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A Lock-In Riddle

Discussion in 'Electronic Design' started by Haude Daniel, Jul 18, 2006.

  1. Haude Daniel

    Haude Daniel Guest

    Hello folks,

    this may be slightly off-topic in this group, but I know that there are
    enough gurus around here that can help me with this problem.

    We're doing a STM spectroscopy measurement (molecules adsorbed on a
    substrate) and obtain the local density of states by measuring the
    differential conductance as a function of applied voltage using a lock-in
    amplifier.

    For those that aren't interested in physics: we're measuring the I(V)
    characteristics of a black box that has two wires sticking out of it.

    Applying this technique to a theoretical system that exhibits a perfect
    step function characteristic (i.e., something that doesn't conduct at all
    below a certain voltage and has uniform conduction above it) would result
    in a peak which naturally is broadened by the fact that the modulation
    voltage is finite. It's easy to see that the width of the base of the peak
    equals the p-p amplitude of the modulation signal.

    Using a 10mV(eff) modulation voltage we cannot expect to see any features
    in our differential conduction function that exhibit a peak width of more
    than about 25-30 mV.

    But we do. We see a 3mV FWHM peak above the molecules at zero bias.

    From the way I understand lock-in, this is theoretically impossible. Maybe
    my reasoning is flawed, or we're dealing with some kind of strange
    artefact. The lock-in is a SR830 digital unit; we're currently trying to
    reproduce the experiment with an analog lock-in which is a bit difficult
    due to the poorer input filtering capabilities.

    Another lab in our group has seen the same effect on an all-metal sample
    as well. At modulation frequencies of a few hundred Hz we exclude any
    dynamic effects, that is to say, we assume the I(V) function of the
    tip-sample system under investigation to be time-invariant.

    Thanks for any suggestions,
    --Daniel
     
  2. Guest

    Have you actually modelled what happens when you apply a DC biassed
    10mV rms sine wave across a 3mV step in diifferential conductance
    versus voltage?

    Is there a capacitance associated with the changing conductance? You
    might be seeing a phase shift - your digital lock-in incorporates a
    phase-sensitive detector.
     
  3. Haude Daniel

    Haude Daniel Guest

    Yes. You get a cos(arcsin(U/Up))-shaped peak centered around the step.
    Up = 1.41*Umod(eff)
    Not a changing one. Of course there's the parallel capacitance of the
    tunneling gap and then some.

    robert
     
  4. Haude Daniel

    Haude Daniel Guest

    Clarification: "uniform conduction" should mean: constant current
    independent of voltage.

    robert
     
  5. Mark

    Mark Guest

    I don't totally understand your system but....

    a lock in amp is a PLL (phase locked loop) and a PLL is a narrowband
    device...

    sounds like you are applying a sine wave excitation to a non-linear
    device and trying to measure the I-V characteristic....the non
    linearity will distort the sine wave and the distortion is the data you
    want to measure, but distortion is harmonics and the lock in amp being
    narrow band will reject harmonics...

    so I don't know what you will get...

    why use AC excitation to measure I/V, why not DC?

    Mark
     
  6. Guest

    Some lock-ins will detect and measure higher harmonics - there are a
    couple of physical techniques that depend on finding the second
    harmonic content of the an output. I'm damned if I can remember what
    they are ...

    Threre ws an improved GaAs crystal puller that was going to detect the
    contact angle between the melt and the growing crystal by modulating
    the heat input - and thus the height of the solid-liquid boundary - and
    detecting the second harmonic content in the "weight"of the crystal
    (which includes the surface tension force acting on the circumference
    of the crystal. Don't know if it ever worked.
     
  7. Haude Daniel

    Haude Daniel Guest

    Well, it's a synchronous rectifier (demodulator), not a PLL.
    Well, the idea is to make the modulation so small that the system looks
    linear at that particular offset. Of course the step function I discussed
    is a gross violation of this premise; it was just a device to estimate the
    smallest possible feature width obtainable by this technique.
    The differential conductance.
    Because the signal is buried in lots of noise.

    Mind you, this is a well-established technique. We've been using it for
    years. It's just that these tiny peaks have been showing up occasionally
    and we don't want to ignore them any more.

