volume40-number4(1).pdf

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In This Issue

Editors’ Notes and Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

D-Day [ The Wit and Wisdom of Dr. Leif—5 ] . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Product Introductions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Ask the Application Engineer—35

Capacitance Sensors for Human Interfaces to Electronic Equipment . . . . . . 6

Lens Drivers Focus on Performance in High-Resolution Camera Modules . . 10

Digital Isolation Offers Compact, Low-Cost Solutions to Challenging

Design Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

www.analog.com/analogdialogue

Editors’ Notes

At the close of two-score years in print, we

look back … heck, we can all look back at

every issue * that ever rolled off the presses,

just as they appeared at the time—including

Volume 1, Number 1 (1967) —thanks to

scanning and the miracle of PDF. Moreover,

a more portable physical embodiment of

the totality of Analog Dialogue’s 40-year

substance through 2006, a CD version,

will soon be available, replacing the four bulging binders that are

currently needed to contain the paper-and-ink version.

When it arrives, we will recommend the CD to our fans, to history

lovers and reference librarians and their clientele everywhere, as a

private refuge from the crowded, noisy, crime-ridden, sometimes

dangerous highways and byways of the Internet.

AUTHORS

Gary Casey (page 10) is a staff engineer with

the DAC Applications Group in Limerick,

Ireland, providing support for lens-driver

products. Gary graduated from the University

of Greenwich, London, with a BEng (Hons)

degree in electronic engineering in 1991. He

joined Analog Devices in 1996.

Mel Conway (page 10) is a product marketing

manager for lens- dr iver products, based

in Limerick, Ireland. In 2000, Mel joined

DAC Marketing at ADI after having worked

i n applicat ions-, desig n-, a nd market i ng

roles at ot her elect ronics compa nies. His

g loba l re spon sibi l it ie s i n G er ma ny a nd

I rela nd are well- ser ved by h is ex per ience

w it h mi xed- sig nal- and power devices—and software. Mel has

many interests, but his wife and daughter are his top priorities.

David K rakauer (page 13) is marketing

manager for ADI’s i Coupler isolation products.

Previously, he was the product manager for

i MEMS gyro products in ADI’s Micromachined

Products Division and strategic marketing

manager for Mixed-Signal DSPs. Prior to

joining Analog Devices, David was a device

and reliability engineer at Digital Equipment

Corporation, and was also product development manager for

DEC’s graphics-accelerator ICs. He holds four U.S. patents and

has authored or co-authored 10 papers on solid-state physics and

reliability. He holds BS and MS degrees in electrical engineering

and computer science from MIT and an MBA from MIT’s Sloan

School of Management.

Mark Murphy (page 10) is a senior engineer

with the DAC Applications Group in Limerick,

Ireland, providing support for lens-driver

products. Mark holds a BSEE from Merrimack

College and an MBA from the University of

Limerick. He joined ADI in 1988.

Dan Sheingold [dan.sheingold@analog.com]

NEW WEB FEATURES FOR 2007

As our screens got bigger and our eyes get

weaker, we chose to stop catering to the

small-screen crowd at the expense of the

overwhelming percentage of readers who

are using screen resolutions of 1024 3 768

or higher. Please let us know if you like the

new online format † —or think we should

revert to the original. We also added a

new feature, the Back Burner , which is sure to become one of

your favorite spots. It will include teasers, design and test tips,

tutorials, and other information of interest to designers. Please

let us know of any topics that you would like to have covered

in future issues.

IN THIS ISSUE

Mechanical buttons, switches, and jog wheels have long been

used as interfaces between users and machines, but their many

drawbacks have led designers to look for more reliable solutions.

Capacitive sensors, which can be used in place of buttons, can

also add versatility. Available ICs can measure the capacitance

of up to 14 sensors, compensate for environmental changes, and

provide a digital output.

The picture quality available from cell phone cameras is constantly

improving. Autofocus is standard in many high-resolution

cameras, and optical zoom, shutter control, and image stabilization

are becoming common. These features require the lens to move

rapidly. Lens drivers power the motors that move the lens in

response to digital signals.

