The Uncertainty Principle Page 2

First, the absolute level (or gain) varies by at least 1dB. This alone vindicates balance controls—even in the unlikely event that the loudspeakers are perfectly level-matched. More importantly, the variation in the population's frequency response around the reference curve in fig.2 is complex. The biggest variation is at least ±0.2dB, and some systems vary by more than ±0.5dB. Although it may be hard to see, there are also one or two "golden" units that have a flatter, therefore more accurate, response than the norm! Joe Smart always buys one of these, especially when the price has been knocked down to $50.

Fig.4 takes the scope of variability further into the real world by doubling all the close (below 10%) part tolerances to predict the effect of the gradual component value changes caused by long-term drift. These changes are accelerated by elevated operating (footnote 3) and storage temperatures, and are caused by diffusion and electrophoresic effects; ie, the migration of chemicals and ions under the prolonged influence of DC current flow. The variance picture is hard to see. MicroCAP's statistical routines can output variance bar-chart data, but qualifying this is outside the scope of this piece; see [2]. But we can see that three distinct response-curve families have developed in fig.4 between 100Hz and 1kHz, and that the net variation is clearly wider. In turn, the graph's span has been exactly doubled to 2.5dB to accommodate this.


Fig.4 Predicted lifetime frequency-response variation in 25 randomly selected systems. Note that vertical scale is now doubled to 0.5dB/division. The variance shown would be typical after several years' use.

Fig.5 looks at a different kind of tolerance, the effect of the components' temperature coefficients. These describe the rate of component value change with temperature. Again, the model is simplified, assuming a linear rate of change with temperature. This is true of good resistors [3] over the likely temperatures endured by hi-fi equipment (generally 25–85°C), but not perfectly true of most capacitors, excepting well-made polystyrene, polypropylene, and Teflon types [4]. Looking at the plots, the "micro" frequency response clearly varies as the equipment warms up—the LF response isn't much changed, but the mid dips while the mild HF rise flattens out. The difference between the "cold" and "operating-temperature" responses is an audible 0.25dB at 4kHz—this preamp will sound better as it "breaks in."


Fig.5 Typical variation in micro frequency response as the minimum disc replay system warms up, from 20° to 70°C. The intermediate temperature of 45°C would be more typical of "solid-state" equipment (0.25dB/vertical div.).

Loudspeakers are even worse than electronic components when it comes to the effect of temperature. A loudspeaker's voice-coil typically cycles between 20° and 200°C when driven by music. Its temperature coefficient is a huge 4000ppm/°C, meaning that its resistance nearly doubles over its operating range (ie, increases by 100%, equivalent to 6dB of variance). The tuning of a typical passive crossover could be quite different at high power levels from what it was specified to be at a typical 1W level.

Altogether, these variations in frequency response are just a convenient abstract of the whole picture, which includes the spread of transient response ("speed" and "dynamics"), of linearity (ie, distortion and the harmonic spectra, hence "timbre"; and intermodulation, hence "detail"), and of noise spectra (hence "ambience" and "depth")—to mention just a few.

At precision's edge
We know there are people who can clearly hear frequency-response differences of below 0.1dB [5]. Toward the low- and high-frequency extremes, where the unit-to-unit variability is most focused, the audibility of small differences will be exaggerated (footnote 4). With reasonably neutral loudspeakers, the kind of variations illustrated will—when set against what balance and performance defects we are presently used to—determine whether we judge the system to be "bright" or "dull," "articulate" or "authoritative," and so on. This applies less to owners than to reviewers, who have less time to strike up a relationship with a product.

A notable passage about audiophiles' questing for the sonic grail comes from the "Letters" column of Electronics World (footnote 5). A retired sound engineer wrote in 1986: "Ultimately, uncontrollable variations in manufacture result in what are, on a scale of perfection, gross differences between individual components..." So every unit will be slightly different.

