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Up a Notch: The Power of Marginal Gains

Now rarely seen on television, the celebrity-chef Emeril Lagasse could once incite audience delight by declaring he was going to “kick it up a notch” by throwing a pinch of his trademark “Bam!” seasoning into the food he was preparing. While not clear just where these “notches” were, he was talking about an incremental improvement, a slight enhancement to what was certainly an already-tasty and nutritious dish.

Similarly, one often hears an athlete vow to “up his game” by implementing a series of small changes to his diet, workout routine, equipment, or skills practice. Some of these seem almost-laughably minor: an Olympic swimmer shaving his legs to minimize drag, runners wearing close-fitting clothing to reduce air resistance, and competitive bicyclists wearing Spandex for the same purpose. And so forth. How could such small changes be important enough to bother with? The short answer is that they’re not–by themselves–but cumulatively they are. They either add up or multiply to make meaningful improvement.

Spice in food and small changes in habits and methods are examples of what system analysts and statisticians call marginal gains. How they impact a system is related, in part (and paradoxically), to chaos theory: small changes can result in accumulating knock-on effects in a non-linear universe (such as the one we live in). Phenomena of this sort was first explored mathematically by Edward Lorenz in the 1950s in connection with weather modelling and prediction. In an older and more colloquial vein, the well-known cautionary nursery rhyme about a dispatch rider in a battle conveys a similar idea:

For want of a nail, the shoe was lost;
For want of the shoe, the horse was lost;
For want of the horse, the rider was lost;
For want of the rider, the battle was lost;
For want of the battle, the kingdom was lost;
And all from the want of a horseshoe nail.

And, of course, we all know at least one person whose life has become a total disaster after a concatenation and multiplication of seemingly-casual fuck-ups leading to still worse ones: lost jobs, bankruptcy, jail, and estranged families.

So how does all this relate to amateur-radio engineering? Another way of asking that is: can radio systems–transmitters and receivers–benefit from marginal gains? Certainly, and the better ones do. That’s one of the reasons why they’re better. For radio systems in mission-critical applications in aerospace and in the military, some of the gains are marginal indeed. Read a few Mil-Spec documents and you’ll find out just how minor some requirements are. You may say, “Sure, but that’s bloated, hundred-dollar-hammer stuff. The kind of pork-barrel excess paid for by deep government pockets. The rest of us get our hammers at Ace Hardware.” Okay, but as it turns out those who bet their lives on critical hardware don’t want any of it coming from the hardware store. They know how things can go sideways when small things are neglected. It’s only a slight exaggeration to say that such specifications were literally written in blood.

But aside from critical links in a chain (such as the horseshoe nail), there are also either improvements or detriments that can add up or detract from the end goal: the quality and reliability of the radio signal. To employ yet another metaphor, consider the effect of compound interest on the value of an investment. The gains aren’t linear, they’re exponential. The same is true of the effects of price inflation: higher costs drive costs still higher in an exponential spiral. For our amateur-radio technology, we want compound interest rather than inflation, don’t we?

This article is the first in a series of Up a Notch posts. Subsequent posts will be more concrete and less metaphorical. They will address the following and more:

  • Use better components with tighter tolerances, lower temperature coefficients, higher Q, lower noise figures, and higher reliablility.
  • Use better circuit topology with such measures as putting chokes on DC power and bias circuits, keeping resistors out of direct signal paths, using good DC decoupling, proper bias on active components to prevent overdriving subsequent component and circuit elements.
  • Do a better job matching impedances. Not only does this improve the transfer of RF power, it also minimizes reflections that can lead to intermodulation distortions and reduced dynamic range. Some circuit elements–such as crystal ladder filters–are virtually unusable without proper matching.
  • Add often-omitted system elements such as diplexers, power-supply filters, audio-tone adjustment, or active audio filters.
  • Elaborate on already-included elements. For example, use a third-order filter instead of a second-order one, or add an additional stage of amplification to minimize noise generation from too-much gain in earlier stages).
  • Shield against noise and interference. This can be overdone, of course, but it’s often dismissed entirely with “it seems to work fine without it.” Working “fine” is fine, but “better” is better.

Next post: Up a Notch: Use Better Components–Resistors

 

Up a Notch: Use Better Components–Resistors

Gertrude Stein by Pablo Picasso

In her 1911 poem, “Sacred Emily,” Gertrude Stein wrote “A rose is a rose is a rose.” Ridiculing that absurdity, for the 1952 musical “Singin’ in the Rain,” the lyricist Adolph Green wrote that “Roses are what Moses supposes his toes is.” So here’s another absurdity: a resistor is a resistor is a resistor. But is it? Au contraire, mon frère!

To begin with, nearly every electronic component is also every other one–a resistor is also a capacitor and inductor, an inductor  has both resistance and capacitance, and a capacitor has parasitic inductance and equivalent series resistance. Transistors can’t avoid having inductance and capacitance, and to an extent that ultimately limits the device’s frequency response. Here’s something every component is also: a noise generator. All those atoms and molecules vibrating and slamming together whenever their temperatures are above absolute zero (that is, all the time) creates noise, noise, noise. It’s not just that they’re picking up external or even cosmic background noise, but each creates its own thermal noise, sometimes called Johnson (or Johnson-Nyquist) noise. There’s also current noise (more on this later).

A-B carbon-composition resistors

With regard to resistors, some types have more thermal and current noise than others. Carbon-composition resistors, such as the classic Allen-Bradley brown-body types, are the noisiest of commonly-available varieties. They were most often made with 10% tolerances. In general, they’re not used much any more, but they still live in many a Ham junk box.

