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Resonant Frequency

Discussion in 'Electronic Basics' started by redhat, Jun 18, 2005.

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  1. redhat

    redhat Guest

  2. redbelly

    redbelly Guest

    Have you considered building the circuit and measuring the frequency?
     
  3. Andrew Holme

    Andrew Holme Guest

    You have a series LC circuit with inductor L, capacitor C5, and the
    capacitance of varactor D1.

    First, you need to know the capacitance of D1. This varies with the DC bias
    voltage. In your case, the bias voltage is Vcc. There should be a graph of
    capacitance vs voltage on the varactor data sheet.

    You can then combine the varactor capacitance with that of C5 using the
    equation for capacitors in series:
    C = (C1*C2) / (C1+C2)

    The resonant frequency of the LC circuit can then be found from :

    2*pi*f = 1 / sqrt(LC)
     
  4. redhat

    redhat Guest

    i want to calculate its resonant frequency not measure it.
     
  5. redhat

    redhat Guest

    Hi redbelly,
    i want to calculate its frequency not measure it
    Hi Andrew Holme,
    this is a resonator fo a vco, the input to the resonator is at the node
    connecting D1, L1, and R3 , so, the bias voltage to the varactor is
    Vinput+ ( Vcc - I*R3) is that correct? if so, how to calculate the
    resonant frequency noting that i don't know I where I is the current in
    R3 branch.
     
  6. Without knowing what is loading the output connection, the problem is
    indeterminate. I(f the output is open circuit, the circuit has no
    resonance worth mentioning. if the output is a short to ground, the
    resonant frequency is the series equivalent capacitance of the
    varactor and the variable capacitor with the inductor w=1/(sqrt(L*C)).
    If the output has other impedance, there is a different solution.
     
  7. redhat

    redhat Guest

    the load to the output is an npn transistor, so i have to take the Cbe
    into consideration, what about the Vcc what is its purpose?.. i mean
    the varactor bias is from the input voltage so is it to increase its
    bias voltage?
     
  8. Andrew Holme

    Andrew Holme Guest

    Please post the complete circuit.
     

  9. The Vcc bias alters the capacitance of the varactor. It also makes
    sure that the varactor stays reverse biased during the signal cycle,
    so that the device always looks like a capacitor. If the varactor
    ever becomes forward biased, it acts like a low value resistor in
    parallel with any junction capacitance.
     
  10. redhat

    redhat Guest

    here is the complete circuit; it is a vco
    http://www.geocities.com/aezzat3/vco1.jpg
    i don't know the capacitance of the varactor because it depends on (
    the input voltage + Vcc-IR3) ,so how to know the resonant frequency
    equation?
     
  11. Don Bowey

    Don Bowey Guest

    The vericap is spec'd with a plot of capacitance:voltage. If you can find
    the part number you can obtain that information. Since it is the FM
    "modulator," off-hand I think it's capacitance value will not affect the at
    rest frequency more than a couple hundred kHz.

    Don
     
  12. Andrew Holme

    Andrew Holme Guest

    You could have included a bit more to the left!

    I'm forced to assume the modulating input is coupled via a large resistor or
    a radio-frequency choke.
    I'm also assuming it's AC-coupled.
    Correct?

    Then the average DC voltage across D1 will be Vcc - get the capacitance from
    the datasheet for this voltage. It's probably in the region of a few pF.

    The series resonant frequency of D1, L1, C5 can then be found.

    I*R3 is negligible.

    BTW Is that supposed to be an inductor in Q1 collector?
     
  13. redbelly

    redbelly Guest

    If you don't know the varactor capacitance, there is no way to
    calculate a resonance frequency. The capacitance (as a function
    of input voltage) would be found on a spec sheet, if it can be
    found anywhere. Do you have a spec sheet for it? If not, have
    you looked on the manufacturer's web site? Or searched with Google?

    It might be helpful to know if an simplifiying approximation is
    valid. Is the input signal small enough so that the capacitance
    is largely determined by Vcc? Then you can use THAT capacitance
    (as determined by the varactor specs) to determine the resonance
    frequency.

    If, on the other hand, the input alters the capacitance significantly,
    then the behavior is highly nonlinear and probably a numerical
    simulation is required to find the resonance. But doing that would
    be well beyond the scope of what's describable in a newsgroup, and
    possibly more time-consuming than measuring the resonance for a few
    different values of L1 and C5.

    Mark
     
  14. Jamie

    Jamie Guest

    Fr = 1/2*PI*sqrt(L*C);
     
  15. Rich Grise

    Rich Grise Guest

    It's a VCO. "I/P" (presumably in-put), is the DC control voltage,
    then, redrawing, it's a simple Hartley oscillator with its output
    shorted to VCC - wait a minute..... Maybe they're taking the output
    off of ...

    There's something wrong with that circuit.

    But the resonant frequency is the series resonant frequency:
    f = 1 / (2 * pi * sqrt(L * Ct)), where Ct is the value of the
    series combination of C5 and the capacitance of D1. The capacitance
    of D1 depends on the sum of the input voltage and whatever proportion
    of VCC, depending on the impedance presented by the input.

    Hope This Helps!
    Rich
     
  16. redhat

    redhat Guest

    what is wrong with it? isn't this a resonator followed by negative
    resistance reflection amplifier? what i don't know is how to calculate
    the resonant frequency
     
  17. redhat

    redhat Guest

    what is wrong with it? isn't this a resonator followed by negative
    resistance reflection amplifier? what i don't know is how to calculate
    the resonant frequency because i don't know the portion of voltage
    remaining from Vcc.
     
  18. Andrew Holme

    Andrew Holme Guest

    The average voltage across the varactor is Vcc. This is the voltage
    you should use to lookup its capacitance.
     
  19. redhat

    redhat Guest

    how could it be Vcc? this means that the varactor has constant
    capacitance, so there is no change in frequency. am i right?
     
  20. Andrew Holme

    Andrew Holme Guest

    No. The *average* is Vcc. I'm assuming there will be a small AC
    modulating signal superimposed on top, but you can calculate the
    carrier frequency of the resultant FM from the average.
     
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