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Capacitors and resonant frequency

Discussion in 'Electronic Basics' started by meyousikmann, Oct 29, 2006.

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  1. meyousikmann

    meyousikmann Guest

    I have a problem that asks about the movement of the second plate of a
    capacitor in order to change the resonant frequency by 10 ppm in an LC
    circuit. I am getting stuck in terminology.

    Here is the information given:

    Area of each capacitor plate (one attached to solid nonmoving post while
    other can move small distances perpendicular to the plates)
    ..01 m^2

    Initial plate separation
    100 micometers

    Inductance
    120 nH

    I have found the initial capacitance and frequency, but the second part of
    the question says "How far must the second plate move to change the resonant
    frequency by 10ppm". I am not entirely sure what this question is asking
    for. Where does ppm fit into any of the calculations. I don't want
    answers, but I would appreciate if somebody can translate the question into
    something I might understand.
     
  2. Baron

    Baron Guest

    Think about the definition of a capacitor ! The value of capacitance
    for a fixed plate area will vary in inverse proportion to the
    separation !
     
  3. delta f = 10/1e6 x f1

    fx = f1 - delta f

    solve for new value of C based on fx

    solve for new plate spacing based on C

    (If I understand the question ;>)
     
  4. Tom Biasi

    Tom Biasi Guest

    I believe you are being asked to determine the capacitance needed for that
    frequency change and then determine the plate areas that must face each
    other at the given distance.

    Tom
     
  5. First you need to derive the relationship between
    capacitance and frequency (the power of proportionality).

    Then you derive the relationship between plate spacing and
    capacitance (another power of proportionality). Then
    combine these two things to get 10 ppm frequency change.
    10ppm is just a fraction 10/1,000,000 times the original
    frequency. So the original frequency must become either 1 +
    10/1,000,000 of its original value, or 1 - 10/1,000,000 of
    it (depending on whether the plates are moved apart or
    together).
     
  6. Eeyore

    Eeyore Guest

    It's another way of representing a small number ( as in parts per million ).
    Compare with per_cent for example which is parts per hundred.

    Graham
     
  7. Guest

    Off the top of my head, I think it's:

    100um (plate spacing) * (10 ^ -6) = 10^ -9 m = 1 nanometer
     
  8. Guest

    Wait, my last post was wrong.

    f = 1/(2 * pi * sqrt(LC))

    so I get 2 nanometers.
     
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