volume40-number1(1).pdf

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

In This Issue

Editors’ Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

The Fourth Dee: Turning Over a New Leif . . . . . . . . . . . . . . . . . . . . . . . . 3

Switching in USB Consumer Applications . . . . . . . . . . . . . . . . . . . . . . . . 6

ADC Input Noise: The Good, The Bad, and The Ugly:

Is No Noise Good Noise? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Wireless Short-Range Devices: Designing a Global

License-Free System for Frequencies <1 GHz . . . . . . . . . . . . . . . . . . . 18

Authors and Product Introductions . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

www.analog.com/analogdialogue

Editors’ Notes

A READER COMMENTS

Last fall, we published an article about adding

stereo audio to a satellite set-top box. The key

idea was to apply a phase-locked loop, with the

vestigial 15.734-kHz pilot signal in the composite

spectrum as the reference, allowing one channel

of the AD71028 BTSC encoder to derive the

primary channel’s master clock while the other

channel provides the MTS stereo-encoded output

for satellite set-top boxes and receivers.

We received the following email from Matt Laun,

at NASA:

“I found your design using the AD71028 as a STB (satellite set-top

box) stereo synthesizer clever and interesting. However, I can suggest

two corrections to the information in the article. One is the RF

spectrum of a modulated NTSC video and audio signal. It appears

in your article as the following:

The vertical blanking normally done on video was not used, three

stereo samples were recorded on each horizontal line, and every ifth

line had a checksum or some kind of redundancy sample for error

detection and correction.With 14 samples for every ive lines, you get

a ratio of 2.8. There was considerable resistance by the AES and the

audio community to have 44.1 kHz adopted as any kind of standard.

We wanted 48.000 kHz because it was nicely synced to movies and

both U.S. and European TV and, being a little higher, gave us a little

more transition band for the antialiasing and anti-imaging ilters

(and we really needed that transition band back before the day of

sigma-delta converters), but Sony and Philips had pretty big guns

and dictated the standard since they owned the technology.

Why would they not let it be 48 kHz? Rumor has it that the president

of Sony wanted all of Beethoven’s 9th to it uninterrupted on a single

CD.The 12-cm diameter had already been carved into stone, and there

was no way for it to it with a 48-kHz sampling rate. I don’t know how

long Beethoven’s 9th is, but a CD can hold 74 min, 33 sec of music.

The frame rate (and horizontal scan rate) was actually

reduced by 0.1% due to the emergence of color TV. Originally,

it was exactly 15750 Hz and the sound subcarrier was

at exactly 4.5 MHz. Color TVs encode R, G, & B into a B&W

luminance signal calledY, and I&Q (in-phase and quadrature) chroma

signals. Y is transmitted just like a normal B&W signal. I&Q are

transmitted using quadrature carrier modulation, and are bumped

up to exactly halfway between the 227th and 228th harmonic of the

horizontal scan rate. There is not much B&W energy up there at the

227th harmonic, so they could stick the chroma up there without

degrading the B&W image too much. In addition, putting the chroma

exactly at 227.5 times the horizontal rate (and all of the harmonics

of the chroma would be halfway between harmonics of the B&W

signal) would cause any interference from the chroma signal to be

exactly negated on the neighboring scan line. The same is true if you

consider the effect that the B&W signal has on the chroma signal: the

B&W signal is at the –227.5th harmonic of the chroma baseband,

so its interference is negated with every other scan line. The sound

subcarrier is a lot closer to the chroma signal than to the B&W signal,

so the color TV guys had to worry about it.

The sound carrier is at exactly 285.71428571 times the

horizontal. The color TV guys wanted it to be an exact integer

multiple (so it would be 1/2 harmonic off from the chroma

signal). So, they decided to make the sound carrier exactly

286 times the horizontal. Unfortunately, instead of bumping

up the sound carrier to 4.5045 MHz (these guys in the ’50s

thought that this would be too far off for existing FM receivers

to lock to), they bumped the horizontal scan rate down to

15734.265734 Hz. This caused the horrible 29.97 Hz drop-

frame mess that today’s technicians have to deal with and

the 44055.944056 Hz sampling rate.