New isolation capabilities—including integrated, isolated power

and truly bidirectional isolation channels—are greatly simplifying

the design of isolated systems. Fueled by a shift from LED-based

optocouplers to chip-scale microtransformer technology that

is compatible with standard CMOS processes, they it more

functionality into a single package.

As always, your comments are welcome.

Susan Pratt (page 6), a senior applications

engineer with responsibility for ADI’s resistive

and capacitive touch controllers, graduated

from the University of Limerick (Ireland)

with a BEng in electronic engineering. She

joined Analog Devices in 2002 and is based

in Limerick.

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-iltered” point of entry to the www.analog.com site—the virtual world

of Analog Devices . For history buffs, the Analog Dialogue archives include all regular

editions, starting withVolume 1, Number 1 (1967), plus three special anniversary issues.

If you wish to subscribe to the print edition, please go to www.analog.com /

ana logd ia log ue a nd click on < subscr ibe > . You r comments are always

welcome ; please send messages to d ia log ue.ed itor @ a na log.com or to

these individuals: Dan Sheingold , Editor [dan.sheingold @ analog.com] or

Scott Wayne , Managing Editor and Publisher [scott.wayne @ analog.com].

Scott Wayne [scott.wayne@analog.com]

* See http://www.analog.com/library/analogdialogue/archives.html

† Take a look at http://www.analog.com/analogdialogue

ISSN 0161-3626 ©Analog Devices, Inc. 2007

D-Day (continued)

[The Wit and Wisdom of Dr. Leif—5]

would be in on the joke, and both smiled together at its poignant

appropriateness. But the bulk of the audience was perplexed by

this unfamiliar four-word exchange, yet increasingly aware of the

unusual rapport and the spirited give-and-take between these two.

Had they been more informed about widowed Hans Sachs and the

young Eva, the parallel would have been evident.

Breaking eye-contact, and seeming to suddenly remember she was

in the middle of a lecture, Niku blushed deeply and visibly for the

second time in an hour.

“Thank you, Dr. Leif. So … uh, back to our little friend, Oscar. A

few minutes ago ...” (Or was it a week? Or a century?) “I showed

that its internal noise—and the enormous noise-ampliication

factor—reduce this time to just a few cycles. So, comparisons of

start-up time are much too close to be of any use as a source of

insight. In fact, for even tiny amounts of [stochastic] noise, the

very notion of a start-up trajectory becomes moot. Rather, the

modulation envelope during startup, which can be seen in this

slide” (Micha-2, which had remained frozen on the screen) “is

determined by the particular L , C , and R of the tank.

“However, to complicate matters further, the effective loading of

this tank, embedded in the active circuit—the in-situ value—is

not the value that is conventionally deduced from measurements

of the tank alone—the ex-situ value. And here, I’m not referring

to any incidental, parasitic effects, for example, as caused by the

shunt loading imposed by the incremental output resistance of

the differential pair. In fact, as I believe I mentioned earlier, to

remove all such complicating factors, the transistors are assigned

Early voltages (VAF and VAR) of 10 9 volts, and the classical dc

beta-modeling factors (BF and BR) are similarly 10 9 .

“This is not as fanciful as it might at irst seem, because the core

properties of the BJT do not depend on these parameters having

moderately low values. Indeed, they represent defects —rather

than assets —of the transistor. We long ago gave up thinking of

the BJT as a current-controlled current source (CCCS); rather,

just like ield-effect devices, they are more properly viewed as

voltage-controlled current-sources (VCCS). The inite output

resistance of a VCCS never did anything useful for it; neither

does the base current of a BJT, unless you were foolish enough to

actually depend on the need for some inite base current.

“Likewise, the depletion capacitances (CJE, CJC, CJS) are just

useless baggage, as are the ohmic resistances (RE, RB-RBC, RC),

and should not be depended on for any speciic circuit behavior.

Between them, they only increase the inertia of a circuit, and

the ohmic parts contribute thermal noise . They are defects of a

BJT. By the way, don’t confuse the diffusion capacitance with

those parasitics. It is a direct measure of the base charge needed to

establish a given collector current.

