volume40-number2(1).pdf

A forum for the exchange of circuits, systems, and software for real-world signal processing

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

Editors’ Notes

ANNIVERSARY

As faithful readers already know (and are perhaps

weary of knowing!), Analog Dialogue is

celebrating our 40 th anniversary in print. But there

is another signiicant anniversary to celebrate:

Exactly 20 years ago, in Volume 20, No. 2 (1986),

we broke with our purely analog past and introduced

the irst 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:

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 inally 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 Blackin 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 Ampliiers

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.

ScottWayne [scott.wayne@analog.com]

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 ampliied,

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 preampliiers, 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—ampliier, 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 dissatisied 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 ampliier, signal conditioner,

and data converter by designing and marketing families of

cost-effective products.

We have always been dissatisied 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 inally, our dissatisfaction with insuficient 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.

www.analog.com/analogdialogue dialogue.editor@analog.com

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].

Dan Sheingold [dan.sheingold@analog.com]

ISSN 0161-3626 ©Analog Devices, Inc. 2006

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 irst 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

inally doing something productive, working under the guidance

of her team leader, Jeff Rawlings, another protégé of Dr. Leif.

It was Leif who irst 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 eficient, and the older ones were broadly

informed about the IC business, their satisfaction came largely

from providing a quick solution to a ield 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 inally grasp the ominous reality

of the science. After years of glory, the older areas of Venice were

the irst 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 izzled 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 irst 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 ine-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

irst 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

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 inite 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 ield, in

the case of an open coil, generates an EM wave.”

“Did you try calculating the radiation loss from irst 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 satisied. 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 conirmed 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 R 2 . 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 irst principles, considering the inherent

dimensions of inductance and capacitance. This concern for what

has to be included and what can be excluded without signiicant 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 14 th -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 conigure 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 ind it Dificult.

“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 , t R , 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 signiicant fraction of the period, up to or even beyond the

full period? One thing was certain: for very slow rise times—when

t R is hundreds of times √( LC )—practically all of the current must

low 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 inite 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 ind it dificult 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, ininite- 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 inite time; and it

provides the Gaussian form, which must be truncated before

t = 0, for any inite delay—though, it’s only 0.148 ppm of the

inal value at a time four times earlier than that needed to get

10% up the edge.

Analog Dialogue Volume 40 Number 2

“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 irst of two sets of plots.

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!

44.72V

10pF

20nH

40V

I(t)

30V

PEAK AMPLITUDE OF THE OSCILLATION

DURING THE RISING INVERVAL

20V

“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?”

SUSTAINED AMPLITUDE OF THE

OSCILLATION DURING THE RISING INVERVAL

10V

~9.7V

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.

“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.”

I(t)

RISE TIME = ONE PERIOD

+44.72V

40V

“Ah, but I did,” said Dr. Leif, “only a few moments ago.”

20V

+14.235V

–20V

–40V

–44.72V

Barrie Gilbert , the irst-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

irst-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 ive books. In 1997, he was awarded an honorary doctorate of

engineering from Oregon State University.

15V

+14.235V

EXPANDED PLOT

OF THE CASE

WHERE tr IS

EXACTLY ONE

PERIOD

10V

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

4.4

4.8

REAL TIME (ns)

Figure 2.

“Well, until I saw this, I expected the amplitude to simply keep

on falling as t R 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

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: