1/4 vs. 1/2 Watt resistors

[Evil Hoodoo]

Sorry advance for the dopey question, but I was wondering if I should dial down the wattage spec on the resistors I use in my fuzz pedal clones (fuzzrite and fuzztone). I'm currently using 1/2 w but it would sure save a lot of space if I switched to 1/4w. The fuzztone is 1.5v and the fuzzrite is 9v. Thanks.

[blooze_man]

1/4 watt will work just fine.

[Unkn0wn Art1st]

Hmm. Which ones sound better? Perhaps the situation is similar to the thickness of the wire - the thicker the better? Ha.

[Evil Hoodoo]

It's not so much a question of sound but failure down the road. Just wondering if 1/4 watt will be high enough a power absorption.

[slacker]

If you do a bit of maths you can find the answer

Power = Voltage²/Resistance so Resistance = Voltage²/Power

If you assume your stompbox is running off 9 volts then that's that maximum voltage any resistor can have across it, so using 0.25 Watt for Power you get.

9²/0.25 = 324

This means a 324 Ohm resistor with 9 volts across it is drawing 0.25 Watts so any resistor bigger than 324 Ohms can be 1/4 Watt. In practice most resistors in a stompbox won't have the full 9 volts across them unless something goes horribly wrong so 1/4 Watt is fine for all resistors.

[R.G.]

Good answer, slacker. Correct.

One final bit of sophistication: derating for long life and reliability. Power rating is intended to tell you how much heat the part can dissipate and not burn out for an indefinite - but relatively modest - period of time. A 1/4W resistor can dissipate 0.25000 W continuously without burning up, for minutes, hours, maybe days. But it will have an increased likelihood of failure in months and years compared to a 1/4W resistor that dissipates 0.125W, which may last decades.

It is not only common, but almost universal among professionals to derate parts so that they are exposed to something like half of their maximum rated power. This extends their working life a lot - to decades of continuous operation.

I would not use a 1/4W resistor at more than 1/8W of actual power dissipation except for a short-term test which will be dismantled.

As slacker correctly notes, with a 9V pedal that does not use an internal converter to increase the voltage, you don't even have to look at resistors bigger than 324 ohms to be sure they don't dissipate more than 1/4W. By the same math, you don't even have to do the math for resistors bigger than 648 ohms to be sure they don't dissipate more than 1/8W. For resistors less than that, it's worth looking at the circuit operating conditions to see what the power in actual operation gets to.

[calpolyengineer]

Now correct me if I'm wrong RG, but I seem to remember hearing that higher power resistors also generate more noise.

[R.G.]

I've also seen it said that higher power resistors generate less noise.

My understanding, based on a number of sources culminating in Henry Ott's "Noise Reduction Techniques in Electronic Systems" is that there are multiple forms and sources of noise. The three most important build-in noise sources are
1. Thermal noise, caused by the unavoidable thermal agitation of electrons, is a function of absolute temperature, resistance, and bandwidth. Everything with resistance has thermal noise, and you can't make them be lower than this value. This is why super-low-noise RF front ends are sometimes cooled with liquid nitrogen - it lowers the absolute temperature. For our purposes, it's resistance and temperature. The frequency/power distribution is white noise, and it's proportional to the square root of temperature and resistance.
2. Shot noise; this is associated with current carriers flowing across a voltage barrier, where a carrier near the boundary randomly gets tipped over the edge. It happens in all situations where charge carriers get across a barrier, such as in cathode emission in tubes, collector current in bipolars, and zener/avalanche in diodes. It's frequency distribution is white, and it depends only on the DC current, so more current, more shot noise. It's proportional to the square root of current.
3. Contact noise, caused by the fluctuating conductivity between two imperfectly contacting materials. It happens in all contacts, including relays and switches, the connecting wires of transistors and diodes, especially in composition resistors, where it's referred to as "excess noise". It is directly proportional to DC current and heavily dependent on the materials involved, as well as being inversely proportional to the square root of frequency. It's sometimes called flicker noise or 1/F noise.

A fourth noise source that turns up is popcorn noise. It's generated by imperfections in the manufacture of semiconductors, and sounds like corn popping when amplified. It differs in that it *can* be eliminated by good manufacturing practices.

With that as background, resistors have thermal noises and contact noise. Thermal noise is not dependent on material, power rating, or DC current. Contact noise is dependent on material and DC current. So in resistors, the only way to get a lower noise is to (1) lower the temperature (2) lower the resistance (3) change the material and/or (4) lower the current.

There is some truth in the idea that if you use a higher power rating resistor, it will lower the operating temperature and therefore lower noise. Notice that this only works if the resistor is being self-heated, and at the same time is in a circuit position where it contributes noise to the signal. If the resistor's internal self-heating is negligible compared to the surrounding temperatures, raising the power rating does nothing much except spend more money. Likewise, if it can't contribute its noise to the signal (e.g. it's heavily bypassed to ground) then its noise doesn't much matter, as it won't show up in the result. But it's not the power rating that matters, it's how hot it gets. If a 1/4W resistor gets 200K hotter than a 1/2W resistor, then using a 1/2W will lower the temperature  and also the thermal noise by a factor of the ratios of the absolute temperatures;  SQRT(473K/273K) = 1.32, so for the same resistance, material, and bandwidth it would have 32% more noise power, a 2.4db increase in thermal noise.

If however, the difference in temperature was 10C (same as 10K), then the difference in thermal noise would be a factor of 1.018, or 0.156db more noise. Like with other forms of noise, this only matters if it gets into the signal, so if the resistor is in a place that is bypassed or otherwise isolated from the signal path, its noise is further immaterial to the signal.

Resistors don't (or shouldn't, if made properly!) have shot noise or popcorn noise.

We're pretty much stuck with at least two contacts, for the leads. So we can't lower contact noise much when the resistance itself is a continuous material, like wire or metal film. But only two contacts is much less noise than the several zillion contacts between carbon granules in carbon composition resistors, so carbon comp ought to, and does have when measured, vastly more excess noise than wirewound or metal film.  There is some carbon-carbon contact inside carbon film, but much less than carbon comp, so carbon film has much less excess noise than carbon comp; CCs are practically a textbook exercise in how to make excess noise be objectionable.

In either material for excess noise, lowering the DC current lowers the noise toward the unavoidable thermal noise. Lowering current *may* make it cooler too, as long as the self-heating of the devices involved actually change their temperature.

These ideas are embodied in so-called "noiseless biasing" where a resistor divider creates the desired bias voltage but is not directly connected to the device being biased. Instead, the resistor junction is bypassed to ground with a capacitor, shunting the noise power to ground. The voltage is then connected to the desired point with a high value resistor. The high value resistor has a high value for thermal noise, but does not self heat because the current through it is very low, and also any excess noise, which is proportional to current, is very low. If you make the resistor be the value you needed for the input impedance anyway, you have not hurt yourself in terms of the non-reduceable impedance you had to have anyway, but you have essentially eliminated the noise from the DC in the biasing string.

[defaced]

Cross posted with RG.  Check this out for more info: http://www.aikenamps.com/ResistorNoise.htm

[stezza]

Thanks for all the info guys!

So I'm building a Fender champ 5F1 and while I'm still unsure about the mojo of the original caps (a question for another day), I'm sure using carbon comp resistors wont contribute to any of the 'magic'. So what resistors would be best suited for this circuit?