“This perspective—and the practice of stripping the BJT model

of all nonuseful attributes during preliminary investigations of

new and unfamiliar topologies—is called ‘Foundation Design’

by Dr. Leif. When every nuance of the cell has been thoroughly

understood and accounted for, using what he calls this ‘Level

0’ model, it is permissible to move forward to a ‘Level 1’ model,

which, for example, might irst add in more realistic values of

the dc betas and Early voltages, the consequences of quasistatic

depletion-layer modulation by the terminal voltages …”

Some in the audience, listening to what was beginning to sound

more like philosophy, were manifesting spaced-out expressions;

but most were working hard to follow the convoluted contour of

Niku’s thinking. Leif again wanted to comment and again was

polite enough to signify this by raising his hand.

“Dr. Leif?”

By Barrie Gilbert [ barrie.gilbert@analog.com]

Niku’s Daedalus Day presentation began in Volume 40, Number 3.

The complete series can be found online at www.analog.com/library/

analogdialogue/leif1.html.

“This next study will show some results comparing the relative

effects of mismatches and noise. Such comparisons can never

be precise, for reasons I gave earlier. Not only are mismatches

just interesting cases ; the onset of strong oscillations—the

start-up trajectory—also depends on such controllable factors

as the rise-rate of the tail current, I T ; the overdrive beyond

the critical value, I CRIT ; and the load resistance, determining

the tank’s effective Q . Once these have been chosen, we can

compare start-up times, deined as the time from when the tail

current crosses I CRIT to the time the oscillations reach 90% of

their inal amplitude.

“I’m sure all of you appreciate that, frequently, the potency of

simulation in gaining insights does not necessitate the use of

accurate parameter values, or reliable process statistics, such as are

essential in predicting the performance of a production microsym.

Rich insights are to be gained from pursuing a well-planned set of

comparative studies using relative values that are just as valuable

as the conirmation of an original design using absolute parameter

values …”

Dr. Leif raised his hand politely. Niku caught the gesture and

invited his comments. “Yes, sir? Do you have a little song for

us?” she teased.

“Perhaps we ought to say ‘ far more valuable,’ since we should never

forget that learning is as much a part of an engineer’s job as getting

new products to market—and this is as important for our Fusers

as for Originators. We must always set aside time in our busy lives

to think about those Fundaments, and ceaselessly ask ourselves

those vital questions: ‘What If?’, ‘How About?’, ‘Why does that

Happen?’. You need to be acutely aware that, while your latest,

thoroughly robust, high-yielding, and trend-setting product, which

you have managed to get to market in a competitive time-frame,

and yet meets every one of its highly challenging performance

speciications and goes on to make us all fabulously rich …” (Leif

grins as the audience groans, and he takes a brief sip from his water

glass) “… while all that is very important, it is the new insights that

you gained throughout the experience, as well as from the time

you put into facing up to independent , self-assigned challenges—of

the sort that Niku is urging you to undertake—they will be

the foundation stones of your career. New product development

frequently requires the use of several distinctively clever ideas.

But that is a one-time event. On the other hand, the new insights

that opened to you, during the experience, become the precious

gems you’ll add to your own unique treasure trove of tools. These

diamond-hard gems of insight will never be far from you, waiting

in your subconscious to illuminate and inform the creative work

of a long and productive career. I …”

Leif stopped abruptly, as suddenly as he had apparently felt the

need to make these interlineal observations. Returning to his

front-row seat, he seemed uncharacteristically self-conscious.

What next thought that he decided to suppress was in his mind?

