In high-end audio equipment, careful selection of resistors is one of the best ways to avoid or minimize noise and distortion in the signal path. This paper describes the noise generation in resistors manufactured using the various available resistor technologies and quantifies the noise insertion typical for each type.
Noise is an unwanted wide spectrum signal that may be superimposed on any useful signal, including DC. Resistors, like other passive components, are noise sources to various degrees, depending upon resistance value, temperature, applied voltage, and resistor type.
Many experiments have been done to show why some resistors are "noisier" than others. But the only test that audio experts and audiophiles have agreed on is comparing the level of fidelity that results when different resistor technologies are used in actual audio systems.
Noise in resistors
Overall resistor noise has several components. The most relevant for audio applications are thermal noise and current noise.
Thermal noise is notable for being independent of the resistive material. In fact, the thermal noise level is the same for any type of resistor provided the resistances and temperatures are the same.
The voltage power spectral density (PSD) of thermal noise ST [V2/Hz] is uniformly distributed through the entire range of frequencies. It may be presented by the following expression [1, p.76]:
ST = 4kTR
R - resistance of a resistor [Ω],
T - resistor temperature [K],
k = 1.3807×10-23 J/K - Boltzmann's constant.
Current noise, on the other hand, has a direct relationship to the type of resistive material. The spectral density of voltage of current noise SE is found experimentally to be directly proportional to the square of DC voltage drop U across the resistor and inversely proportional to the frequency f [2, p.164]:
SE = (C • U2) / f
C is a constant that depends on material of the resistive element and its manufacturing process. The spectral density S of the total noise voltage in the resistor is presented in Fig. 1.
Figure 1. Spectral density of total noise voltage in resistor.
The current noise level in a resistor is commonly expressed in units of µV/V or in decibels (in terms of Noise Index [NI]dB
[NI]dB = 20log[(u / U) • 106]
where u is root mean square noise voltage over a decade bandwidth, and U is the DC voltage drop across the resistor. Both u and U are measured in volts. The lower the Noise Index, the lower the level of current noise in the resistor.
The Noise Index of resistors manufactured using different technologies is presented in the graph below [2, p.168].
Figure 2. Average noise indexes of commercial resistors.
As the graph shows, resistors based on composition resistive materials such as carbon and thick film have the highest level of current noise. Why? Because of the significant non-homogeneity of these resistive element materials. The conduction path in composite materials is formed by the conductive particles touching one another in an isolative matrix. Non-stable contacts in these "touching sites" generate noise when electrical current runs across them.
Thin-film resistors have a considerably more homogeneous structure and consequently are less noisy. Thin films are deposed using evaporating or sputtering of resistive material (for example tantalum nitride TaN, silicon chromium SiCr, and nickel chromium NiCr) onto a ceramic substrate. The thickness of the layer varies typically from 10 to 500 angstroms depending on the resistance value.
The noise in thin films results from the occlusions, surface imperfections, and non-uniform depositions which are more significant when the film is thinner. That is why the thicker the resistive film, the lower the resistance value and thus the lower the noise level.
The lowest noise level is observed in resistors with bulk metal resistive elements: foil and wirewound. Wire is made of metal alloys similar to foil material, but additional noise may come from the junction of the fine wire of the resistive element and the comparatively coarse resistor terminals. In foil resistors, the terminals and the resistive element are parts of the same piece of the foil, so this problem is avoided.
But the major objection to wirewound resistors is their inductance, which results in chopping the signal peaks1, and the significant dependence of resistor impedance on signal frequency. In addition, special attention must be paid to the following effects associated with reactance of wirewound resistors:
- The audio amplifier may oscillate spontaneously at 5 MHz to over 50 MHz affecting audio quality [3, p.22-6].
- Equivalent series inductance (ESL) can cause large phase shifts affecting audio tone [3, p.22-6].
- The wire coil may act as a pick-up of EMI that may surpass the level of usual current noise [2, p.167].
Foil resistors avoid these problems because they are structured using chemical etching of a flat bulk metal foil so that the current in adjacent current carrying paths runs in opposing directions, cancelling parasitic inductance of these paths. Also, path-to-path capacitances are connected in series, which has the effect of minimizing the parasitic capacitance of the resistor. These low-inductance/capacitance resistors are characterized by nonmeasurable peak-to-peak signal distortions.
1 The effect of peak chopping originates from the entire amplifier circuit that comprises wirewound resistors. ESL in wirewound resistors (sometimes together with parasitics of other components) may result in signal phase shift that is sufficient for amplifier “ringing” on signal transitions (peaks). This high-frequency "ringing" (chopping signal) fills relatively low-spectrum audio signal peaks (chops them). It is illustrated graphically below: