also be high. Feedback
`is often used because high loop gain improves performance—
`suppressing distortion caused by nonlinearities in the forward path
`and reducing power-supply noise by increa