“ War das eu’r lied ?” Niku again teased, with a little quote from

Die Meistersinger —as asked by Hans Sachs, the humble cobbler,

of Sextus Bessemer, the town clerk of 16 th -century Nuremberg

who was attempting to serenade the heroine Eva. From the chats

they frequently enjoyed over at Galaxybux, Niku knew that Leif

Analog Dialogue Volume 40 Number 4

“Ah, well, let’s see now. First, if you’ll forgive me Niku, you’re

running a little short on time, and I know you have some really

interesting discoveries to share with us, about Oscar. I suspect you

didn’t plan to digress so deeply into these peripheral ideas at the

expense of the main theme, did you? Secondly, neither the term

‘Foundation Design’ nor its principles are mine, although I admit

I am a passionate advocate of them. They go way back to the last

century, and the lectures given by a long-departed ADI Fellow,

of whom we hear very little these days. When I get back to my

ofice, I’ll issue a cy-mail, and include a reference to his lectures,

for the engineering community. Okay. That’s it.”

“Oh, yes; now I recall, you did tell me that Foundation Design

came from a long time back. I’m sorry I got that mixed up. And

you’re right: I got a bit carried away with some incidental

ideas. I was about to explain that another approach to tracing

the start-up trajectory is to disable the modeling, and run the

simulations in the old SPICE-like mode, when they didn’t model

noise as a time-process. Then, using a variety of representative

mismatches we can simply observe how the start-up times compare

to the noise-driven case.

“In fact, now that we have seen how very short this delay can be,

provided that noise mechanisms are fully modeled, we need to

extract some other insights from these studies. To be candid, that

was the only reason for starting down this path. I was pretty sure

from the outset that noise had to be the driver—in both senses:

‘was bound to be’ and ‘had better be,’ and that in all cases where

this wasn’t so it would be due to unplanned mismatches. But

never due to glitches ! Any oscillator that needs to be started by

such gross inluences is, as a matter of practical deinition, a poor

design, since this very sensitivity is almost bound to degrade the

phase noise after it reaches its periodic steady state.”

“Dr. Yeng?” It was a rather mature lady’s voice from two rows

back. “That’s not quite true. There are times when one wishes to

preserve a very high effective Q in a different class of oscillator,

which would indeed eventually start up because of noise, and in a

certain sense right away , but would reach its cyclostationary state

only after perhaps tens of thousands of cycles; whereas its services

are needed immediately following a logic edge that deines t = zero.

So one needs to introduce a particularly well-managed start-up

strategy to do this; and with it, the oscillator not only starts up

instantly, but at exactly its inal amplitude.”

“That’s really interesting!” said Niku, clearly genuinely pleased

to learn of something that sounded so close to her own recent

discoveries. “Can you say a little more about this?”

“I can, although I don’t wish to steal too much of your time. I have

a couple of visuals prepared. By the way, I’m Hjørdis Björklund.

May I open my Michaday channel to the screen?”

“Oh … yes, of course,” said Niku, slightly lustered by having

forgotten that her own access to the GE8E had been suspended,

in its capacity as a surrogate presenter.

“Michaday, this is Björklund. Show 101.37.01.255.”

was all business—a simple schematic instantly appeared. She

wondered why she’d never met this individual; and why Dr. Leif

was apparently suppressing his mirth. What was going on?

“This is just an illustrative example I prepared. It’s nothing more

than two ideal gm/C integrators in a loop, forming a sine/cosine

oscillator, of the sort one might need in an I/Q demodulator. The

rapid start-up is essential because such a subsystem is shut down

between active time-slots, until valid data is available. When this

happens, the phase-locked loop, of which this is a part, needs to

acquire the carrier within a few cycles. On the other hand, a high

effective Q is essential to minimize phase noise; and normally

that would result in the oscillator’s start-up process being far too

sluggish. So it appears there’s a basic conlict, here.

“Now, keep in mind,” continued the mysterious Dr. Björklund,

“that this is an illustrative circuit. Practical integrators used in a

loop as basic as this will cause the amplitude of the oscillations

to either decay—if their poles move off the imaginary axis into

the left side of the s -plane, due to the shunting of the capacitors

by the inite incremental output resistance of the gm cells—or the

amplitude will rise exponentially when there is some additional

hidden phase lag in the gm cells causing the resonant poles to

move into the right plane.

