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effect of shot noise on measurement

Discussion in 'Electronic Design' started by [email protected], Jan 16, 2008.

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  1. Guest

    Hi everyone,

    From the Internet definition of the shot noise, it seems that charge
    is flowing as clumps rather than a smooth, continuous function. So,
    will the effect be that if you are measuring something that remains
    constant, you will see small fluctuations in the measurement value
    because of the shot noise? How is this manifested and is there a way
    to compensate for it?

    Cheers,
    Luca
     
  2. Phil Hobbs

    Phil Hobbs Guest

    Shot noise arises from ordinary sqrt(N) fluctuations due to the counting
    statistics of electrons, unless the electrons are forced to be
    correlated. A given current can have no shot noise, partial shot
    noise, or full shot noise (i.e. i_n = sqrt(2eIdc) amps per hertz).
    After amplification, it can even have more than full shot noise.

    Not all measurements exhibit shot noise. Most purely electronic ones do
    not, e.g. strain gauges, accelerometers, capacitive gauges, and most
    kinds of temperature sensors. Most measurement folks run into shot
    noise primarily in photocurrents, i.e. the output current of a
    photodiode. Photocurrents have exactly full shot noise essentially
    always.(*) There's no way to get round this limit, except by narrowing
    the bandwidth (i.e. using a lock-in amplifier or trace averaging) or
    finding some more light from somewhere.

    Shot noise in circuits usually arises from conduction in
    transistors--the collector current of a bipolar transistor with no
    feedback applied will have full shot noise. That sort of problem is
    fixed using feedback, and enough feedback can suppress it to any degree
    you like. Photocurrents are another matter.

    Cheers,

    Phil Hobbs


    (*)There are a very few instances, using quantum measurement techniques,
    where the noise can be a couple of dB less, and if you're looking at the
    long-wavelength tail of an extremely hot and extremely small thermal
    source, the noise can be a few percent more. Otherwise, any unamplified
    photocurrent will exhibit exactly full shot noise.
     
  3. Any kind of noise amounts to fluctuations. When measuring a constant
    value, you can easily compensate by filtering (averaging).

    As to shot noise, it isn't going to be a factor in a 1.5 meter wire:

    "However, shot noise is absent in a macroscopic, metallic resistor
    because the ubiquitous inelastic electron-phonon scattering smoothes
    out current fluctuations that result from the discreteness of the
    electrons, leaving only thermal noise."

    http://www.lorentz.leidenuniv.nl/beenakkr/mesoscopics/topics/noise/noise.html

    What are you actually trying to do?
     
  4. Guest

    If you are measuring a current of - say - 100 electrons per second, or
    - to be more realistic - a light intensity that only delivers 100
    photons per second to your detector - that 100 electrons or photons in
    any one second is merely the number that you are most likely to see.

    In fact, over a long series of one second measurements you will get a
    distribution of numbers.

    The mean number of hits per second will average out to one hundred,
    but the standard deviation of the distribution will be ten - more
    generally, the square root of average number of hits over the
    measurement period.

    The fluctuations from one measurement to the next look exactly like
    random noise. The only way you can compensate for it is to average a
    lot of observations.

    This does assume that successive photons or electrons are not
    correlated - the electrons are not coming from some of charge pump
    that spits one one electron every ten milliseconds, on the ticks of of
    a 100Hz clock. This true for most situations where one wants to take a
    measurement, but there are occasional exceptions - electrons coming
    from a photocathode or a electron gun can be emitted a bit more
    regularly than you'd expect, because the space charge of the last
    electron emitted can make it less likely that the next electron to be
    emitted while its predecessor is still close to the source.
     
  5. Guest

    Ahhhhhhhh ok...so it is somehow related to the Poisson distribution
    and hence probably truly random.
     
  6. [...]

    I suppose one could argue that there is always the shot noise of the
    individual electrons. Or is shot noise defined so as to exclude this
    component? ("Quantization" noise?)
     
  7. Phil Hobbs

    Phil Hobbs Guest

    It's true that you can't have a fractional number of electrons, and this
    sets the lower limit of charge granularity. But that's not a
    _measurement_ issue, really, it's a question of whether what you want to
    measure is itself actually a well-defined quantity. Both feedback and
    bandwidth-narrowing have effects on circuit operation (i.e. reduced gain
    and slow measurements) that eventually limit how well you can do in any
    practical case.


