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.Thermal noise
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.
The thermal noise of a resistor is equal to:Contact noise
Vt = SQRT(4kTBR)
Vt = the rms noise voltage
k = Boltzmann's constant (1.38∙10-23)
T = temperature (Kelvin - room temperature = 300K)
B = noise bandwidth (Hz - typical audio bandwidth = 20kHz, typical guitar amp bandwidth = 5-10kHz)
R = resistance (ohms)
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.
For example, using the above equation with a 1Meg resistor, a bandwidth of 10kHz, and room temperature (300K), you get a noise voltage of 12.9uV. If this resistor is on the front end of a typical non-master Marshall, which has a gain of around 83dB (14,125) at 1kHz with all controls at mid and the bright volume at full, you'll get around 0.182V of noise at the 16 ohm output tap. That might not sound like much, but run the numbers for your average high-gain amp, and it starts to add up quickly. It helps that the typical guitar amp pickup impedance is lower than 1Meg, and is in parallel with the input resistor, so it tends to swamp this noise source
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.Shot noise
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 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:
- Keep resistance values low, because thermal noise is directly proportional to resistance value.
- Wirewound resistors are the best choice for noise, followed by metal film, metal oxide, carbon film, and lastly, carbon composition. However, wirewound resistors are not readily available in large resistance values, and are usually inductive, which can cause instability problems in some cases. Bear in mind, however, that many people prefer the "sound" of carbon comps, claiming they sound warmer than film or wirewound types. This is possibly due to distortions generated by the modulation of the contact noise current by the AC signal. Since this noise has a 1/f frequency characteristic (similar to pink noise), it is more pleasing to the ear than white noise. However, pleasing noise is still noise, and in my opinion, it should be reduced to the lowest possible level. The signal distortion is a different topic altogether.
- Use the largest practical wattage resistors (unless you are using wirewound resistors) because contact noise is decreased in a larger geometry material.
- Keep the DC and AC currents to a minimum because contact noise is proportional to current.
- Don't forget that potentiometers are also resistive elements, and are almost always carbon composition, and generally are large values (such as 1MEG for the volume control). These can be a major source of noise in a guitar amplifier. For absolute lowest noise, conductive plastic element pots should be used, again, the lowest practical value, and the largest practical power rating.
- The first stage of an amplifier is the most critical; in order to maximize the overall amplifier signal-to-noise ratio, the first stage gain should be maximized. This will raise the signal level farther above the noise floor of following stages. Triodes can be paralleled to increase the signal-to-noise ratio. This is because the noise sources of the two triodes are uncorrelated and add as the square root of the sum of the squares of the individual noise sources, while the signal is correlated and adds directly, giving a 3dB improvement in signal-to-noise ratio. Pentode input stages should be avoided if possible, because they suffer from another type of noise, division noise, caused by the insertion of the screen grid element into the electron path between the cathode and the plate. If very high gain is needed, the self-biased cascode stage is the preferred method, as it has the same or higher gain than a pentode, but no extra noise. In addition, the cascode connection does not suffer from the high microphonics of the most common pentode, the EF86. The self-biased cascode approach is better than the fixed biasing of the upper tube grid because it eliminates the direct influence of the DC supply on the upper tube grid, and has a warmer tone.
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.
- Since noise is proportional to resistor value, the 1Meg to ground resistor on the first stage of a guitar amplifier will create much more noise than the 68K grid resistor, because the value is 14.7 times larger. This means that carbon comp vs. metal film is more noticeable and important for the 1Meg resistor than the 68K input resistor. However, when a guitar is plugged in to the amplifier, the pickup resistance/inductance and cable capacitance is in parallel with the 1Meg grid resistor, so its effect on noise is greatly reduced. When the guitar is unplugged or turned all the way down, the 68K series grid resistor becomes the predominant noise source. Depending on the tube type and input stage topology, the resistor noise may be greater than the tube's referred input noise. To reduce the noise to a minimum, use the smallest possible input grid resistor value that still provides RF suppression.
- Also, since resistor noise is proportional to current flow, a 100K grid resistor is going to be quieter than a 100K used as a plate resistor. There is around 1 to 2 mA of current flow in a typical plate circuit, but the grid current flow is practically negligible. This means that it is better to use metal film for plate resistors. The exception to this rule comes when two resistors are used as a voltage divider from the plate of one tube to the grid of the other. There is no grid current flowing, but there is current flowing in the voltage divider string, so metal films should be used in these positions for lowest noise.
- Lastly, the noise contribution is greatest at low-level stages, such as input stages, reverb recovery stages, and effects loop recovery stages, so the plate resistors, grid-to-ground resistors, and grid divider attenuation resistors in these locations should be metal films for lowest noise, while locations where there is little gain from that point to the output can use noisier resistors without adding too much to the overall noise level of the amplifier, because the signal level at that point is many times greater than the noise level produced by the resistors.
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 © 1999-2009 Randall Aiken. May not be reproduced in any form without written approval from Aiken Amplification.