Analog Design Tradeoffs

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Noise

Noise is associated with all electronic circuits. Noise is defined[1]

as unwanted disturbances

superposed on a useful signal that tend to obscure its information content. Noise is not the same as

signal distortion caused by a circuit. Noise may be electromagnetically or thermally generated, which

can be decreased by lowering theoperating temperatureof the circuit. Other types of noise, such as

shot noisecannot be removed as they are due to limitations in physical properties.

Electronic noise

[1]

is a random fluctuation in an electrical signal, a characteristic of allelectroniccircuits. Noise generated by electronic devices varies greatly, as it can be produced by several

different effects.Thermal noiseis unavoidable at non-zero temperature (seefluctuation-dissipation

theorem), while other types depend mostly on device type (such asshot noise,[1][2]

which needs steep

potential barrier) or manufacturing quality andsemiconductordefects, such as conductance

fluctuations, including1/f noise.

Incommunication systems, the noise is an error or undesired random disturbance of a useful

information signal, introduced before or after the detector and decoder. The noise is a summation of

unwanted or disturbing energy from natural and sometimes man-made sources. Noise is, however,

typically distinguished frominterference, (e.g.cross-talk, deliberatejammingor other unwanted

electromagnetic interferencefrom specific transmitters), for example in thesignal-to-noise ratio

(SNR),signal-to-interference ratio(SIR) andsignal-to-noise plus interference ratio(SNIR) measures.Noise is also typically distinguished fromdistortion, which is an unwanted alteration of the signal

waveform, for example in thesignal-to-noise and distortion ratio(SINAD). In a carrier-modulated

passband analog communication system, a certaincarrier-to-noise ratio(CNR) at the radio receiver

input would result in a certainsignal-to-noise ratioin the detected message signal. In a digital

communications system, a certainEb/N0(normalized signal-to-noise ratio) would result in a certainbit

error rate(BER).

While noise is generally unwanted, it can serve a useful purpose in some applications, such asrandom

number generationordithering.

Types

Thermal noise

Main article:JohnsonNyquist noise

JohnsonNyquist noise[1]

(sometimes thermal, Johnson or Nyquist noise) is unavoidable, and

generated by the random thermal motion of charge carriers (usuallyelectrons), inside anelectrical

conductor, which happens regardless of any appliedvoltage.

Thermal noise is approximatelywhite, meaning that itspower spectral densityis nearly equalthroughout thefrequency spectrum. The amplitude of the signal has very nearly aGaussian
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probability density function. A communication system affected by thermal noise is often modeled as

anadditive white Gaussian noise(AWGN) channel.

Theroot mean square(RMS) voltage due to thermal noise vn, generated in a resistanceR(ohms) over

bandwidth f(hertz), is given by

where kB isBoltzmann's constant(joulesperkelvin) and Tis the resistor's absolutetemperature

(kelvin).

As the amount of thermal noise generated depends upon the temperature of the circuit, very sensitive

circuits such aspreamplifiersinradio telescopesare sometimes cooled inliquid nitrogento reduce the

noise level.

[edit] Shot noise

Main article:Shot noise

Shot noise in electronic devices consists of unavoidable random statistical fluctuations of theelectric

currentin an electricalconductor. Random fluctuations are inherent when current flows, as the current

is a flow of discrete charges (electrons).

[edit] Flicker noise

Main article:Flicker noise

Flicker noise, also known as 1/fnoise, is a signal or process with afrequency spectrumthat falls off

steadily into the higher frequencies, with apinkspectrum. It occurs in almost all electronic devices,and results from a variety of effects, though always related to a direct current.

[edit] Burst noise

Main article:Burst noise

Burst noise consists of sudden step-like transitions between two or more levels (non-Gaussian), as

high as several hundredmicrovolts, at random and unpredictable times. Each shift in offset voltage or

current lasts for several milliseconds, and the intervals between pulses tend to be in theaudiorange

(less than 100Hz), leading to the term popcorn noise for the popping or crackling sounds it produces

in audio circuits.