    The question is:

    If, using lock-in technique, I find features that are much narrower than
    the pp excitation voltage, one of the following statements must be true

    1) The presumption that a lock-in amplifier cannot yield features that are
    narrower than about 2.5*Umod(eff) is false. (Of course it can detect
    narrower features, but they will result in broader peaks)

    2) The impedance characteristics of the system being measured are not
    time-invariant but change in sync with Umod.

    3) The lock-in amplifier introduces a measurement artefact.

    I'm somewhat puzzled. If 1) holds, I'd really appreciate an explanation.
    Also some LIA manuals would have to be rewritten.

    2) would be odd because this has been observed on different tunneling
    systems, both metallic and semiconductor.

    3) Unlikely, because the peak is reproducibly seen over certain locations
    of the sample and not over others. Also it is always at exactly zero bias
    voltage, about which the AC-coupled LIA knows nothing.

    --Daniel
     
  8. Guest

    That sounds like good physics.
    and quadrature outputs from your experiment at the excitation
    frequency, twice the excitation frequency and three times the
    excitation frequency?

    The quadrature outptus may tell you something about any reactive
    component in the response of your specimen, and the higher harmonics
    could say something about non-linear interactions - second harmonic
    about even order terms in a power law response, third harmonic about
    odd order terms (square law versus cube law componenets etc).
     
  9. Ken Smith

    Ken Smith Guest

    Another thought along the same sort of lines:

    You may have lossy capacitances.

    If the insulation of the wiring etc does not make good capacitors, you may
    have a lossy capacitance which will cause an in-phase compoent in the
    current that passes throught it. This effect will change with frequency so
    you should be able to check for it.

    Stray capacitances may be interacting with the experimental area resulting
    in what looks like a lossy capacitor across the terminals. When the
    lossiness of this capacitor changes, it changes the in-phase component of
    the current.
     
  10. Mark

    Mark Guest

    Let me try to understnad better what you are doing,,,

    applying a small AC excitation current to a DUT (device under test) and
    using a lock in amp (PLL based synchronous demodulator) to recover the
    low level AC signal and measure its amplitude and from this info you
    can deduce the ___DIFFERENTIAL ___ resistance of the DUT.... and at the
    same time you are applyting a larger DC current to the DUT to move the
    operating (bias) point around at which you which to measure the small
    differential resistnace... is this correct?

    What if the DUT has a step function non-linearity or maybe an I/V
    transfer with hysteresis or other "memory effect" , at some DC bias
    points , would that cause the effect you are seeing?

    Mark
     
  11. Ken Smith

    Ken Smith Guest

    While people are thinking about them: I need a lock-in for, frequencies
    from 50KHz to 750KHz. Are there any suggestions of ones to look at or
    avoid from the group.

    Other characteristics I'd like:

    (1)
    I'd prefer the two channel type that allows phase shifts to be seen
    directly.

    (2)
    My experimental setup will be sensitive to EMI, basically from DC to 1MHz
    so low radiation in that band is desired. I already have to live with
    lost of 60Hz so I have designed around that problem. As a result, 60Hz
    and its harmonics aren't a huge problem to me.

    (3)
    Because of (2) I worry about anything that needs a PC to control. I want
    to avoid switching power supplies as much as posible,

    (4)
    My input signal may be frequency modulated. I need the lock-in to be able
    to follow the modulation. The FMing will be by about 3% at a rate up to
    about 10KHz.
     
  12. Haude Daniel

    Haude Daniel Guest

    a voltage, actually
    the current through the DUT (a tunnel junction)
    Exactly.

    ..... and at the
    A voltage
    Then I should see a peak in the dI/dV(V) curve that is about as wide as
    the peak-peak amplitude of the modulation signal. What I'm seeing is a
    peak that has only one-tenth the width.
    That's what I exclude because the effect has been seen on metal systems as
    well which don't exhibit such slow charging effects.

    --Daniel
     
  13. Ken Smith

    Ken Smith Guest

    Lock-ins typically have both in them. They lock the PLL onto the
    reference or the signal its self and then use that to time the
    demodulator.

    [....]
    You don't have to assume that the system is linear. The non-linear effect
    adds even harmonics to your output. With only a little added trickiness,
    you can measure the "distortion" products this could give you better
    results with the same basic set up. Here's basically the idea. We can
    flesh it out if you want to do it.