“Such practical details are taken care of by regulating means on

top of what I’m showing here. But they are not germane to the

key idea that, sometimes, one does use a sort of glitch to get the

ball rolling; though that would be a particularly inept description

of the elegant way in which this start-up means is implemented.

Michaday, show * .256.”

–

GM1

–1M

GM2

–

Figure 2. Dr. Björklund’s second visual.

“Here’s the key idea. Notice the two switches, one connecting a

dc voltage source, which I am showing as 1 V, to the output E 2 ,

while the other simply connects the output E 1 to ground. These

switches remain closed right up to the moment we wish to start the

oscillations. Now, Miku, what happens when we suddenly release

the initial conditions of this describing function?”

 E 1 ( gm / C ) dt = −  E 2 ( gm/C ) dt

“It’s Niku , ma’am.” This was not fair! She had allowed this lady

a moment or two, to show a sort of quick example of something

or another that had admittedly sounded relevant to her own talk,

and a bit interesting. But now, here was this … this lady , calling

her ‘Miku,’ and putting her on the spot, in her time! Fortunately,

while Niku might show her inexperience, and was perhaps being

a bit too familiar with Leif, and did play cheeky with Michaday

(Gosh! Can a GE8E get embarrassed in public, she suddenly

wondered)—for all that, she was a warrior, too (for she knew that

Hjørdis means ‘Sword Goddess’).

“Well, that’s trivial ...” (whoa, careful , girl) “uh ... Dr. Björklund”

(that’s better; don’t let her see you’re rattled). “When the initial

values are released this equation will execute a harmonic pair, of

stable peak amplitude ( E 1 , E 2 ) = 1 V, at an angular frequency of

 = gm/C , which, with the values shown, will be at 159.155 MHz.”

“Yes … that’s … right,” said Björklund, who promptly sat down.

–

GM1

–1M

–

GM2

Figure 1. The mysterious Dr. Björklund’s irst visual.

With no chummy banter, of the sort that Niku always expected

from Micha, but just a curt “Certainly, Dr. Björklund”—which

suggested to Niku that this lady was no newcomer to Solna and

Analog Dialogue Volume 40 Number 4

“Dr. Leif,” said Niku with a coy grin, “may I please have Micha

back on my team?”

“He has been waiting for you for some time, Niku.” Was that a

trace of empathetic tenderness in Leif’s voice, she wondered, now

kicking herself for probably looking foolish in front of all those

guys, or appearing to be angling for brownie points from the old

fellow. Well, old is a matter of degree. Leif carried his 79 years

remarkably well. His bronzed features, athletic form, white

casual shirt and slacks, and the upscale gold watch gave him the

appearance of one having just sailed up from Monte Carlo.

“Thank you, sir. Okay, Micha, you must have heard what was just

discussed. Please take that equation and show us how this way of

starting an I/Q oscillator plays out.”

That part of the GE8E currently servicing Dr. Björklund—her

still-open channel—though operating within the one framework,

was not in any sort of loyalty clash to the channel assigned to Niku.

These machines shared at least that much with the old digital

juggernauts. Micha probably had no idea what it meant to be “fair”

or “even handed” in its dealings with those who used it. But, in

the time since these latest models had arrived, it was becoming

clearly evident—a surprise even to Neuromorphix, Inc.—that they

developed a closer rapport with some users than others. It didn’t

affect the speediness of their service, even less the accuracy of the

results they produced. But it was almost as if they enjoyed working

with some more than others. Leif had been made especially aware

of this phenomenon during the past few minutes. It was evident

that Micha was acting like … well, a pal to Niku, while merely a

coolly eficient servant to Björklund. In the few seconds Leif had

been pondering this, the requested solution had been generated

and the screen showed the result.

To Niku’s delight, the audience’s applause was generous. The

hand-clapping—at irst a random noise—quickly phase-locked

into the rhythmic foot-stomping common in Europe, no less in

Scandinavia. She thought, “How apt a metaphor for how little

Oscar struggles up from the noise loor!” Still standing, Dr. Leif

was the last to cease clapping. It was abundantly evident that he

was very pleased with how Niku had progressed since he hired

her, only a few months ago. Her determination to track down the

root causes of observed effects, in a manner that went far beyond

the mediocre, shallow, repetitive, and unsatisfying explanations

so often found in textbooks, gave him the strong assurance that

this young woman was destined to become a major innovator in

the coming years.

