[Engineering Essentials]
What Was That Noise?
Learning the basics of noise in amplifiers against the backdrop of some new ideas on how to cope with it offers fresh perspectives on a plan of attack.
In general, voltage or current noise spectral density in the 1/f region is:
where k is the level of the “white” current or voltage noise level, and FC is the 1/f corner frequency. A good low-frequency, low-noise amplifier will have corner frequencies below 10 Hz. JFET devices and general-purpose op amps have values up to 100 Hz. Very fast amplifiers may achieve their high speed at the cost of a high FC, but that’s not much of a concern in a wideband application.
To obtain a value for rms noise, the noise spectral density can be integrated over the bandwidth of interest. In the pink-noise region, the rms noise from F1 to FC would be represetned by Equation 6, where en is the voltage noise spectral density of the white noise, F1 is the lowest frequency of interest in the pink-noise region, and FC is the corner frequency. Note that the corner frequency for a voltage noise needn’t be the same as the corner frequency for current noise.
Voltage noise is expressed in nV/vHz, and current noise may be expressed in terms of µA/vHz. One characteristic of 1/f noise is that the power content in each decade is constant. Keep in mind that white noise has equal energy per frequency. Its rms value is set by F2. Pink noise has equal energy per octave, and its rms value is set by the ratio of F2 to F1.
In the white-noise area above FC, the rms noise is given by:
Combining the last two equations, the total rms noise from Fl to F2 would be represented by Equation 8. At higher frequencies, the term in the above equation containing the natural logarithm becomes insignificant, and the expression reduces to:
Shot (Schottky) noise is a component of white noise. It occurs whenever a current passes through PN junctions. Barrier crossings are random events, and the total current is the sum of those random elementary current pulses. The expression for shot noise is:
where q is the charge on an electron (1.6 × 10-19 C), Ib is the bias current, and ?F is the bandwidth in Hz. If Ib is expressed in picoamperes, it simplifies to:
Then, of course, there’s thermal, or Johnson noise, from the thermal agitation of electrons in the gain-setting resistors, and:
where k is Boltzmann’s constant (1.374 × 10-23J/K), T is Kelvin temperature, R is resistance in ohms, and ?F is bandwidth in hertz. (For convenience, 4kT = 1.65 × 10-20 W/Hz.) The less the resistance, the less the thermal noise. Halving the resistance decreases the noise by 3 dB because R is under the radical sign.
Popcorn or “burst” noise is rarely encountered these days because parts are screened for it in the fab. It represents step-function voltage changes at the output of an amplifier caused by random current-gain transitions in bipolar transistors, which then cause variations in input offset. If it happens at all, it’s at low frequencies, so it’s part of 1/f noise.
Avalanche noise is also rare. It’s encountered in PN junctions operated in reverse breakdown modes. It occurs when electrons acquire enough kinetic energy under the influence of the strong electric field to create additional electron-hole pairs by colliding with the atoms in the crystal lattice. If that happens to spill over into an avalanche effect, random noise spikes may be observed.
A very common equipment design error, referred to as the "pin 1 problem", causes it to output hum or buzz when a shield (delivering ground current) is connected to it. It is all too common since XLR connectors are mounted on PCBs rather than metal chassis. A paper on this is in the same June 1995 AES Journal as my paper. I'm working on a new paper that finally explains the origin of ground voltage differences among AC outlets. Readers may also be interested in a new IC that, for the first time, truly imitates the excellent CMRR behavior of a good audio transformer (see http://www.thatcorp.com/1200-series_High_CMRR_Balanced_Line_Receiver_ICs.html).
Bill Whitlock -June 22, 2009
As an audio technician I appreciate this article.These are good points to bring up for future designs.I discovered the wonderful world of noise trying to mate a floating ground power supply device with a referenced ground,(actually used 0 ohm resistors to the chassis),supply.It came down to lifting the ground on the inter- connect on just the input side and lifting the ground of the referenced supply,on the cable end,( very dangerous,some musicians like to drink on stage and this was the mixer for the stage sound),oh and did I mention that the input side was transformer isolated.This is common in my industry as they like to think we don't mix and match different brands of gear.Digital technology has helped,but getting it right in the first place can help with compatibility down the line.The audio world is extremely subjective and we will continue to mix and match brands,( with their different design philosophies),with out much thought of noise and compatibility.
Graham Pearson -June 22, 2009
Where is Figure 4?
Anonymous -June 15, 2009
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