But is this not true of all things in the universe? Excepting transient alignments, 100% conformity—with all the will and technology in the world—is bugged by the impossibility of 100% precision. In the real, competitive world, would-be king Conformity is cheated by people who pick out the best parts before the poor audio manufacturer gets to buy them, jostled by the random motion of molecules, undermined by the laws of entropy and chemical diffusion, then made uncertain by Quantum Mechanics. Finally, Conformity's mental processes are thrown into a self-similar illogical chaos as number theory disintegrates at the portals of infinite numeric precision! [6]

Ultimately, seeking precision willy-nilly is foolish; long before, it becomes explosively inefficient and expensive. To be realistic, we who care about fidelity in music reproduction can only concern ourselves with the scale of the variation and ask, on the basis of the latest psychoacoustic knowledge and listening experience, "Will it be enough to be audible—not just now, but maybe later?"

Ramifications of imperfect sameness
"They've all got better things to do / They may be false, they may be true / But nothing has been proved." (footnote 6)

The ramifications of tolerance concern everyone, but in different ways. As a QA-conscious manufacturer, I would have to pray that I was able to verify something the ear is quite fussy about by discovering the right objective test. Then I'd be worried about the extra cost of reworking units that failed the more exacting tests, and about the time taken to positively locate the part(s) causing the sonic variability. In the end, it comes down (in part) to employing sensitive humans who are able to couple their instinct and intuition to machines and objective knowledge. Today, automated test equipment like the Audio Precision enables manufacturers to accumulate performance data, but very little of this is ever seen.

As a reviewer, I would be concerned about the single sample. If both channels sound (and continue to sound) the same, that's a good start, and readers should be informed accordingly. To be sure, after getting used to the first sample, I would also like to hear at least three others, ideally with quite different serial numbers, or acquired randomly and incognito. In knowing the signature of the first unit, these would only require a brief listen by a well-endowed reviewer. The problem of progressive improvements made by the maker over time then arises. At the very least, I'd like to see some overlaid performance plots of a number of units, from the makers' QA department, to see how much they vary.

As an owner, I might, depending on personal psychology, worry that the unit(s) I'd purchased weren't typical or the best example. In an existing system, if both channels sound about the same (eg, listen in mono to each channel in turn), the main worry of a skewed stereo balance is cast aside. If not, untangling which units are causing the deviation, or which part of the deviation, is another story.

Before purchase, knowing about tolerance reinforces the need not just to listen yourself and preferably to "burn-in" components, but also to make sure that the unit you auditioned is the unit you take home. Seeing how operating temperature influences performance suggests leaving equipment switched on as much as possible when you are the owner, but not before. Y'see, after learning that temperature cycling increases the rate at which initial component tolerances spread (compare fig.2 to the greater spread in fig.3), you will now ask the poor dealer to please cycle the power on/off for a week before you accept the home listening trial!

The designer's challenge is not just to create stunning accuracy in reproduction, but also to have confidence in its repeatability and maintainability. In 1984, I wrote, "If we count the components inside each op-amp, there are around 350 in the signal path...and yet AMP-01 (an all-dancing, IC op-amp–based preamplifier) has so far outmaneuvered the folklore that the minimum number of parts is automatically the best, in the same way that a BMW overtakes a rickshaw on the road south from Kuala Lumpur." [7] A valid reason for manufacturers using op-amp chips as the principal active devices in audio equipment is the consistency such devices promise. Mere transistors, whether bipolar-junction transistors or FETs, are exceedingly complex devices, with more and more variable variables than the resistors, capacitors, and pots that surround them.

You may ask, if transistors are already complex, surely employing a complicated array of them in an IC just exacerbates the complexity? Well, first, IC design focuses on accepting large tolerance variations and on the special ability of monolithic parts to cancel out each other's variations. Second, large amounts of negative feedback and a high gain-bandwidth-product together force uniformity. Third, the Central Limit Theorem of statistics predicts a counterintuitive concept: that complex systems can end up more predictable than simple ones.

