Right after wire, insulation, switches and connectors, resistors are one of electricity’s most essential components. Without resistors, levels couldn’t be adjusted, nor could tubes, transistors or FETs be biased into their sweet spots. Resistors can do two of math’s basic functions — division (attenuation) and addition (mixing) — while amplifiers and transformers handle the multiplication and subtraction.

Long Division

Resistors for this Millennia Media preamp module are Vishay 1-percent- tolerance metal-film types providing precise, repeatable control of gain settings. The colored bands around each resistor conform to the standard resistor color-code, which provides information about tolerance and the impedance of each component, without using numerical values.

There are lots of electronic analogies — plumbing being perhaps the most popular — but for resistors, I think bungee cords do the job nicely. Imagine an “eye hook” in the ceiling and another “eye” in the floor. When stretched eye-to-eye, two identical bungees will divide the floor-to-ceiling distance in half (an example of a “series” circuit). If you’ve ever gotten 6 dB of gain reduction from an LA-2A or 1176, you’ve pretty much done the same thing to electrons using one standard resistor in series with either a photosensitive resistor or a Field Effect Transistor (FET).

Another example of a series circuit is a string of holiday lights, where removing one bulb (or LED) interrupts current flow. By contrast, power distribution is a giant parallel network where anything can be plugged in or removed without affecting any of the other circuits that are already online.

Math Explains Reality

To continue the bungee analogy, assume the distance from floor to ceiling is the voltage (V, in volts) and the tension in the bungee is the current (A, in amperes). The elasticity of the bungee (as determined by the type, length and/or thickness of the elastic material) is the resistance in ohms (R = O). A short, thick bungee has a low resistance — it doesn’t like to be stretched — so the current (tension) is high. A long, skinny bungee is easily stretched so the current (tension) is low.

The tools for measuring amps, volts and ohms are found in one device called a multimeter. In the bungee world, inserting a spring scale between the resistor and the eye will measure tension (amps), a ruler or tape measure spans the distance (volts), and Ohm’s Law is used to calculate the resistance (how easily the bungee is stretched). Therefore, if I = V divided by R (I = V/R), then a bungee stretched 1 foot with 1 pound of tension is equivalent to 1 ohm (Ω). Note that I’ve assigned quantities for the sake of demonstration, but I have little doubt about the possible translation.

Thermal Noise

All electrical conductors — wires and resistors, along with semiconductors such as tubes and transistors — can generate random white noise (also known as Johnson noise) that is proportional to the conductor’s temperature. The noise, which results from electron agitation, “limits” the usable dynamic range in high-gain circuits (like a mic preamp) and/or low-level resolution in digital converters (A/D and D/A).

The table at left shows the relationship between resistance and noise as determined by an online calculator (www.sengpielaudio.com/calculator-noise.htm). These relationships were more or less confirmed in the physical domain, though I chose the easy way, using a Decade Box, which unfortunately introduces other noises like buzz. A better way would have been to solder individual resistors to XLR plugs to test one at a time. As you can see, doing the math first would save time because the relationship between resistance and noise quickly becomes obvious.

EIN

Equivalent Input Noise (EIN) is a specification that quantifies the amount of noise an amplifier (such as a mic preamp) adds to the signal. To measure, a resistor of 150 to 200 ohms is connected to an XLR plug to simulate the microphone’s source impedance. Impedance is AC’s equivalent of DC’s resistance, or as I like to define it, impedance is resistance with resonance (a frequency-related component). If a preamp at max gain has a noise floor of -70 dBu, we can subtract the gain from that amount to determine the actual noise level. Preamps typically have at least 60 dB of gain, so -70dB (noise floor) minus 60dB (gain) yields an EIN of -130 dB.

We know that 16-bit digital audio has 96 dB of resolution; this translates to 6 dB per bit. By dividing an EIN of -130 dB by 6 dB, the equivalent digital resolution is 21.6 bits, which is what you can expect from a good 24-bit converter. Simply put, 144 dB of resolution is theoretically impossible given the inherent component noise, but it is more than enough for audio purposes — unless you need more (and can record at the north or south poles).

Trade-Offs

Tubes and semiconductors used in high-gain applications must be pretested for noise. Once that’s out of the way, the type of resistors and the noises they generate can be sorted out. And thermal is but one of three noise categories. Of the two other resistor-related noises, shot noise is the result of current flowing and contact noise is related to the material used to make the resistor itself — its geometry. (See “Audio Science” sidebar for more.)

Suffice to say that aside from choosing a resistor type for low noise, all of the other noises are related to circuit design. The fact that some circuits sound and perform better at higher currents contrasts directly with the fact that resistors are quieter at lower currents.

Audio design is a series of compromises made for the collective good. The most obvious example of this might be interference immunity; keeping out unwanted radio and television signals might result in additional circuitry that can compromise the signal integrity, albeit well outside of the range of hearing. Another trade-off is using off-the-shelf parts vs. specialized parts. The latter might be better, but as with all obsessions, performance is a battle between value pricing and the law of diminishing returns.

*Visit Eddie Ciletti at*

www.tanglible-technology.com.

Thermal noise increases 3 dB each time the resistance is doubled. Note the change of 1.18 dB from 32F/0C (96.86 dB) to 100F/37.7C (-96.3 dB) to 185F/85C (-95.68 dB).

NOISE LINKS

People always ask me about “how to get started” books. Two I can recommend are Walter Jung’s *IC OpAmp Cookbook* series and *The Art of Electronics* by Paul Horowitz and Winfield Hill. Here are a few useful online resources.

**The Math of Noise**

www.analogzone.com/avt_1204.pdf

**Rane’s Audio Specifications**

www.rane.com/note145.html

**Resistor Noise** (from a guitar amp manufacturer’s perspective)

www.aikenamps.com/ResistorNoise.htm

AUDIO SCIENCE

Resistor Types

Wire-wound resistors have the lowest noise. These exhibit only thermal noise, but they also tend to be inductive, causing frequency anomalies or, worse, a tendency toward instability (oscillation). Metal-film resistors are next in line — and most popular — while carbon-composition resistors have the highest noise. I’m not going to debate the sound of resistors except to say that older carbon resistors are not trustworthy. My personal preference is metal-film types due to their low noise, reliability, longevity, availability and price. These types offer the most control over type and wattage — higher-wattage resistors can dissipate heat faster and keeping cooler helps to reduce noise and extend life.

— *Eddie Ciletti*