[edit] Avalanche noise

Avalanche noise is the noise produced when a junction diode is operated at the onset ofavalanche

breakdown, asemiconductor junctionphenomenon in which carriers in a high voltage gradient

develop sufficient energy to dislodge additional carriers through physical impact, creating ragged

current flows.

[edit] Quantification

The noise level in an electronic system is typically measured as an electrical powerNinwattsor

dBm, aroot mean square(RMS) voltage (identical to the noisestandard deviation) in volts,dBVor a

mean squared error(MSE) in volts squared. Noise may also be characterized by itsprobabilitydistributionandnoise spectral densityN0(f) in watts per hertz.
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A noise signal is typically considered as a linear addition to a useful information signal. Typical signal

quality measures involving noise aresignal-to-noise ratio(SNR or S/N),signal-to-quantization noise

ratio(SQNR) inanalog-to-digital coversionand compression,peak signal-to-noise ratio(PSNR) in

image and video coding,Eb/N0in digital transmission,carrier to noise ratio(CNR) before the detector

in carrier-modulated systems, andnoise figurein cascaded amplifiers.

Noise is a random process, characterized bystochasticproperties such as itsvariance,distribution,

andspectral density. The spectral distribution of noise can vary withfrequency, so its power density is

measured in watts per hertz (W/Hz). Since the power in aresistiveelement is proportional to the

square of the voltage across it, noise voltage (density) can be described by taking the square root of

the noise power density, resulting in volts per root hertz ( ).Integrated circuitdevices, such as

operational amplifierscommonly quoteequivalent input noiselevel in these terms (at room

temperature).

Noise power is measured in Watts ordecibels(dB) relative to a standard power, usually indicated by

adding a suffix after dB. Examples of electrical noise-level measurement units aredBu,dBm0,dBrn,

dBrnC, and dBrn(f1f2), dBrn(144-line).

Noise levels are usually viewed in opposition tosignal levelsand so are often seen as part of asignal-

to-noise ratio(SNR). Telecommunication systems strive to increase the ratio of signal level to noise

level in order to effectively transmit data. In practice, if the transmitted signal falls below the level of

the noise (often designated as thenoise floor) in the system, data can no longer be decoded at the

receiver. Noise in telecommunication systems is a product of both internal and external sources to the

system.

[edit] Dither

If the noise source is correlated with the signal, such as in the case ofquantisation error, the

intentional introduction of additional noise, calleddither, can reduce overall noise in the bandwidth ofinterest. This technique allows retrieval of signals below the nominal detection threshold of an

instrument. This is an example ofstochastic resonance.

[edit] See also

Generationrecombination noise Phonon noise

[edit] Notes

1. ^abcC.D. Motchenbacher, J.A. Connelly (1993). Low-noise electronic system design. WileyInterscience.

2. ^L.B. Kish, C.G. Granqvist (2000). "Noise in nanotechnology (invite paper)".Microelectronics-Reliability40: 1833.

[edit] References

White noise calculator, thermal noise - Voltage in microvolts, conversion to noise level indBu and dBV and vice versa

This article incorporatespublic domain materialfrom theGeneral Services Administrationdocument"Federal Standard 1037C"

(in support ofMIL-STD-188).
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[edit] Further reading

Sh. Kogan (1996). Electronic Noise and Fluctuations in Solids. Cambridge University Press.ISBN0521460344.

linearity

Linearity is the behavior of a circuit, particularly anamplifier, in which the outputsignal

strength varies in direct proportion to the input signal strength. In a linear device, the output-

to-input signal amplitude ratio is always the same, no matter what the strength of the input

signal (as long it is not too strong).