By the way, 15734.265734 is a truncation of 15750/1.001, or

15734.2657342657..., while 15750 3 0.999 = 15734.25. Now, here is the

last word from Matt Laun:

“Thank you too for the fascinating Google ‘.doc’ about the origins

of 15734.265734! I am a recording engineer as well as an electronic

hobbyist with a nostalgic love for analog N TSC and BTSC

modulations. I never knew that audio 44100 kHz was derived from

video (and not even standard NTSC sync at that)! Incredible!”

If only Beethoven had known! A few bars less, and he might have simpliied

life for designers in the Age of Media.

Dan Sheingold [dan.sheingold@analog.com]

VIDEO

CARRIER

SOUND

CARRIER

AUDIO

VIDEO

1.25MHz

5.75MHz

The frequency information may be misleading to a reader not familiar

to the standard. More commonly, the audio carrier frequency is

measured relative to the channel carrier frequency or the video

carrier frequency.The audio subcarrier would be 4.5 MHz. It is more

intuitive to view the spectrum as seen below:

VIDEO

CARRIER

SOUND

CARRIER

AUDIO

VIDEO

1.25MHz

0MHz

4.50MHz

The second correction is minor but may be signiicant if a reader

is trying to understand the design by performing calculations.

When describing the need for a precision N-divider, the

value N is listed as 780.9838... The precision value is actually

780.9706666... { = 48 kHz 3 256/15.734265734 kHz};

[fractionally: = 49201152/63000]. I understand the clever design

eliminates the need for a separate precision divider, I just thought

a more accurate number would help a reader understand how that

number is derived.

Thanks for a relevant, practical, and interesting article.”

Lead author, Jeritt Kent, responded:

“First of all, thank you very much for this kind letter. I am very pleased

that you enjoyed the article. Victor and I worked hard to ensure that

the paper was clear and easy to understand.

Your two clariications are very valid. The irst one was likely an

interpretation by the graphic designer, as the original intended igure

would have matched Fig. 2 in this document http://www.sencore.

com/custsup/pdf/TT213.pdf

The second observation shows an example where rounded

mathematics can generate problematic results, albeit this is not a high

volume Intel Pentium processor design nor the Hubble telescope:)

Nonetheless, a Google search on <15734.265734 Hz> provides some

excellent history on the subject from the University of Victoria,

Canada (UV).” ( www.ece.uvic.ca/~yli/misc/discussion.htm )

That UV document, titled “44100,” was a fascinating bit of history. An

abbreviated version follows:

The original appearance of 44.1 kHz was with the Sony F1 digital

audio recorder. It recorded digitized stereo audio as an emulated video

signal onto Betamax tape. You might recall that the horizontal

scan rate for NTSC video is 15750 Hz (actually 99.9% of that

but we’ll get to that later).This comes from 30 frames/sec 3 525

lines/frame. Note that 44.1 kHz is exactly 2.8 times 15.75 kHz.

SIMULATED REALITY

In addition to three outstanding feature articles,

this issue includes the second installment of

Barrie Gilbert’s fantasy. In it, Barrie introduces an

example showing the power of circuit simulation.

In a short time, Niku was able to gain valuable

insights regarding the behavior of an ideal

oscillator and to debunk the commonly held

belief that it would start up given a spike on a

supply or bias line.

In this column, Dr. Leif has provided some clues

regarding the fourth “Dee” of Analog. We invite our readers to guess what

Barrie has in mind, and to provide anecdotes from your experiences with

simulators or with analog design in general.

Scott Wayne [scott.wayne@analog.com]

ISSN 0161-3626 ©Analog Devices, Inc. 2006

THE FOURTH DEE:

TURNING OVER A NEW LEIF

their constituent components, as well as the actual signals, have a

crucial Dimensional aspect.”

