Noise

Overview

An ideal electronic circuit produces no noise of its own, so the output signal from the ideal circuit contains only the noise that was in the original signal. But real electronic circuits and components do produce a certain level of inherent noise of their own. Even the simple fixed-value resistor is noisy. Figure 5-14a shows the equivalent circuit for an ideal, noise-free resistor. The inherent noise is represented in Figure 5-l4b by a noise voltage source, V_n, in series with the ideal, noise-free resistance, R_i. At any temperature above absolute zero (0°K or about —273°C), electrons in any material are in constant random motion. Because of the inherent randomness of that motion, however, there is no detectable current in any one direction. In other words, electron drift in any single direction is cancelled over short time periods by equal drift in the opposite direction. Electron motions are therefore statistically decorrelated. There is, however, a continuous series of random current pulses generated in the material, and those pulses are seen by the outside world as a noise signal. This signal is called by several names: Johnson noise, thermal agitation noise, or thermal noise.


This noise is called white noise because it has a very broadband (nearly Gaussian) spectral density. The thermal noise spectrum is dominated by midfrequencies (10⁴ to 10⁵ Hz) and is essentially flat. The term white noise is a metaphor similar to the term white light, which is composed of all visible color frequencies. The expression for Johnson noise is:

where

V_n is the noise voltage (V)
K is Boltzmann's constant
(1.38 X 10^-23 J/°K)
T is the temperature in degrees Kelvin (°K)
R is the resistance in ohms (W)
B is the bandwidth in hertz (Hz)

With the constants collected, and the expression normalized to 1 k W, Equation 5-9 reduces to:

The evaluated solution of Equation 5-10 is normally read nanovolts per square root hertz. In this equation, a 1-M W resistor will have a thermal noise of

Several other forms of noise are present in linear integrated circuits (ICs) and other semiconductor amplifiers to some extent. For example, because current flow at the quantum level is not smooth and predictable, an intermittent burst phenomenon sometimes occurs. This noise, called popcorn noise, consists of pulses of many milliseconds' duration. Another form of noise is shot noise (also called Schottky noise). The term shot is derived from the fact that the noise sounds like a handful of B-B shot thrown against a metal surface. Shot noise is a consequence of dc current flowing in any conductor and is found from:

(I_n)² = 2qIB A²/Hz (5-11)

where

I_n is the noise current in amperes (A)
q is the elementary electric charge
(1.6 X 10^-19 coulombs)
I is the current in amperes (A)
B is the bandwidth in hertz (Hz)

Finally, there is flicker noise, also called pink noise or 1/f noise. The latter name applies because nicker noise is predominantly a low-frequency (< 1000 Hz) phenomenon. This type of noise is found in all conductors and becomes important in 1C devices because of manufacturing defects.

The noise spectrum in any given instrumentation system will contain elements of several kinds of noise, although in some systems one form may dominate the others. It is common to characterize noise from a single source using the root mean square (rms) value of the voltage amplitudes:

Figure 5-15 shows the noise spectrum profile for a typical system that contains 1/f noise, thermal or white noise, and some high frequency noise.

Figure 5-15 Noise spectrum profile when 1/f noise, thermal ('white") noise, and high frequency noise are present.

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