    Cheers,

    Phil HObbs
     
  8. Tim Williams

    Tim Williams Guest

    Not necessarily. An electron can be anywhere on a wire, and there needn't
    be an integral number of electrons, say, on the gate of a FET: there could
    be electrons *near* the gate (or its connections), changing the electric
    field a continuous amount.

    Tim
     
  9. John Larkin

    John Larkin Guest

    The lack of shot noise is (I think?) some sort of e-e interaction in
    metallic conductors. Is that some phonon thing, like the Cooper pair
    effect? If it is, wouldn't it stop working at low currents, as the
    moving electrons start to get very far apart on average? I've googled
    this issue a fair amount and found little good stuff. It's not even
    clear what sorts of conductors have zero shot noise... metal films for
    sure, but what about cermets, or carbon film?

    I put together a semi-crude setup to measure shot noise in various
    resistors, and tried metal/cermet/carbon, and couldn't see shot noise
    in any of them, in a setup that should have easily measured full shot
    noise.


    Hmmm, if you split up a thinfilm resistor into many narrow paths,



    |-----------------|
    | |
    |-----------------|
    | |
    -------|-----------------|--------
    | |
    |-----------------|
    | |
    |-----------------|


    might that increase shot noise?



    John
     
  10. Guest

    That's not how low currents work in metallic conductors - there are
    still a lot of electrons around, but the net rate of movement becomes
    very slow.
    Carbon film resistors do have "excess" noise - more than you would
    expect from Johnson noise in an ideal resistor having the same
    resistance - but it isn't due to shot noise. The stuff I've read seems
    to suggest this has to do with the negative temperature coefficient of
    the carbon film, which leads to a certain amount of "current
    channeling". This doesn't lead to visible instability at at low
    currents (actually low self-heating) but does make the resistance
    slightly unpredictable.
    No. Thin film resistors don't exhibit shot noise - the electrons
    interact and smooth out the effects of their discrete nature.
     
  11. Guest

    You are quite right. It is a Poisson distribution (which looks rather
    like the normal distribution when you've got more than a few electrons/
    photons per sampling period).
     

  12. Think of a carbon composition bulk resistor. It is a semi-conductor
    material. There is going to be friction.
     

  13. I wonder what the shot noise of the guys in the pool in Germany with the
    power strip floating by is.
     
  14. Phil Hobbs

    Phil Hobbs Guest

    According to our late solid state guru, Rolf Landauer, the shot noise
    suppression in a resistor is equal to the mean free path divided by the
    length of the resistor. Inelastic electron-electron scattering smears
    out the clumps. Putting wires in parallel shouldn't do anything one way
    or another.

    Cheers,

    Phil Hobbs
     
  15. John Larkin

    John Larkin Guest

    But summing a large number of zero-shot-noise but uncorrelated current
    sources won't cause shot noise? It's not as if the electron streams
    from the various paths are cooperating.

    John
     
  16. I would think it would average whatever shot noise was emerging from
    each stream, and the result would be sqrt(n) times the noise from one,
    while the current would be n times.
     
  17. whit3rd

    whit3rd Guest

    Both vacuum tubes and semiconductor diodes have shot noise
    associated with current flow, because the electrons that flow
    are localized in these devices. FETs, on the other hand, have
    a continuous channel, and the electrons aren't constrained
    to have local position well-determined in that channel.
    So some amplifier types have shot noise, and others don't.

    Shot noise is just the phenomenon of movement statistics
    in discrete charge packages, i.e. electrons. You can't
    compensate for it, only swamp the noise with statistically
    large numbers of charges. There are LOTS of things that
    require statistically large quantities of charge, it's very
    unusual to find shot noise to be a limitation.
     
  18. Phil Hobbs

    Phil Hobbs Guest

    I don't see why it would. If you have N identical currents, then since
    their residual fluctuations aren't correlated with each other, the
    current goes up by N and the fluctuations by sqrt(N) times the RMS value
    of the individual fluctuations. That means that if the individual
    currents have epsilon times full shot noise, the sum also has epsilon
    times what its full shot noise would be.

    Cheers,

    Phil Hobbs
     
  19. Eeyore

    Eeyore Guest

    What a MORON !
     
  20. So, tell us, asswipe... which is better in one of your glorious mixer
    designs:

    Carbon comp bulk media resistors, or:

    Metal film.

    Your answer will shed yet more light on how many working brain cells
    you possess.
     
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