“Hearing you summarize them so well, Niku, they don’t appear to

be especially profound, do they? Are you inding these issues to be

as important as I have suggested?”

“Not really. I believe you, of course. But any truths of substance

have to be learned, from one’s individually acquired knowledge

and hands-on experience, rather than accepted simply on their face

value,” Niku said, sounding wiser than her years. “Are you going to

tell me what the Fourth Dee is now?”

“Tell you what,” said Leif mischievously. “I dropped by to see what

you’ve been doing, and I’d irst like to hear all about that. Perhaps

the answer you’re seeking will occur to you by the time you have

inished telling me about your project.”

Niku explained that she hadn’t yet been assigned a development

project. She’d been given time to familiarize herself with the lab

environment, the many in-house and foundry IC processes that

would be available to her, and the vast network of databases and

design centers in every corner of the United World. She had also

been familiarizing herself with the large suite of simulation tools

called GE8E, pronounced “gee-oh,” which she was told stood

for general electro O ptical emulator . She had never been exposed to

anything so powerful and all-encompassing, let alone so user-

friendly and fast.

“So how are you getting along with your teammates?”

“Oh, they’re okay.” She briely hesitated—but then mentioned that

several days ago she’d heard a noisy argument in the halls about

exactly how high-frequency oscillators start up. She was quite

surprised that this was a matter for disagreement.

“It appears that Bob somebody—he has a CyberCyte” (Leif ’s wry

smile acknowledged his recognition of this character) “had stated

in no uncertain way that oscillators start only because of a sudden

step on the supply, or on a bias line. A couple of the guys seemed

to agree with him, but most didn’t. They argued that if a circuit

satisies the conditions required for sustained oscillations, it should

only depend on its internal noise to start, and the longer it takes,

the better. The argument got pretty ierce at times!

“So I decided that studying this question in depth would be an

excellent learning experience, as my irst serious exercise in the use

of GE8E. But I have told no one about this, because it might seem

a waste of the company’s time.”

“Absolutely not, my good young lady! If you ever start to believe

that the exploration of such fundamental questions is a waste of

time—even after you have product responsibilities—you’ll hear from

me! Do you know what genius is?”

Niku blinked, startled by Leif ’s sudden intensity.

“Genius is nothing more than this: The curiosity of childhood

constantly recaptured—every day of your life! It wouldn’t be

proper for me to advise you to allow your curiosity to rule your

actions when you become faced with urgent deadlines. But if

those deadlines should ever become the constant feature of your

life, you’ll feel frustrated by the pressure, for perhaps a year or two,

and later miserable and irritable. Eventually, your precious lame of

individualism will be fully extinguished.Years ago, this would happen

to a ine product designer, who would turn into a designing robot

by the pressures of the work. Today, we have a better awareness of

these dangers. In fact, it is my job to ensure that creativity lourishes

in this group, by defending lights of the imagination—such as the

one you are starting to tell me about!”

“Okay, but I’m no genius! Just very curious, simple-minded, and

terribly inexperienced,” she said, blushing deeply. “Well, to start

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

At the time NikuYeng received an oficial offer of employment from

Analog Devices in 2025, shortly after her interview with Dr. Leif,

she had briely considered two others. All held the prospect of an

exciting and rewarding career in advanced microelectronics. But she

recalled that the interviewer at one of the companies seemed to be

unusually concerned about her willingness to accept highly detailed

directives and to rapidly produce solutions in response to speciic

market demands. She’d been trained to expect this, in an industry

that had become just another provider of commodity items—much

like hyperphase foods or disposable clothing—she nonetheless felt

that a strong emphasis on products focused only on near-term needs

was myopic, and it was bound to discourage originality and clash

with any aberrant, singular vision, leading to mediocrity and a poor

reputation for quality and service.