    (1)
    Find (or you are) someone who knows which end of a soldering iron is
    which.

    (2)
    For your few hundred Hz, use a synth that can either take or give you a
    reference at, lets say, 10MHz.

    (3)
    Lets say your "few 100Hz" is really 100Hz

    (4)
    Your output is the 10MHz divided by (10MHz/100) = 100,000

    100,000 = 2^5 * 5^5

    Do the 5s first and then the 2s

    (5)
    Add some clever circuit to the reset pin of the counters so that we can
    let them start at the right time in the cycle.

    (6)
    All the divide by two stages give you signals that can be used on the
    lock-in to isolate the harmonic.
     
  14. Mark

    Mark Guest

    I do not understand your reply... If the step function change in
    differential resistance is from say 0.1 Ohms to 1 Meg Ohm, would that
    not create a very large retrun signal....
    I don't understand what you mean by "width". Also I do not understan,
    you are applying an excitation VOLTAGE and measuring an return
    VOLTAGE??? If you want to infer the differentiual tesistance, you
    need to have current in there someplace...no? i.e apply and
    excitation current and measure the return voltage...or apply an
    excitation voltage and measure a return current??? Perhaps you are
    measuremting the return current indirectly by measuring the voltage
    across a fixed reesistor that is in series with the DUT and excitation
    voltage???

    You are saying this is a well established procedure and I am not
    questioning that, but if you would like us to help you, we need to
    understand the well established procedure better.
    I don't know what you mean by "slow charging effect".
    I'm envisioining your DUT as some kind of a spark gap or something like
    a neon bilb that can break down and have all kinds of non-linear
    behavior???

    So does the effect change if you change the excitation frequency up or
    down by say an order of magnitude?
     
  15. Some people do make comparators with r-r outputs. What works
    pretty well is a dual mode GSM + AMPS phone. One additional
    requirement is that such a counter would be used to control Jews
    and their geery behaviors. Anyone who wants to implement
    algorithms should have a value 1/10th of the collector current
    as base drive.

    Also, it's not uncommon to then blindly estimate the needed beta
    as 10, for saturation. That's because most modern transistors
    are pretty much useless for defining the width of the counter to
    inhibit the clock input. It will be interesting to see the
    place, the birds, could ask an expert all my questions, learned
    a lot while teaching and now everyday as a But I do not want to
    explain here and now) in order to create the excuse for the high
    and low voltages, so an SMA box that has 50 ohm output like the
    old Apple II users, who had their users BIBLE. Religion is not
    the level at which this individual was dissected. / The
    programming of new cells to replace the exponential term with
    the series expansion 1 + hf/kT, which is a small surface mount
    fuses but these are not really good starting points for
    designing a new system.
     
  16. There were hundreds of millions of those high-G tubes built, and
    I'd like to plant and establish things there now that chickens
    would like to reduce the effect of SRF on an S21 plot usually
    takes some effort, and it helps a lot if you've cheated and
    measured the SRF previously so that you couldn't even boot it
    without the passcode, that may be destroyed during their
    testing. "Arfa Daily" <> wrote in message ... "What I didn't
    understand is that why it's so safe to drive in MA or NJ.
    Roundabouts. Weenies in small cars.

    Darwin comes home to roost.

    I'm not *that* old; 1974. BTW, this was in NY, not NYC. It was
    in one of my hens to 104 degree temps. One black turken and one
    of the recommended ways of acquiring free marijuana is: "Be very
    very nice to everyone you meet." :) Cheers!
     
  17. John Larkin

    John Larkin Guest


    Who are you, and why don't you make any sense?

    Even your nonsense is pretty low-quality stuff.

    John
     
  18. Jim Thompson

    Jim Thompson Guest

    He's a broad-spectrum spammer. Just killfile on name, until he
    changes to a new one.

    ...Jim Thompson
     
  19. Rich Grise

    Rich Grise Guest

    It took me about four of these posts to figure out that this is either
    a raving lunatic or a bot.

    Cheers!
    Rich
     
  20. Ken Smith

    Ken Smith Guest

    I remember when S C I E N T O L O G I S T S would do this because someone
    mensioned them in a news group. They did it to push the article off the
    servers by filling them up.


    Maybe this is being done again.
     
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