Resistor Types - Does It Matter?

General

The subject of resistor types comes up quite often in guitar amplifier discussions.  Some people will recommend only using carbon composition resistors, others will tell you that metal film resistors are better.  Who is correct?  Well, the answer depends on what your design goals are.  From a noise aspect, there are several things to take into consideration.

Resistor noise is made up of three main types: thermal, contact, and shot noise. Thermal noise is mainly dependent on temperature, bandwidth, and resistance, while shot noise is dependent on bandwidth and average DC current, and contact noise is dependent upon average DC current, bandwidth, material geometry and type.

Wirewound resistors are the quietest, having only thermal noise, followed by metal film, metal oxide, carbon film, and lastly, carbon composition.

Following is a description of each type of noise, along with methods of reducing its impact on the circuit, along with some general guidelines for low-noise amplifier design.

Thermal noise
The thermal noise of a resistor is equal to:

           Vt = SQRT(4kTBR)

where:

         Vt = the rms noise voltage
         k = Boltzmann's constant
         T = temperature(Kelvin)
         B = noise bandwidth
         R = resistance

Since the characteristics of thermal noise have a Gaussian probability density function, and the noise of the two separate sources is uncorrelated white noise, the total noise power is equal to the sum of the individual noise powers. If you model the individual resistors as noise generators, the output noise voltage will be equal to the square root of the sum of the squares of the individual noise sources.

The above equation shows that the noise varies in direct proportion to the square root of the resistance, so if you take two resistors of half the value and square the square root and add them and take the square root of the sum, you end up with the exact same value as you would if you took the square root of a single resistor of twice the value. Therefore, the total noise remains the same.

In general, the thermal noise of any connection of passive elements is equal to the thermal noise that would result from the real part of the equivalent total impedance. If we are dealing with pure resistances, the thermal noise is equal to the thermal noise produced by an equivalent resistance.  Therefore, the thermal noise of a 1K carbon resistor is the same as a 1K metal film; it is independent of material. The only way to reduce this noise is to reduce the resistance value. This is why you don't want those 10 Meg resistors on your input stage.

Contact noise
Contact noise is dependent on both average DC current and resistor material/size. The most significant contributor to noise in guitar amplifiers is the use of low-wattage carbon composition resistors. Since the noise is proportional to resistor size, the use of 2W carbon comp resistors will improve the performance over that of 1/2W resistors. Studies have shown a factor of 3 difference between a 1/2W and a 2W carbon comp resistor operating at the same conditions.

The predominant noise in carbon comp, carbon film, metal oxide, and metal film is composed of contact noise, which can be very large at low frequencies because it has a 1/f frequency characteristic. Wirewound resistors do not have this noise, only resistors made of carbon particles or films. This noise is directly proportional to both the current flowing in the resistance and a constant that depends upon the material the resistor is made of.

If no current (AC or DC) flows in the resistor, the noise is equal to the thermal noise. The contact noise increases as the current is increased. This means that for low noise operation, the DC and AC currents should be kept low.

The material and geometry of the resistor can greatly affect the contact noise.  Therefore,  if you double the power rating of the resistor, which increases the size and area, you will reduce the contact noise generated by the resistor.

Shot noise
Shot noise is dependent upon current, so the more average DC current through a resistor, the more noise you get. In order to reduce this type of noise, you must keep the DC current to a minimum. This is best done in the first amplifier stage or in low-level stages such as reverb-recovery amps, where it is the most critical. Unfortunately, higher DC currents usually sound better in tubes, so it is a tradeoff. Best practice is to use a wirewound or metal film in these applications, unless you are making a high-frequency amp where the inductance of the wirewound resistor comes into play. This is not generally a factor in guitar amps.
Conclusions
In general, for low-noise design:
A few practical notes:
Since high-quality metal film resistors are more expensive than cheaper carbon films, a player may want a quieter amp without having to change all the resistors to metal film.  From the above information, a few general rules can be determined, and a compromise can be reached.
 

One more consideration for resistors: it is sometimes overlooked that resistors have a max voltage rating. The 1/2 watters and some 1 watters usually are only rated for 250-350V. Be sure to get a resistor rated for the appropriate voltage in the amplifier. I use only 1W, 500V min (continuous, 1000V surge) or 2W, 750V rated resistors.



Copyright © 1999,2000,2001,2002,2003  Randall Aiken.  May not be reproduced in any form without written approval from Aiken Amplification.

Revised 11/08/03