The third offer was quite different. During that interview, all the

questions were concerned with very tentative technologies, facets

of the ongoing struggle to make nanostructures not only as crude

logical elements but in the vastly more complex arena of analog

design—where device quality is of paramount importance.Very good

progress had been made in applying hybrid neural networks (such

as those in the greeter at Galaxybux) having quasi-analog circuits

on silicon substrata acting as message concentrators for the layers

of super-stressed ibers of dimethyl-3, 5-ribocarbon—which provide

the fast-learning, slow-fading memory cells with massive parallelism

for noise immunity and redundancy. But the broad promises of the

nanodisciplines, peaking just after the turn of the century, had all but

evaporated between 2012 and 2018, as more pragmatic concerns

dictated which technologies could deal with the peculiar demands

of analog signals. Furthermore, with atmospheric CO 2 rising at an

imminently perilous rate, research in global climate control now

held center stage in every country. Degree courses in this ield had

become the irst choice of many a young scientist who aspired to

a place in history.

But, more than any other factor, it was the sheer enthusiasm of

Leif, his keen interest in exploring some still-unanswered, though

seemingly rudimentary, questions about analog circuits that led

Niku to accept ADI’s offer for a position as Entry-Level Product

Originator . At irst, she was upset to discover that her work would

not be under Leif—who was, it seemed, a sort of roving consultant

to various groups in the company. (She later discovered that he got

involved in entry interviews only in cases where exceptional talent

was evidenced during prescreening, a revelation that had helped to

assuage her initial disappointment.)

By now, though, she felt sure she’d made the right decision. Leif

was no mystical hermit. He regularly wandered around the local

design groups, asking penetrating questions about their projects,

vigorously engaging in theoretical issues here or offering advice

there, and applying a deft technique of asking leading questions

that left no one feeling put down. It was on one of these routine

visits, roughly two months after Niku had joined her team, that he

sat down with her for a while. Before long, she was reminding Leif

that he had never gotten around to telling her what the “Fourth

Dee” of analog design was all about.

“Ah, yes, those ‘Dees.’ What do you remember about them?”

he quizzed.

“Well, you told me that analog products are far more Durable than

digital, often having generations measured in decades; and that

the little circuits that go into them are highly Diverse —like the

myriad musical tunes composed out of just a few notes; and that

Analog Dialogue Volume 40 Number 1

with, it seemed obvious that if an oscillator actually did start up

through being disturbed by a supply transient, it would be a pretty

poor circuit!”

“How does that follow?” said Leif, knowing full well where this

was going.

“Well, the guys in the hall were talking about RF oscillators, for

which phase noise is a critical performance issue; and if such an

oscillator is easily upset by supply noise—enough to induce it to

start up from cold—then I reasoned it would not be in the league

they were talking about. It was only a short step to conclude that

oscillators for demanding applications, as in this TransInformer”

—Niku put her PDA on the table— “must use a fully balanced cell

topology, if for no other reason than to reject the common-mode

noise voltages, but also to minimize the even harmonic terms.”

“Splendid!These are quite remarkable leaps of the imagination! I’m

beginning to think that the Fourth Dee may not be one you need

to worry about! But—keep going!”

“Well, it just seems like common sense to me. Anyway, I wanted

my test cell to be as simple as possible, to reduce the number of

unknown inluences, so I used this ...” Niku pulled up the circuit

on the screen of her PDA (Figure 1). “I know it’s not a practical

oscillator. For example, I learned in one of my courses at Nova

Terra that once it does start oscillating, the amplitude will build

up until the transistors start to saturate, and then the frequency

plunges. I was interested not only in whether it will start under

disturbed conditions; I also wanted to verify that the circuit noise

is important to startup, and to learn exactly how this process unfolds

over time—the oscillator’s start-up trajectory, I suppose you’d

call it. And I wanted to discover the relationship between the tail

current required to sustain oscillation and the size of its resistive

load, and ...”

“Okay. Let’s see. Oh yes! I felt it would be a good idea to further

minimize the unknowns by using ideal bipolar transistors. I knew

that, as long as the fundamental shot noise was modeled—and of

course the BJT’s beautifully straightforward transconductance—

then, including the realism of the complex full transistor model

would add nothing to help me gain the insights I was looking for.

