This article is about intrinsic noises—that is, noises that arise within an electronic circuit itself, making the response of the circuit to external inputs less than ideal. It is intended for readers who know, in general terms, what an amplifier and an analog-to-digital converter (ADC) are intended to do. The terms discussed include white noise, pink noise, popcorn noise, shot noise, avalanche noise, and thermal noise, as well as noise figure and noise floor.

Table of Contents

  1. Noise Sources
  2. White Noise, Pink Noise, And Noise Floor
  3. Shot Noise
  4. Thermal (Johnson) Noise
  5. Popcorn Noise
  6. Avalanche Noise
  7. Combining Noises
  8. References


Noise Sources
All ICs contain inherent noise sources. In amplifiers, they can be modeled as zero-impedance voltage generators in series with the input (en) and infinite-impedance current sources in parallel with the input (in). The noise from these intrinsic sources has different characteristics, depending on how it arises.

Other characteristics can be derived from noise. For example, an amplifier’s noise figure (expressed in dB) is the amount by which the amplifier’s noise exceeds the noise of a perfect amplifier in the same environment. It’s generally only used in communications work.

White Noise, Pink Noise, And Noise Floor
A system’s noise floor is the base level of its intrinsic noise. Anything below the noise floor is “buried in the noise.” It largely comprises white or “broadband” noise. Observed in the frequency domain, it is the flat part of the circuit’s intrinsic noise spectrum.

Distinguished from white noise, pink noise (also called flicker, or 1/f noise) occurs below a certain value called the corner frequency. In that lower region, it increases inversely with frequency at 3 dB/octave (see the figure).


On a spectrum analyzer, “white” noise is the flat part of a circuit’s intrinsic noise spectrum. “Pink” noise is more intense at lower operating frequencies, rising out of the white noise approximately at the “corner frequency” and increasing at 3 dB/octave at lower and lower operating frequencies.

(Actually, there is no hard corner. The transition occurs gradually. You can determine corner frequency by extending the straight-line portions of white and pink noise and noting where they cross.)

Pink noise only occurs under conditions where current is flowing. It’s a manifestation of charge carriers being captured arid released randomly. In bipolar transistors, that’s due to contamination and imperfect surface conditions at the base-emitter junction. In CMOS devices, it’s primarily associated with extra electron energy states at the boundary between silicon and silicon dioxide.

In expressing white noise, it’s necessary to specify bandwidth. If F is frequency:

or more simply:

or:

If F1 is much lower—say, 10 times lower—than F2, then it can even be approximated as:

That is, it can be approximated as simply en times the square root of the upper frequency limit.

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 a 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 doesn’t matter that much 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:

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 need not be the same as the corner frequency for current noise.

Voltage noise is expressed in nV/√Hz, and current noise may be expressed in terms of μA/√Hz. One characteristic of 1/f noise is that the power content in each decade is constant. Another thing to keep in mind is that white noise has equal energy per frequency. Its RMS value is set by f2. Pink noise has equal energy per octave. 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 F1 to Fn would be:

At higher frequencies, the term in the above equation containing the natural logarithm becomes insignificant, and the expression reduces to:

Shot Noise
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 x 10-19 C), Ib is the bias current, and ΔF is the bandwidth in Hz. If Ib is expressed in pA, that simplifies to:

Thermal (Johnson) Noise
Then, of course, there is 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 ΔF is bandwidth in hertz. For convenience, 4kT = 1.65 × 10-20 W/Hz. The lower the resistance, the less the thermal noise. Halving the resistance decreases the noise by 3 dB because R is under the radical sign.

Popcorn Noise
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. Since if it happens at all, it happens at low frequencies, it’s part of 1/f noise.

Avalanche 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.

Combining Noises
It’s rare to encounter only one source of intrinsic noise. If those sources are uncorrelated, they can be combined as the square root of the sum of the squares:

Thus, the total effect of two noise sources that have the same energy is a 3-dB increase in total noise energy. More importantly, any noise voltage more than three or five times greater than any of the others will dominate, and the others may be neglected.

The key components of amplifier noise are the white noise, which is flat above the corner frequency, and the pink noise below the corner frequency, which increases inversely with frequency at 3 dB/octave.


Reference

  1. Analog Devices’ Op Amp Applications Handbook, (2006) edited by Walt Jung.
  2. Webcast: Noise Optimization in Sensor Signal Conditioning Circuits (Part I)