Their resistance values were determined in manufacture by the size of carbon grains and the degree to which they were compressed. Variation in the grain size and random arrangement was the cause of their relatively-high noise figures.

It’s worth noting that the structure of carbon-composition resistors is very similar to carbon-microphone elements, so it’s not surprising that in addition to the genera-tion of higher levels of Johnson-Nyquist and current noise than other resistor types that carbon-composition types can also exhibit a microphonic effect and pick-up ambient vibration.

Carbon film resistors have taken the place of carbon-composition types as the garden-variety resistor in most commercial and industrial applications. They typically have tolerances of 5% and they’re available with a variety of thermal characteristics. They are manufactured by depositing carbon crystals on a ceramic core at high pressure and temperatures. The deposit is fairly (though not perfectly) uniform and, unlike carbon-composition methods, it contains no binders. For these reasons, they generate much less noise.

Carbon-film resistors are trimmed to value by cutting a spiral in the film. Here you see one source of the resistor’s parasitic inductance.

—–Carbon-film resistors even look like inductors, don’t they?

It’s important to remember, though, that the parasitic inductance is dominated by the resistance, and that as an inductor it has an extremely-low Q. That same is true, by the way, of a wire-wound resistor made with resistive wire such as nichrome or manganin. That is, it’s not worth a damn as an inductor even if it can be measured to have a few μH of inductance.

The best and quietest generally-available resistor type uses a deposited metal film as the resistive element. Its structure looks very-much like a carbon-film resistor.

Because metal deposition can be more-precisely controlled and the resulting deposit more precisely trimmed, metal-film types can be more-cheaply made to precise values and tolerances. They are, in fact, sometimes called precision resistors. More to the point here, because their metal films are more molecularly-coherent than carbon films, they’re a lot quieter in terms of both Johnson-Nyquist noise and virtually free of current noise. Here’s a graph that shows current noise as measured from 10KΩ resistors of several technologies:

from Youhei Miyaoka and Minoru Kuribayashi Kurosawa, “Measurement of Current Noise and Distortion in Resistors,” in Proceedings, 23rd International Congress on Acoustics (2019)

It’s not surprising that a trimmer resistor is the noisiest of all, followed closely, though, by carbon composition and carbon film. Note that you’ll find metal film (the dark-blue trace) way in the far lower-left-hand corner. The difference between the carbon types and the metal types is very striking.

Given the outstandingly-low noise performance of metal-film resistors, though it’s best not to but if you must put a resistor directly in a signal path (instead of their peripheral use for biasing and current limitation), use metal-film types.

An additional benefit of metal-film resistors is that the 1% (“E96”) series of resistance values contains almost five times the number of values than the 5% (E24) series used for carbon-film types. Each series consists of base values from 1.0 to 9.9 which are then multiplied by orders of 10 (x10, x100, x1000, etc.). Here’s the E24 (5%) series:

1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1

and the E96 (1%) series:

1.00, 1.02, 1.05, 1.07, 1.10, 1.13, 1.15, 1.18, 1.21, 1.24, 1.27, 1.30, 1.33, 1.37, 1.40, 1.43, 1.47, 1.50, 1.54, 1.58, 1.62, 1.65, 1.69, 1.74, 1.78, 1.82, 1.87, 1.91, 1.96, 2.00, 2.05, 2.10, 2.15, 2.21, 2.26, 2.32, 2.37, 2.43, 2.49, 2.55, 2.61, 2.67, 2.74, 2.80, 2.87, 2.94, 3.01, 3.09, 3.16, 3.24, 3.32, 3.40, 3.48, 3.57, 3.65, 3.74, 3.83, 3.92, 4.02, 4.12, 4.22, 4.32, 4.42, 4.53, 4.64, 4.75, 4.87, 4.99, 5.11, 5.23, 5.36, 5.49, 5.62, 5.76, 5.90, 6.04, 6.19, 6.34, 6.49, 6.65, 6.81, 6.98, 7.15, 7.32, 7.50, 7.68, 7.87, 8.06, 8.25, 8.45, 8.66, 8.87, 9.09, 9.31, 9.53, 9.76

Obviously, it will be much easier to find close to the exact value you need in the 1% series than the 5% series. In most cases, such precision serves little purpose, but in some it does.

Fortunately, the tighter tolerance and lower noise of metal-film resistors come at a surprisingly-inexpensive price. All resistors for mass-produced commercial and industrial use are cheap as dirt, and metal-film types are only slightly-more expensive than carbon-film ones.

Here’s the Digikey price for 100 pieces of a 1KΩ, 1/4W, 1% metal film resistor from Yageo (a major manufacturer):

As I said, dirt cheap at less than 2¢ in 100-piece lots. By the way, here’s a piece of advice: don’t buy in quantities smaller than that.

Finally, if there’s one underlying rule that applies to the use of better components, be they resistors or of any other type, it’s that you should buy from a major supplier and not from unknown sources. In most cases, there’s no problem of actual counterfeiting. The problem comes from the fact that the source is unknown. A great deal of what’s sold on Amazon or eBay are from either stock surplus or buyer-rejected lots of parts. The surplus sources aren’t necessarily bad, but there’s no way to distinguish between legitimate surplus of good parts and components rejected by an OEM manufacturer for whatever reason (out of tolerance, failure of reliability [MTBF] tests, etc.).

You’re an amateur building one-off projects with no profit motive behind them. You don’t have to use extremely-cheap parts when known-quality components from major suppliers are cheap enough.  – – . . .   . . . – –

Sources and further reading:

EETimes, Selecting Resistors for Preamp, Amplifier, and Other High-End Audio Applications

Cermet Resistronics, Carbon Film vs. Metal Film Resistors

Wikipedia, E Series of Preferred Numbers