So I set the junction resistances and capacitances to zero, and the

forward and reverse betas, as well as the forward and reverse early

voltages, to ininity. Everything else used default values; except that,

even though I wasn’t interested in exactly modeling the base charge

terms, I included a  F of a few picoseconds.”

“That leaves very little of the reality, Niku! Are you conident that

these drastic simpliications can be justiied?” asked Leif. But he

was not frowning, only putting her to the test.

“Yes, I think so. Originally, these experiments were intended to

demonstrate only that an exactly balanced, noise-free oscillator

will not start up when the tail current switches on suddenly, even

if its rise time is less than the tank period, and even without any

load. I also had a hunch that it wouldn’t start up if I introduced a

deliberate imbalance, provided the rise rate of the tail current was

below a critical value, which I wanted to quantify; and certainly

not with a load resistance below a critical value across the tank. By

the way, I could have used two equal and separate tanks as loads,

but that would introduce one more capacitor and another degree

of freedom in the behavior.”

“Good thinking. So, how did you upset the perfect balance?” asked

Dr. Leif.

“I just altered the relative size of one of the transistors, using the

SIZE parameter,” she explained. (Note: Although GE8E is a far cry

from SPICE, a surprising number of its commands, variable names,

and other parameters can be traced to that earlier era.) “And, Dr.

Leif, I wanted to add that as these studies progressed, the circuit

opened up its many secrets to me; and I was glad I’d chosen to

use primitive models because, even with these, there were times

when I had to think hard to explain what was going on. It’s safer

to add in the additional reality of the full transistor model in small

steps. Then you can see precisely at what point some puzzling new

phenomenon irst appears.”

“Yes, many of us appeal to that paradigm, particularly when we are

exploring a novel cell topology. It was called ‘Foundation Design,’

about 50 years ago, by one of ADI’s Fellows. Well, now that you

have whetted my appetite, Niku, tell me: How did you start your

journey, and what did you discover irst?”

“The irst thing I did was to demonstrate that the application of a

10-mA tail current, I E , having a 1-ps rise time, would never start this

perfectly balanced oscillator under any of the conditions I tested.

Of course, such a shock probably would be the primary reason for

startup in a real circuit, which is always unbalanced, to some degree.

But bias currents don’t appear this quickly!”

“Now, from what you are telling me, I gather you are running GE8E

in its primitive mode, as a SPICE emulator; because none of today’s

circuit simulators will nicely leave such an oscillator circuit in its

meta-stable condition. By the way— why is that?”

“Oh, I know what you’re getting at! Yes, that’s correct. I chose to run

the initial simulations in the old SPICE mode because I wanted to

temporarily eliminate real-world noise processes.The SPICE-based

simulators of, say, 2005 could predict small-signal noise values quite

well, provided the device models were correct. However, SPICE

only ‘knows about’ noise in a numerical sense, and merely handles

the math to add up all the numbers. It has no idea about noise as a

process in time —it does not treat the noise mechanisms in the various

elements as a set of time-stochastic variables , whereas GE8E does.”

TO MINIMIZE THE INTRODUCTION OF

DISTRACTING COMPLICATIONS OF THE

KIND FREQUENTLY ENCOUNTERED IN

PRACTICAL OSCILLATORS, Q1 AND Q2

ARE INITIALLY ALLOWED TO BE “IDEAL”;

THAT IS, BF = BR = VAF = VAR = INF. AND

THE DEVICE RESISTANCES AND

CAPACITANCES ARE ZERO; T f = 10ps.

LIKEWISE, FOR THE INITIAL EXPERIMENTS,

THE TANK IS ASSUMED TO BE LOSS-LESS

AND WITHOUT A LOAD.

