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Resonator Calculations

Discussion in 'Electronic Design' started by redhat, Jun 29, 2005.

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  1. redhat

    redhat Guest


  2. The natural resonance frequency is simply
    (1/2 Pi) * sqrt( (1/C7 + 1/C7A + 1/C7B) / L )
    The capacitors are just in series w.r.t. the resonance.
    The actual peak frequency will depend on the source
    and load resistances and be somewhat lower, especially
    with 50 Ohms at each port.
     

  3. At the 94MHz or so frequency of interest, you convert the ends from parallel
    to series form.

    33pF in parallel with 50R at 94 MHz transforms to 76pF in series with 30
    ohsm.

    Now your capacitance is 76 pF in series with 76 pF in series with 5p5. The
    5p5 dominates.

    Q at resonance is 1 / (2 Pi f C R ) = about 5. With such a low Q, the ends
    won't have that much effect on tuning. Especially if L7 is not adjustable,
    you would want a low Q or else component and construction variations would
    move your frequency around too much.

    The end capacitors are there to set the Q and hence bandwidth and losses in
    the filter.

    Roger Lascelles
     
  4. redhat

    redhat Guest

    Hi Larry,
    how could the capacitors be in series with each other, you haven't
    considered input and output ports?
    Hi Roger,
    you have assumed a frequency of 94MHz to convert the capacitor to
    series, what if i don't know the resonant frequency?

    regards
     
  5. I just took the L7 C7 series resonant frequency to get in the ballpark.
    Using the transformed ends I could calculate a new resonant frequency, then
    recalculate the ends again etc.

    Its quite common to do the transformation at one frequency then use the
    result over a narrow band of frequencies.

    Easiest to just whack it into SPICE, 50 ohms source and load and look at the
    response.

    The schematic looks as though non of the components is adjustable. In a
    commercial piece of equipment, you just might get away with selecting your
    components to give the pass frequency you want and always fitting the same
    brand and value parts onto the same PCB. Otherwise, you'd make L7 or C7
    adjustable and tune it up.


    Roger Lascelles
     
  6. Andrew Holme

    Andrew Holme Guest

    Download SCILAB from http://scilabsoft.inria.fr/
    You only need a "Compact" installation
    Run this script (paste into editor window, then execute):

    s = poly(0,'s');

    xL7 = s*540e-9;
    xC7 = 1/s/5.5e-12;
    xC7A = 1/s/33e-12;
    xC7B = 1/s/33e-12;

    Ri = 50;
    Ro = 50;

    z1 = 1/(1/Ro+1/xC7B);
    z2 = xC7 + xL7;
    z3 = 1/(1/xC7A + 1/(z1+z2));

    f = z3/(Ri+z3) * z1/(z1+z2);

    xbasc(0);
    bode(syslin('c', f), 1e7, 9e9, .01);


    Voila! A beautiful Bode plot. Even better if you do "set old_style
    on" first. With 50 ohm terminations, the resonant frequency is close
    to 100 MHz.
     
  7. Andrew Holme

    Andrew Holme Guest

    Phase passes through 180 degrees around 125 MHz
    bode(syslin('c', f), 1.24e8, 1.26e8, .01);
     
  8. Kevin Doyle

    Kevin Doyle Guest

    Is there a formula for calculating the phase shift of the resonator circuit
    shown.
    That would be interesting to compare it with a computer calculated model.

    Cheers,
    Kevin.
     
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