May 2013

Resistors
Once upon a time, the tolerance of resistors was an issue.
Article By Grey Rollins

  My interest in electronics began at an early age. The folks who lived diagonally across the street from our family would throw out old pieces of stereo gear that no longer worked. Now, you could argue that perhaps they should have paid a little more so as to get higher quality equipment that wouldn't fail so quickly, but I'm grateful that they didn't. As soon as I saw the tell-tale glint of sun on metal and plastic by the road, I would scuttle across the road as fast as my eight year-old legs would carry me to claim my new prize. I would take it apart and stare at the multi-colored parts for hours, trying to figure out how it worked. I stood no better chance than an alien attempting to make sense of a square dance, but that didn't stop me.

Time passed and I learned to distinguish between resistors, capacitors, inductors, transistors, and tubes (this was a while back). I even managed to gain some sense of how they did what they did, but the ways and means of hooking them together was far from self-evident. Why was there an inductor there instead of a resistor? Why were there so many resistors and so few caps? Why would the signal suddenly take a left-hand turn, only to rejoin the rest of the signal further on?

Mysteries. More mysteries. Always mysteries. Riddles wrapped in enigmas with a side order of What The Hell Were They Thinking?

With no one I could ask questions of and no money to buy books (which weren't available in the town I lived in, anyway), it took quite some time to piece the story together. These days you can find all sorts of things on the web, but this was pre-PCs, pre-Web, pre-pretty much everything that people take for granted these days. Suffice it to say that my learning path was far from linear. I had to make up my own explanations — ones that made sense to someone who was still learning basic math. Fortunately, the basics aren't all that hard.

Imagine, if you will, that electrons are bowling balls. Suppose the objective is to get these bowling balls over a hill. There's a nice, smooth, paved road, so we won't have to worry about hitting trees or plopping into a stream, but still, there's that hill to contend with. Gravity and friction will work against you. It's not perfect, but let's use the hill as an analog for a resistor.

Resistivity
The steepness of the slope corresponds to the resistivity of a conductor. Some things conduct electricity better than others. A piece of copper wire has low resistivity; electrons flow through it readily. The carbon in the old composition resistors that I was so fascinated with as a child had much higher resistivity. Any conductor that you can force an electron through has resistivity. (We're going to ignore superconductors for the time being, as they aren't yet practical for use in ordinary electronic circuits.) There are tables that show the resistivity of every conductive material you've ever heard of and even a few you haven't, but for present purposes we'll simply accept that most resistors that we're likely to face in audio use incorporate metals and since one of the defining characteristics of a metal is that it conducts electricity, then it's not too hard to imagine that we can vary the resistance of the finished resistor by choosing one metal (or metal alloy or metal compound) over another.

The length of the slope on our hill also factors into the equation. If the slope is gentle, but the road is long, you'll still have trouble getting the bowling ball over the hill. If the way is short, then the steepness becomes the determining factor. In like manner, the length of the conductive element inside a resistor helps determine the resistance of the resistor.

Suppose that several buddies decide that this new hobby of rolling balls over hills sounds like fun and decide to play alongside one another. If there are enough people trying to roll balls up the hill at the same time, the road will not be wide enough to accommodate all those balls, and that will create problems. Conductors are prone to the same problem, so we'll need to account for the area available for rolling balls as part of the analogy. Bear in mind that wires, at least as far as electrons are concerned, have two dimensions instead of the one-dimensional flat roadway. That helps create more space for electrons to pass through, but the basic idea still applies. We're pushing the limits of the hill-and-ball analogy; best to stop before it breaks down entirely.

With these factors in mind, we can see how the resistance of a resistor comes about:

R = ρ (l/A)

Where:

R = the resistance

ρ = the resistivity of the conductor (that's the Greek letter rho, if you want to be formal about it)

l = the length of the conductor

A = the cross sectional area of the conductor

Now, no one expects you to roll your own resistors, but the formula helps to visualize things like why larger diameter speaker cables have lower resistance than smaller cables.

Other Factors And Considerations
There are other things we'll have to keep an eye on, the most important one being the wattage rating of the resistor. An electric current flowing through a conductor will create heat proportionate to the current and the resistance. To a first approximation, the wattage rating is simply a measure of the physical size of the resistor's body. Think of the body of the resistor as a heat sink. The more surface area, the more heat it can radiate. The cooler the resistor, the less likely it is to melt or burn...and yes, this spec matters, so don't try to cheat. As a rule of thumb, don't run a resistor over half its rated wattage — by the time you reach the rated wattage the resistor is very hot. Hot enough to burn you if you touch it. At half power, it'll still be warm to the touch. The further below the rating you are, the better.

Incidentally, resistors also have voltage ratings, but that will rarely be a problem with solid state equipment. If you're building a tube circuit, you should be okay as long as you stick with ½W or higher resistors. Be careful about using 0.25W resistors in high voltage circuits.

