Is this real? Are Carbon Comps really magic tone mojo?

Maybe. Like everything else, there's the hype, and then there's the real world. A good maxim to remember about electronics is that if you can't express it in numbers (that are also measurable by someone else, not just made-up numbers... there are those around too 8-) then you really don't know the thing at all, you're only believing the myth.

The vintage amps we all love had CC's in them, and they certainly have their share of mojo, but the makers of those amps in the 50's and 60's used them because that's what was available. Today we have lots of resistor options. What's different about carbon comp, and can we express it in numbers so we don't keep being superstitious?
 
So I went to the internet and searched for manufacturer's info on CC's. The makers themselves admit that carbon comps have excess noise, high drift, high pulse power, and high variability. They also have a high voltage coefficient of resistance. Voltage coefficient of resistance?? What's that?
 
That means that the resistance actually varies with the voltage across the resistor. The resistance is actually different if you put 100V across the resistance than if it's got 0V across it. What that means to us is that if you put a 50V DC level across a CC resistor and a 100V sine wave superimposed on that, the sine wave will be measurably distorted by the resistor itself. We have resistor distortion.
 
The distortion is pretty much pure second harmonic. In small amounts, you can't hear second harmonic as distortion, only a certain amount of "sweetening" or liquidity to the tone. That's what carbon comp resistor mojo really is - the resistors are distorting, but in a way our ears like.
 
The manufacturers also document that CC's have excess noise and bad drift with temperature and aging. That makes them a two-edged sword. Put everywhere in an amp, and they'll both sweeten the tone, and at the same time induce hiss. A little thought leads us to the following guidelines for using carbon comps for tone mojo:

1. high voltage across the resistor is necessary, in the range of 100V on up
2. large signal swings across the resistor are needed - ideally, a large fraction of the static DC voltage so you have signal swings of 50 to 100V too.
3. only positions in the amp that have both high DC voltage and wide signal swings as in 1 and 2 will give you enough resistor distortion to benefit from; other places should be chosen for low noise and/or economy.
4. resistor power rating should be the minimum needed to work for a reasonable life in the circuit to maximize resistor distortion. Maybe a good guideline is that the dissipation should be selected to be as close to two times the average dissipation as possible.
5. as a corollary to the power guideline, we should be prepared to replace CC's every few years as the life at high temp makes them drift and get noisy(-er).

Guidelines 1 and 2 are simply the recognition that the voltage coefficient of resistance is not very big. In fact, although the coefficient is small, it was specified to be small by the makers and controlled tightly, indicating that it was a recognized problem. In the Radiotron Designer's Handbook ( 4th edition, pg. 1345) they list the JAN-R-11 specification for CC resistors as less than 0.035% per volt for 1/4 and 1/2W resistors, and 0.02% per volt for higher power ratings. Given that the max voltages for these parts was 1/4W- 200V; 1/2W - 350V; 1W and 2W - 500V, that works out to a 7% change in resistance for a 1/4 W part used at its max voltage, a 12.3 % change for a 1/2W, and a  10% change for bigger resistors. That's one of the thrusts of guideline 4 - pick the smallest dissipation resistor you can, to maximize the coefficient. 

Of course, that's as big as the effect can get, and you would have to carefully set up the situation to get that much resistor distortion. In an amp, you probably won't be able to get that close to max voltages or signal levels. Realistic levels might be 200V across a 1/2W resistor, and a 75V signal swing. That would give you a 2.6% distortion - enough to be audible as sweetening. That's the point of guideline 3 - you have to have a big enough signal swing across the resistor to have the signal distorted significantly by the voltage coefficient.

But with a 10V signal, you only get 0.35% distortion, and it starts down the slippery slope to inaudibility. More importantly, these percentages represent the maximum beyond which a resistor would have been rejected in the 1950's. Today's CC resistors are much lower distortion. From IRC's web site, we find some numbers. A typical resistor voltage coefficient can be seen at http://www.irctt.com/pdf_files/IBT.pdf - which shows carbon comp at 0.005%/volt for that company's products. Another was 0.008%/V. These are smaller than the max allowed under the JAN military spec.

So where do they work best? Where can we use CC's for their soft distortion, and where can we sidestep them to lower noise?

First, they do no good and lots of noisy bad where the signal level is small and the following amplification is high - a classical description of an input stage. The input to an amp should probably have a metal film plate resistor to minimize noise. Grid resistors in all but output stages also do no good, because the signal level is typically too low. A 12AX7 can be driven from cutoff to positive grid voltage with a couple of volts of signal, so the grid resistor never has a big enough signal to be distorted appreciably.

Cathode resistors are another poor use of CC. They typically only have a few volts across them, and they're often decoupled with a capacitor, both of which would minimize the resistor distortion. In cathode followers, there can be substantial DC and signal voltage across a cathode resistor, but in this case, the resistor is driven by the low impedance of the cathode, and the voltage across the resistor is controlled by the grid voltage very tightly, so the exact resistor value doesn't matter much - there won't be significant distortion. 

The place to use CC's is where there's big signal - plate resistors, and ideally the stage just before the phase inverter. The phase inverter would otherwise be ideal, with plate resistors carrying the highest signal voltage in the amp, but phase inverters are often enclosed in a feedback loop. The feedback minimizes the distortion  the resistor generates.

Use CC's sparingly - only where your personal ears tell you that they make a difference. 
 
I'm always amused at people who advertise putting carbon comp resistors in their 9V powered effects to give them some kind of magical vintage sound. Urban legend is tough to kill, though - and magic mojo always makes for dynamite advertising copy.

So now you know what's happening, and something of the numbers involved. The effect is real, though slight. 
 
R.G.