I E IS TURNED ON VERY RAPIDLY, AND THE

CONSEQUENCES ARE OBSERVED FOR A

VARIETY OF CONDITIONS, WHICH WILL BE

ELABORATED ON IN DETAIL DURING

FURTHER DISCUSSIONS WITH DR. LEIF.

Figure 1. Niku’s First Basic Experimental Oscillator.

Note that the only “supply” is the current I E , further

minimizing sources of enigma.

10nH

10pF

I E

“Niku! Whoa!” said Leif, again looking rather serious. “Are you

aware that you have set forth a series of studies—solely for your

own enlightenment and pleasure—on a complex topic that others

have regarded as a suficient basis for a thesis degree?”

“Oh, not really. I didn’t expect these virtual experiments to take

very long, using GE8E. As it turned out, these studies brought to

my attention a long, connected sequence of questions, as I saw

various effects coming into play—some quite puzzling at irst—and

I wanted to explain them all. I have written them up, in case anyone

else might be interested,” said Niku.

“I have no doubt of that! May I put your name into our schedule

of Daedalus Days?”

“What’s a ‘Daedalus Day’?” she giggled.

“Oh, I don’t want to break your train of thought right now, but we

will certainly get back to that, sometime,” said Leif.

Analog Dialogue Volume 40 Number 1

“Precisely! Good. I assume that you used tight convergence

tolerances to ensure the simulator wasn’t simply stuck inside a broad

numerical tolerance range. And I guess you chose 10 mA simply

as a representative tail current for this type of oscillator. Okay, so

at this juncture, you felt justiied that those ‘start-by-spike’ fellas

were incorrect?”

“Oh, no; it was just the irst step. I really wanted to demonstrate that,

in practice, the noise voltages across the tank at resonance would

be the more signiicant source of disturbance, and that in a real

circuit, with or without mismatches, noise is the root cause of the

start-up trajectory. In fact, during my CyberFind studies, I turned

up an article in Analog Dialogue about this, going back to 2006. It

was very helpful. But I had to ind out for myself.”

Leif smiled with a mixture of approval and growing affection for

this unusually curious and perceptive young mind.

“My next step was to introduce a 20% mismatch, equivalent to

about 5 mV of V BE difference, by giving Q1 a SIZE factor of 1.2

and again pulsing the tail current. Clearly, if this current appears

very rapidly, with a rise time similar to the oscillator’s period, it is

bound to generate a voltage change across the tank, and even the

slightest disturbance will get things going. So, I thought it would

be interesting to ask how large that voltage would be.”

Her mentor struggled to be ready with a quick calculation, in

case Niku asked, “Do you know what I found?” Alas, it wasn’t

immediately obvious to him how to igure it out.With his eyes loosely

closed in concentration, he could have been asleep.

“Dr. Leif? I said, ‘Do you know what I found?’”

“Well, let me see now,” he replied, still not having the answer he

had hoped would come to mind. “The amplitude of the initial

step of differential voltage across the tank, labeled V OUT in your

sketch, must be proportional to the step in tail current, I E , and to

the 20% mismatch—which gives us a factor of 0.2 times I E for the

current step into the tank, which is 2 mA. But then, the load resistor

complicates things ...”

“No, wait! The difference current is [(1.2/2.2) I E – (1/2.2) I E ], and

that’s only 0.909 mA,” she corrected him. “And remember, these

initial studies assumed an open-circuit tank. Also, my idealized circuit

assumed no other losses in the tank inductors, the capacitor, or

the transistors. But I reduced this to an even more basic question.

Setting aside the active circuit, and the effect of its power gain, what

happens if an almost instantaneous step of current is applied to an

LC tank? What is the voltage waveform just after t-zero? And since

there is no damping, that question is equivalent to asking: ‘What

is the amplitude of the undiminished ringing, a true oscillation at

1/2p√(LC) in the tank voltage?’”

The situation was suddenly reversed. Leif was likely to have said,

“I dunno. What is it?” even if he did know; he understood that the

art of teaching must necessarily involve a great deal of humility,

and allow students to feel the full glow of their proud discoveries.

