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Determine LC ring freq

Discussion in 'Electronic Design' started by Stuart Hall, Jul 16, 2007.

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  1. Stuart Hall

    Stuart Hall Guest

    When I feed a squarewave into a resonant tank circuit (LC network)
    what component determines the _frequency_ of the resulting ringing?

    I know the Q, or persistence, relates to how well the network is
    tuned. But what about the actual ringing frequency?

    Stuart Hall
     
  2. Phil Allison

    Phil Allison Guest

    "Stuart Hall"

    ** The ringing frequency seen is that of the LC network itself.

    The frequency of a driving square wave is irrelevant except to the
    repetition rate of the ringing behaviour - this assumes the square wave
    frequency is at least several times lower than the ringing frequency.




    .... Phil
     
  3. Fred_Bartoli

    Fred_Bartoli Guest

    Phil Allison a écrit :
    More precisely, several times lower than the ringing frequency divided
    by the tank Q.
     
  4. Phil Allison

    Phil Allison Guest

    "Fred_Bartoli"


    ** Purest bollocks.

    Yawn - yet again ..........




    ......... Phil
     
  5. Fred_Bartoli

    Fred_Bartoli Guest

    Phil Allison a écrit :
    As you say: yawn
     
  6. Phil Allison

    Phil Allison Guest

    "Fred_Bartoli"


    ** Make your damn point - Fred.

    **** knows what the hell it is, but do have the decency to put the poor,
    mangy, bedraggled thing out of its misery .... ASAP.





    ........ Phil
     
  7. MooseFET

    MooseFET Guest

    Several can be as low as three. Three isn't quite enough. Make that
    many and it will be better.
     
  8. Guest

    When you feed a square wave into a resonant tank circuit, the tank
    circuit presents a frequency dependent impedance to the the harmonic
    content of the square wave.

    The square wave can be resolved into a series of sine waves, the first
    having the same period (frequency) as the square wave, while the rest
    are the odd harmonics of that sine wave, with frequencies of three,
    five and seven (etcetera) of the first sine wave and amplitudes
    decreasing in proportion to the harmonic number (one third, one fifth,
    one seventh etcetra).

    If one of these harmonics is close to the resonant frequency of the
    tank circuit the tank circuit may appear to ring at that frequency,
    but what you will see will depends on the relationship between the
    output impedance of the source of the square wave and the impedance of
    the tank circuit.

    If the resonant peak of the tank circuits overlaps a couple of
    harmonics, the waveform appearing across the tank circuit can look
    rather odd.

    Get hold of a copy of LTSpice (Linear Technologies Switcher Cad III)
    and see for yourself.
     
  9. Fred_Bartoli

    Fred_Bartoli Guest

    MooseFET a écrit :
    I thought several could be as low as two :)

    The exponential factor term is Exp(-t Wo/(2Q))
    Now let several be as low as two.
    The exponential factor is now
    Exp(-(2Q/Fo)/2 2.Pi.Fo/(2Q)) = Exp(-Pi) = 0.043
    That's low enough to make all the 'strange effects' small enough.
    With several as high as three, the residuals get under 1% and at
    several=4 that's 0.2%.

    Can we agree on many starting at three? ;-)
     
  10. John Larkin

    John Larkin Guest


    Pretty close to

    F = 1 / ( 2 * pi * sqrt(L * C) )


    John
     
  11. MooseFET

    MooseFET Guest

    No, that would be a couple or a few.

    Yes, for large values of three.

    While I don't dispute your math, I do suggest that you may be applying
    the wrong math to what is really cared about here. The OP wanted to
    measure the frequency of the ringing. For low frequency squarewaves,
    this could come out quite exact.

    I was thinking in terms of how well the frequency can be measured.
     
  12. me

    me Guest

    snip

    several is 2 to 7
    a few is 3 to 11
     
  13. Jim Thompson

    Jim Thompson Guest

    [snip]
    Is that definitive ?:)

    ...Jim Thompson
     
  14. Robin

    Robin Guest

    If you grab hold and force a garden swing to move at some frequency,
    slow or fast then it will. Likewise if you connect a "powerful" (low
    impedance) squarewave generator to an LC then it will do that square
    wave - the harder the drive, the more slavishly the copying.

    Alternately, if you "ping" a garden swing, it will, as soon as the
    push disconnects, start to move "freely" at its natural frequency.
    Likewise the LC, you have to "ping" it and then let go to allow it to
    move freely.

    If you know the frequency of the swing then you can adjust your
    pushing in sympathy for best effect. Likewise the LC if you connect a
    sinusoidal generator to it but it *would* have to be just right it
    there was a "direct" (low impedance) connection.

    To give the LC a bit of freedom, to release it a little from the hard
    grip, put a resistor in series with the sinusoidal generator,
    (increase the driving impedance) now, as you swing the generator's
    frequency through the LC's resonance, it is allowed to build up an
    amplitude of its own. If you get it just right, the amplitude will
    keep increasing (just like the garden swing) to greater than the
    driving force! The greater this effect is, the greater must be the Q
    i.e. the bigger the series resistance the bigger the Q.

    I.e. as the resistance gets greater so the generator is less connected
    to the LC and the less the generator *damps" the swing, the greater
    the Q.

    As the other poster says, if you use a square wave instead, then you
    will be using a whole bunch of sinusoids simultaneously (because a
    square wave is ~ the sum of all the odd harmonics of its fundamental
    i.e. f + 3f/3 + 5f/5...) so it is likely one of these harmonics will
    "rattle" the LC at the its resonant frequency - by chance.

    But only if that square wave it (appreciably) below the LC's
    resonance.

    Robin
     
  15. Robin

    Robin Guest

    If you grab hold and force a garden swing to move at some frequency,
    slow or fast then it will. Likewise if you connect a "powerful" (low
    impedance) squarewave generator to an LC then it will do that square
    wave - the harder the drive, the more slavishly the copying.

    Alternately, if you "ping" a garden swing, it will, as soon as the
    push disconnects, start to move "freely" at its natural frequency.
    Likewise the LC, you have to "ping" it and then let go to allow it to
    move freely.

    If you know the frequency of the swing then you can adjust your
    pushing in sympathy for best effect. Likewise the LC if you connect a
    sinusoidal generator to it but it *would* have to be just right it
    there was a "direct" (low impedance) connection.

    To give the LC a bit of freedom, to release it a little from the hard
    grip, put a resistor in series with the sinusoidal generator,
    (increase the driving impedance) now, as you swing the generator's
    frequency through the LC's resonance, it is allowed to build up an
    amplitude of its own. If you get it just right, the amplitude will
    keep increasing (just like the garden swing) to greater than the
    driving force! The greater this effect is, the greater must be the Q
    i.e. the bigger the series resistance the bigger the Q.

    I.e. as the resistance gets greater so the generator is less connected
    to the LC and the less the generator *damps" the swing, the greater
    the Q.

    As the other poster says, if you use a square wave instead, then you
    will be using a whole bunch of sinusoids simultaneously (because a
    square wave is ~ the sum of all the odd harmonics of its fundamental
    i.e. f + 3f/3 + 5f/5...) so it is likely one of these harmonics will
    "rattle" the LC at the its resonant frequency - by chance.

    But only if that square wave it (appreciably) below the LC's
    resonance.

    Robin
     
  16. Jasen Betts

    Jasen Betts Guest

    few is more than several ? I would have expected it to be fewer!



    Bye.
    Jasen
     
  17. Rich Grise

    Rich Grise Guest

    I once read somewhere that there are primitive cultures that count:
    "One, Two, Three, Many."

    Cheers!
    Rich
     
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