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UCSC PHYS 160 - Lecture 11 Notes

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Physics 160Lecture 11R. JohnsonElectronic Noise• I will skip through this quickly, because most students in Physics 160 are already challenged enough by more basic circuit issues.•BUT!!• For a physicist this is often the most critical aspect of circuit behavior that must be well understood and optimized, because– amplifiers are likely being used to detect very small signals and– noise is unavoidable, tends to be amplified by the amplifier, and can easily obscure the signal.May 6, 2014 Physics 160 2Thermal Noise• Thermal noise in a resistance R (Johnson noise):– This is the minimum possible noise in any resistance– Applies also to dynamic resistances, such as for a diode– The power frequency spectrum is flat (“white” noise, up to some limit)BvVn22noisekTRvn42withKlidiJ/K 1038.123Tk• B is the bandwidth, which is the frequency range over which you are looking at the noise (e.g. the maximum frequency response of nnoisenKelvindegreesin Tg(g qypyour amp or the 60 MHz bandwidth of your lab scope).– For example, for an audio amp, B would typically be 20kHz20Hz, or simply 20kHz.• Low-pass filters are good for reducing white noise, because they reduce B.– So don’t make an amp with frequency response that goes way above May 6, 2014 Physics 160 3the signal you are interested in! This is the main reason for the bandwidth-limit button on the lab scope, for example.Shot Noise• Diffusion of electrons across a diode junction is a random process, with each electron acting independently.–This isnotthecaseinametalwire or a resistorwhere theThis is notthe case in a metal wire or a resistor, where the electrons tend to move coherently.• If the current is small enough, this stochastic flow can become apparent and appears asrandomnoise called shot noise.apparent and appears as random noise called shot noise.BeIBiIn 222noise• Note how the power (I2R) is again proportional to B, indicating that this also is “white” noise.Wh th t fl th h i t th h t i•When the current flows through a resistor, the shot noise naturally gets translated into voltage noise.BeI2rmsnoiseNote that the percentage noise level May 6, 2014 Physics 160 4IInoisepgdecreases with increasing current:Flicker Noise (1/f)• Excess noise beyond the fundamental thermal and shot noise contributions almost always has a 1/f spectrum (“pink noise”)–There is no single physical source of flicker noise and the–There is no single physical source of flicker noise, and the amount depends critically on details of the electronic device.– It’s not obvious why in general the noise falls like 1/f, but one way or another the higherfrequency noise tendsto getway or another, the higher frequency noise tends to get suppressed.– 1/f means that each decade will have the same noise power.e g in an audio amp the flicker noise power contribution•e.g. in an audio amp, the flicker noise power contribution from 20 Hz to 200Hz is the same as from 200 Hz to 2kHz, which is the same as from 2kHz to 20kHz.High pass filters are good for reducing flicker noise–High pass filters are good for reducing flicker noise. • e.g., if we lowered the 3dB point of the audio amp from 20 Hz to 2 Hz, the flicker noise power would go up by 33%May 6, 2014 Physics 160 533%.Transistor (BJT) Noise Model• Spice transistor models generally include noise models– But be careful about flicker noise, which often is omitted from the model or set to zero, if you care about low frequencies.model or set to zero, if you care about low frequencies.• Think of the transistor as an ideal noiseless device, but with a voltage noise source in series with the base and a current noise source in parallel with the base-emitter junction.source in parallel with the baseemitter junction.Remember, whatever noise is present at the input gets amplified along pg p gwith the signal!May 6, 2014 Physics 160 6Transistor Noise• The source resistance plays two evil roles:It contributes thermal noise which the amplifier amplifies–It contributes thermal noise, which the amplifier amplifies– It converts the shot noise in the base current into voltage, which also gets amplified.•Thus this transistor model alone contributes anrmsnoise of•Thus this transistor model alone contributes an rmsnoise of22(rms)ampnSniRee May 6, 2014 Physics 160 7()pSee the next slide.Transistor White Noise2224eCbnreIkTre Voltage noise:Thermal noise of the intrinsic base Effect of shot noise in the collector current flowing resistance (~5 ohms)gthrough the intrinsic emitter resistancenV 29.04 bkTrnV4502reIfor rb=5 ohmsforIC=1mABeIi22nV45.02eCreIfor IC=1mACurrent noise:BvVnnrms :RememberMay 6, 2014 Physics 160 8BneIi2Current noise:BiInnnnrmsBias Network Noise• The bias network contributes noise very differently from the source impedance because it is in parallel with the source, not in series.– Therefore, its contribution to vnwill go like 1/sqrt(R), instead of like sqrt(R).– Bootstrapping would essentially eliminate the bias contribution.RS CThe noise current from RB sees an impedance in this node of RSin parallel with the amp, so it should be dominated by RS(i.e. amp Zin>> RS).to ampRBBnRkTRi4SnRRkTv4The voltage noise of the bias resistor RBproduces a noise current BnRSBnRpthat flows into the amp input node and develops a noise voltage that depends on the impedance of the inputNote that if there were no source resistance, then this noise source May 6, 2014 Physics 160 9impedance of the input node, dominated by RS.es sta ce, t e t s o se sou cewould be insignificant.Voltage-Amplifier Noise Example1 mACascode, to avoid Miller effect and keep ithihfgain up to high f.IB=7.7 AScope loadBMay 6, 2014 Physics 160 10Bypass REto get high gain of ~290.Noise Predictions (referred to the input)HznV54.045.029.022ne4kTTransistor base:HznV1414kkTHznV8.111.54 kkkTThese 3 contributions go away if the sourceBias network:Source resistance:HznV1.414kkTHznV6.112  keIBaway if the source impedance is zeroSource resistance:Base current:Sh t i f ll tHznV46.02905.712Gain2kmeReICCShot noise of collector current, flowing into the collector load resistor:SpicePredictsHznV71.046.054.022Total noise with zero source impedance:Ttl i ith1kSpice Predicts0.63 nV/ sqrt(Hz)May 6, 2014 Physics 160 11HznV9.471.6.11.48.12222Total noise with


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UCSC PHYS 160 - Lecture 11 Notes

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