But the fact was, today he didn’t have a clue. He honestly replied,

“Niku, you have a way of asking the darnedest questions! This one

is simple, as are all the best questions; but it’s not one I’ve thought

about before. Classically, it would be solved by using Laplace

transforms. But experience teaches us that there are often more

direct ways of seeing ‘What Must Be,’ just by thinking about the

Fundaments.”

There was that word again. “I have to tell you, Dr. Leif, that it was

your passionate concern for what you call the Fundaments that most

excited me during the interview! I want to spend my life thinking

afresh about the Fundaments, as it is evident you have.Well, I confess

that at irst I cheated! I used the simulator, and this is what I found.”

Niku pulled up a waveform on her PDA, showing what happens

when a current step of 0.909 mA with a 1-ps rise time is applied

to a parallel tank of 20 nH (that is, L 1 + L 2 in Figure 1) and 10 pF

( C T ). The voltage immediately assumes a steady sinusoidal form,

with a continuous amplitude of 40.65... mV (top panel, Figure 2).

Furthermore, over many periods, the amplitude remains within

much less than one part per billion, at 40.651715831... mV.

–10

–20

–30

–40

V(OUT)

–50

V(OUT)

40.6517162mV 40.6517154mV

PERIOD 2.81ns, FREQUENCY 355.88MHz

40.6517165

40.6517164

40.6517163

40.6517162

40.6517161

AMPLITUDE = 40.65171583mV

40.6517160

40.6517159

40.6517158

40.6517157

40.6517156

40.6517155

40.6517154

40.6517153

40.6517152

40.6517151

40.6517150

100

TIME (ns)

Figure 2. Result of applying a sudden step of current of

0.0909 3 10 mA directly to a tank of 2 3 10 nH and

10 pF. Niku’s calculated amplitude is 40.65171583 mV.

The vertically expanded trace (lower panel) showing

the tips of the sine wave fully validates her theory. The

added marker lines are at 6 1 part per billion. This result

incidentally illustrates the excellent conservation of charge

provided by the GE 8 E simulator.

“GE8E gave me this result in less than a second,” Niku enthused,

“but my immediate instinct was to ask: ‘Where does this funny

number come from?’ It implies that the tank presents a rather low

impedance of (40.651... mV/0.909 mA), or 44.72135955... V,

which is just another funny number. But doesn’t a parallel-tuned

tank exhibit an ininite impedance at resonance? And this tank was

manifestly resonating in response to my stimulus!”

“Excuse me, Niku, but my TransInformer has just reminded me of

a meeting, so I’m afraid I will need to leave in a few minutes. But

before I go, I would like to say something about this notion that

using a simulator is ‘cheating.’ Mathematicians once used to scorn

‘numerical methods’ as a way to gain insights, or to prove theorems.

And any engineer who relied on ‘computer-aided design’—in other

words, simulation—to gain an understanding of circuit behavior was

regarded by some as weak-minded and poorly equipped. But for

decades we have viewed such methods in a very different light.

“Circuit designers once had to rely entirely on mathematics—and

on their slide rule, pens and paper, and erasers—working through

the night, fueled by endless cups of GalaxyBusters, because that

was the only way of getting all the calculations done—like the way

in which our transmobiles used to have four wheels and an engine

that bravely managed to convert tens of thousands of explosions per

minute into forward motion at 150 kilometers an hour on the old

nonautomated MainWays. We simply didn’t have anything better

back in the 20th century.

“But we grew out of these things. Today, we no longer speak of

computer- aided design, because so much of the old drudgery of

calculation and optimization is managed by resourceful systems

like GE8E.The equations in a modern simulator represent, in every

important respect, an almost-perfect analog of the reality—whether

a new molecule, a space elevator, or a clever circuit—and this

allows us to examine numerous boundaries and optima to serve

the immediate needs, while at the same time allowing us to gain

(continued on page 22)

Analog Dialogue Volume 40 Number 1

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