Conversely, the equations used to generate fractal patterns bordering on chaos are simple ones; the "never-quite-the-same" complexity comes from partial positive feedback. Simple tube circuits with high impedance nodes are susceptible to inadvertent positive feedback, and, with messy wiring, can exhibit high variability in production. If both channels sound different, what good is the minimum signal path? But even small amounts of negative feedback—which can be intrinsic to even allegedly "feedback-free" topologies—are highly effective at limiting the degree to which hi-fi systems' "tunings" can vary.

In my own designs I use not only precision, tightly QA'd op-amp ICs, but tighter-tolerance parts than the norm. I typically use 0.5 or 0.1% resistors with temperature coefficients of 15ppm, compared to hundreds of ppm for cheaper metal-film parts. But unless you make (or control the make-up of) complete systems, this is gilding a lily with a growth on its leaves: the owner's cable parameters, not to mention countless transducer tolerances, vary widely; worse, they're outside the electronics designer's control.

Footnote 3: Leaving gear on, for example. If this alarms you, note that the alternative is worse, as switching components on and off is associated with temperature cycling, which accelerates time-to-death or catastrophic change.

Footnote 4: Look at the Fletcher-Munson and related equal-loudness contour maps to see how the ear perceives a 4–5dB spl change as a doubling of loudness at 80Hz or 13kHz, compared to needing a 10dB change in spl at mid-frequencies.

Footnote 5: Founded in 1912 as The Marconigraph, later Wireless World, Electronics World is the world's oldest electronics journal, and has covered quality audio since the 1930s.

Footnote 6: From "Scandal," by Neil Tennant and Chris Lowe, given urgency by Dusty Springfield in 1989.

jimtavegia's picture

If we all felt smug about the quality of any of our audio gear, that all just went away. lol In a world constantly being flipped on its head lately, all we need was something else to think about going badly.

MontanaMontanaDana's picture

Very insightful information. But how does this translate to the listening experience for the average audiophile? I enjoyed the Goldberg Variations on my carefully selected and matched mid-fi system last night, and got completely lost in the music -- just like I do when I hear it on my friends megabuck system (presumably) constructed to close tolerances.
Guess I'm like the lady driving her kids to soccer practice in the SUV. So long as it gets me there, I don't care how.

jimtavegia's picture

Contentment. How to achieve it? I have learned since I began seriously recording over the last 15+ years there are so many hands in the soup that how can any one system be the "right system"?

I have learned to love what I have and get more into the music, but that is not to say that I don't have some clunker recordings, many in vinyl, that I just can't listen to anymore. I don't have a great system, but it is better, sadly, than most of the systems of my friends and acquaintances. That is a problem to me to think that audio quality is cared for so less today. I wonder if many midland audio gear owners really agonize over what they have purchased? Have they bothered to read the likes of Stereophile and get educated? Even if they just went to the internet sites of Stereophile, Analog Planet, InnerFidelity, or AudioStream they would be partially educated to all the possibilities of what makes a great playback system.

It is time to start steering some of my friends and acquaitences to doing some homework. Hopefully, some will.

Bogolu Haranath's picture

You could also recommend your friends and acquaintances to attend some of the hi-fi shows like AXPONA, RMAF, FAE, CAF etc. :-) ........

jimtavegia's picture

getting to and from these shows costs more than many have invested in their gear.

I just posed a YouTube video on my page on the 4 web-pages managed by Stereophile in hopes that some of my friends and acquaintances that view my FB page might take a look at and read some articles that might interest them and get them into the hobby in a bigger way. It was easy enough for me to do with my NCH Debut Video Capture software and get to more folks faster and hopefully motivate them to at least read about our hobby. The least I could do and one can learn much just from going to these 4 websites.

Ortofan's picture

... tube circuits without negative feedback are good while circuits using op-amps with negative feedback are bad?

Trevor_Bartram's picture

I seriously doubt tube circuits without negative feedback exist. Feedback is necessary to stabilize circuit bias and reduce distortion. I believe what you are alluding to is global versus local feedback. I bet tube circuits have local feedback. Op-amps by their very nature may only use global feedback.