And while we're at it, note that MILSPEC resistor's wattage ratings are conservative. If you buy a 0.5W "normal" resistor and a 0.5W MILSPEC resistor, the MILSPEC will be twice the size of the normal one. A MILSPEC 0.25W resistor is equivalent to a normal 0.5W resistor for our purposes; they are essentially the same size.

Once upon a time, the tolerance of resistors was an issue. Companies routinely used 20% tolerance parts (no, that's not a typo) and reserved 10% or 5% parts for particularly critical parts of the circuit. These days, it's practically raining 1% resistors and they are perfectly adequate for our purposes. The price is reasonable, so don't fret about the cost. There are resistors with even tighter tolerances, but 1% parts are overkill for all but the most finicky audio applications.

One of the nice things about 1% resistors is that they frequently have the values printed on them. This removes a lot of ambiguity. For some reason, many manufacturers persist in using reds that look remarkably similar to their browns and blues that look a lot like grays. Assuming that the ink is dark enough to read (the printed resistor value system isn't perfect, either) there are a couple of points to keep in mind:

It takes three significant digits to render a 1% resistor's value, so the first three digits of 1000 tell you that it is 100 somethings, and the fourth digit, which is also zero in this case, tells you that there are no zeros to be added to the end, so it's a 100 Ohm resistor. If the resistor reads 1001, then that's 100 with one zero after it, hence 1k. Following the same set of rules, 6811 is 6.81k; 6, 8, and 1, followed by one zero. Note that there are 96 values in the usual 1% scale (called E96) and while some of them are close to the more familiar E24 value system, others tend to vary a bit. For instance, 47K becomes 47.5k, 2.2k becomes 2.21k, etc. Don't let the differences spook you. If you're building a circuit that requires such precision that the relatively small divergence will make a difference, you'll probably end up choosing another E96 value or using a pot to trim the circuit in situ.

Reading A Resistor's Value
For smaller values — those below 100 Ohm — you will see an "R" where the decimal would normally go. Little bitty dots tend to get lost, whereas a nice, fat R is an unambiguous way to separate the ones from the tenths.

Not all manufacturers use printed numbers, so it's not unusual to see resistors with color bands. The color code has not changed since cavemen walked the Earth:

Black = 0

Brown = 1 (or 1% when used as a tolerance band)

Red = 2 (or 2% when used as a tolerance band)

Orange = 3

Yellow = 4

Green = 5

Blue = 6

Purple = 7

Gray = 8

White = 9

Gold = 0.1 when used as a multiplier, 5% when used as a tolerance band

Silver = 0.01 when used as a multiplier, 10% when used as a tolerance band

So a Brown, Black, Black, Brown resistor is going to be 1k, but be aware that there will be one or more additional color bands to indicate tolerance and possibly other characteristics. To help determine which band is the first one, look for the band closest to an end of the resistor body. If one band is widely separated from the others, it's probably tolerance or some other characteristic; start at the other end. If the manufacturer was sloppy in putting the color bands on, they may be more-or-less equidistant from both ends of the resistor body. If you find yourself getting confused as to where to start, whip out a meter and measure the confounded thing. For the record, I prefer the printed nomenclature, but if you like colors, go for it.

What The Future Holds...
Ten thousand years from now, they will dig up records that well-meaning archeologists will interpret as meaning that the internal components of resistors were at the core of rival religions. They won't be far wrong. Thin film, thick film, wire wound, metal alloy, metal oxide, carbon, tinned steel leads, copper leads, silver leads...people get passionate over this stuff, claiming that one sounds better than the other. I will say that I've heard some components that sound audibly better than others, but rather than risk starting a war, I will simply say that if a resistor is the right value and is operated within its voltage and wattage ratings, then any circuit you build with it will work well. Once you've got your circuit up and running, you can try substituting parts to see if you can tweak the performance. When in doubt, go with metal film resistors. That's what most of the people (including most manufacturers of high end audio gear) use most of the time and there are many, many fine audio circuits out there built with metal film resistors.

If you're going to be using a resistor in a high power application, it's a good idea to mount it up off the circuit board. The wattage ratings for resistors assume that the resistor has good air circulation on all sides of the part. If, in your circuit, the resistor is mounted snugly against the PCB, then that tends to restrict air flow under the resistor, thus reducing the amount of heat it can safely dissipate. You don't have to go crazy about it — a few millimeters will go a long way towards dissipating heat. It won't be as good as free-air dissipation, but it's a lot better than mounting it tightly against the PCB.

High Heat
Examples of potentially high heat situations would be emitter resistors in the output stage of power amplifiers and resistors in passive crossovers in speakers. Incidentally, a neat trick for speaker crossovers — assuming that your speaker design has a port — is to place the crossover where the air moving through the port will play across the crossover. The louder the music is, the more heat the crossover will produce, but at the same time, more air will move through the port, cooling the resistors. Automatic cooling for free! This is not an excuse to replace a 20W resistor with a 10W resistor, but it will help keep the operating temperatures down.