In an amplifier that exhibits linearity, the output-versus-input signal amplitude graph appears

as a straight line. Two examples are shown below. The gain, or amplification factor,

determines the slope of the line. The steeper the slope, the greater the gain. The amplifier

depicted by the red line has more gain than the one depicted by the blue line. Both amplifiersare linear within the input-signal strength range shown, because both lines in the graph are

straight.

In analog applications such as amplitude-modulation (AM) wireless transmission and hi-fi

audio, linearity is important. Nonlinearity in these applications results in signal distortion,because the fluctuation in gain affects the shape of ananalogoutputwaveformwith respect to

the analog input waveform.

Even if an amplifier exhibits linearity under normal conditions, it will become nonlinear if

the input signal is too strong. This situation is called overdrive. The amplification curve

bends towards a horizontal slope as the input-signal amplitude increases beyond the critical

point, producing distortion in the output. An example is a hi-fi amplifier whose gain is set to

the point where the VU (volume-unit) meter needles kick into the red range. The red zone

indicates that the amplifier is not operating in a linear fashion. This can degrade the fidelity

of the sound.

2.
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A relationship between two or more quantities which can be expressed in terms of linear

algebraic, differential, or integral equations. A system in which all quantities (or variables)

can be described in terms of such equations is said to be a linear system. By definition, linear

systems satisfy theprinciple of superposition. By this principle, the response of a linear

system to multiple inputs is given simply by the sum of the responses due to each individual

input. In addition, if all inputs aremultipliedby a common constant factor, the resultingresponse is multiplied by the same factor. See also Differential equation; Integral equation;

Linear algebra.

As an example of a simple linear relationship, the voltage Vacross an ideal (ohmic) resistor is

directly proportional to the currentIthrough it, as given by the equation below, whereR is

the constant of proportionality. Here, the customary notation V(I) is used to denote Vas a

function ofI.

Linearity is a desirable characteristic of all systems where an output response is required to

be a faithful reproduction (except for a constant scale factor) of one or more inputs. Forexample, electronic amplifiers used in measurement and signal transmission and reproduction

systems are designed with linearity as a primary goal. Although physical systems are

generallynonlinearto some degree, in practice the objective is to realize a good

approximation to an ideal linear system by minimizing nonlinearities as far as possible. Any

departure from linearity in these systems causesunwanteddistortion of the original signal

and results in adegradedanderroneousresponse. See also Amplifier;Distortion (electronic

circuits).

gain

Inelectronics,gain is a measure of the ability of acircuit(often anamplifier) to increase thepoweroramplitudeof asignalfrom the input to the output. It is usually defined as the mean

ratioof thesignal outputof a system to thesignal inputof the same system. It may also be

defined on a logarithmic scale, in terms of the decimallogarithmof the same ratio ("dB

gain"). A gain greater than one (zero dB), that is, amplification, is the defining property of an

active electronic componentor circuit, while apassivecircuit will have a gain of less than

one.

Thus, the term gain on its own isambiguous. For example, "a gain of five" may imply that

either thevoltage,currentor thepoweris increased by a factor of five, although most often

this will mean a voltage gain of five for audio and general purposeamplifiers, especially

operational amplifiers, but a power gain forRFamplifiers, and for directional aerials will

refer to a signal power change compared with a simple dipole. Furthermore, the term gain is

also applied in systems such assensorswhere the input and output have different units; in

such cases the gain units must be specified, as in "5 microvolts per photon" for the

responsivityof a photosensor. The "gain" of abipolar transistornormally refers to forward

current transfer ratio, either hFE ("Beta", the static ratio ofIc divided byIb at some operating

point), or sometimes hfe (the small-signal current gain, the slope of the graph ofIc againstIb

at a point).

Inlaser physics, gain may refer to the increment of power along the beam propagation in a

gain medium, and its dimension is m1

(inverse meter) or 1/meter.
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voltage swing

The peak-to-peak voltage range of a signal in a circuit.

Documents

Analog Design Tradeoffs