“Well, that’s it for another D-Day. Now we can all get back to

some serious invention-making! And Dr. Björklund, I’d like to

see you in my ofice, please.” With that the audience dispersed,

and Leif approached Niku, who listened for a moment, smiled,

and then two sets of eyes twinkled conspiratorially. But their brief

resonance was lost in the noise loor.

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 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.

PRODUCT INTRODUCTIONS: VOLUmE 40, NUmBER 4

Data sheets for all ADI products can be found by entering the model

number in the Search box at www.analog.com

–1

October

Accelerometer, 2-axis, 63- g range ........................................... ADXL323

Converter, Synchronous Buck, 2-/3-phase, 8-bit VID code ..... ADP3193

Converter, Synchronous Buck, 2-/3-/4-phase,

8-bit VID code ........................................................................... ADP3198

Multiplexers, i CMOS, 4-/8-channel, low-capacitance,

615-V operation ....................................................... ADG1408/ADG1409

Temperature Sensor, Digital, 2-channel,

over-/under-temperature alarms ................................................ ADT7482

Temperature Sensor, Digital, 1-wire data interface .............. ADT7484A

Temperature Sensor, Digital, 2-channel,

1-wire data interface ................................................................ ADT7486A

Transceivers, RS-485/RS-422, ESD protected ..................... ADM307xE

Transceivers, RS-485/RS-422,

ESD protected ............................ ADM3486E/ADM3490E/ADM3491E

November–December

ADC, Pipelined, 8-channel, 12-bit, 40-/50-MSPS,

LVDS outputs .............................................................................. AD9222

ADC, Successive-Approximation, 16-bit, 750-kSPS,

±1.5-LSB max INL ...................................................................... AD7612

Controllers, Hot Swap, monitor supply voltage

and current .......................... ADM1175/ADM1176/ADM1177/ADM1178

Converter, Synchronous Buck, 2-/3-phase, 8-bit VID code ..... ADP3199

Detector, Signal-Power, 50-MHz to 4-GHz ............................. ADL5501

Front-End, Mixed-Signal, broadband modems .......................... AD9857

Monitors, Digital Power, over-current alert ........... ADM1191/ADM1192

Regulators, Low-Dropout, 500-mA loads ............... ADP1715/ADP1716

Switch, HDMI/DVI, 4:1, equalization and pre-emphasis ............. AD8191

Temperature-Sensor/Voltage-Monitor, Digital,

one-wire data interface ............................................................ ADT7488A

Transmitter, HDMI/DVI, high-performance ........................... AD9889A

Transceiver, RS-485, high-speed, isolated, ESD protected .... ADM2490E

–1

TIME (ns)

Figure 3. The instant start-up and exactly-sustained

amplitude of Dr. Björklund’s “illustrative” oscillator.

“Thank you very much, Micha. Yes, that’s a useful technique to

remember for relatively low-frequency oscillators. Of course, it is

not usually as easy to preset the initial conditions in a resonant-tank

RF oscillator, but in fact, that is one of the slides I will show in a

few moments. So, after that little detour, let’s irst get back to the

start-up trajectory of the basic Oscar oscillator.”

Standing, Dr. Leif once again found he needed to intervene.

“Niku, I’m quite sure this audience could listen to you all day; I

know I could,” he quipped. “But you may not have noticed that

we’ve exceeded the allocated one hour by a generous margin, and

I have yet to pose the traditional teaser. So, may I suggest that you

open-access the rest of your work on Michaday, so that interested

engineers can check in from time to time at the same address, for

the inal pages of this interesting story? I suspected you would

have too much material to cram into one hour, but even though

you didn’t get to the best part I don’t think anybody here today

will feel their time was ill-spent. Am I right?”

Analog Dialogue Volume 40 Number 4

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