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calculate the Q factor of LC bandpass

Discussion in 'Electronic Design' started by power boy, Mar 9, 2013.

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  1. power boy

    power boy Guest

    Hi:

    Anybody knows how to calculate Q factor for LC bandpass?
    checked many online pdfs and books but got nothing.

    the circuits is

    ----------Ls---Cs------------
    | |
    Lp Cp
    | |
    --------------------------------

    We know there are too many types but I just want to know if all values
    are given,
    how to calculate the Q or BW. f0 is easy to calculate but I forget how
    to calculate Q.

    Thanks.
     
  2. rickman

    rickman Guest

    The Q relates to the resistance relative to the reactive components. Do
    you know the values for your resistances? It will depend also on
    whether you model the resistances as parallel or serial to the other
    components. Typically the L will have an ESR (equivalent series
    resistance). But if you are working at high frequencies such as power
    supply distribution, for example, the ESR of the capacitor might be the
    significant factor.

    I just solved the equations for resonance of this circuit. But I left
    out the R values to simplify the math. With typical Q values the R does
    not change the resonance significantly.

    What formula do you use for f0?
     
  3. Phil Allison

    Phil Allison Guest

    "power boy"

    ** You sure about that schem?



    ..... Phil
     
  4. Guest

    In order to calculate the Q for the individual section, you still
    would have to know the parasitic components, usually the series
    resistance of the inductor. From there calculate separately the Q for
    the series LC as well as separately for the parallel LC.
     
  5. Lee

    Lee Guest

    I omitted the series source resistor Rs and load resistor RL in the
    schematic. As I said, there are many types of LC bandpass. When you do
    a design:
    1. you can convert LC bandpass from LC low pass.
    2. you can get a book, they tell you a chart, you calculate the
    attenuation, and ladder # to get a bandpass type, sometimes you have
    to convert based on LpCp=LsCs the fundamental equation. (chebychev,
    butterworth, elliptical, linear phase, bessel, gaussian, constant-K,
    etc), then convert from basic topology to final circuit.

    But if all values a given, you simulate and find this is a bandpass,
    you want to calculate the Q or Bw. How can you do? I couldn't find a
    formula to do this.
    I can find RLC series bandpass formula and RLC parallel(resonance)
    formula.
     
  6. power boy

    power boy Guest

    I omitted the series source resistor Rs and load resistor RL in the
    schematic. As I said, there are many types of LC bandpass. When you do
    a design:
    1. you can convert LC bandpass from LC lowpass.
    2. you can get a book, they tell you a chart, you calculate the
    attenuation, inband ripple, and ladder # to get a bandpass type, sometimes you have to convert based on LpCp=LsCs the fundamental equation. (then find type like chebychev,
    butterworth, elliptical, linear phase, bessel, gaussian, constant-K,
    etc), then convert from basic topology to final circuit.

    But if all values are given, you simulate and find this is a bandpass,
    you want to calculate the Q or Bw. How can you do? I couldn't find a
    formula to do this.
    I can find RLC series bandpass formula and RLC parallel(resonance)
    formula.
     
  7. rickman

    rickman Guest

    I'm no expert on filters, but my undestanding is that each of the two
    sections, series and parallel, are resonant at some frequency with
    bandwidths defined by the resistances in the circuits. When you connect
    the two with the input across the two terminals on the left of your
    diagram and the output across the parallel cap and inductor on the right
    of the diagram, you get two peaks of resonance defined by all four
    components. The Q of each peak is again defined by the resistance. To
    the best of my knowledge this is *not* a band pass circuit. I wrote the
    equation for this circuit in by treating it as a voltage divider using
    the impedances of the parallel and series circuit. When you solve the
    equations you get two roots, so two resonances. I only did this with
    the reactive components and ignored the resistance. The resistance
    makes the math a lot more complex. Feel like solving some very messy
    equations?

    Vout/Vin = Zp/(Zp+Zs) I'm sure you can find the equations for Zp and
    Zs. If not I can provide them. Radiotron Designer's Handbook, very
    old, but science doesn't change much. Download this and go to page
    number 193 in the PDF (labeled 152 in book), section E. Z1 and Z2 are
    Zs and Zp. Construct the formula above and find the roots... simple
    right? Well, actually that gives you the resonances, but not the Q. I
    don't actually know how to figure the Q in this circuit. That's another
    section of this book I haven't read completely...

    Neither of these sets of components are low pass filters, so I don't
    know why you refer to converting from a low pass to a band pass. I
    guess if you drop Cs and Lp you get a low pass...

    As someone else said, are you sure you have the schematic right? Move Cp
    to the point between Ls and Cs and you get a band pass... or a band
    reject... But then they wouldn't be named with s and p for series and
    parallel, would they?

    If this is a band pass with Q not defined in terms of the resistance, I
    don't get it.

    BTW, try simulating this. I'm pretty sure you will get two peaks.
     
  8. rickman

    rickman Guest

    I *did* the math. This circuit has two peaks in response. This morning
    I went back to the equations to see if/when the two peaks could overlap
    to form one peak. The discriminant can't be zero with positive values
    of inductance and capacitance, so the circuit will *always* have two
    peaks and is never a simple band pass.

    The width of each of the two peaks is defined by the resistances in the
    circuit.

    The amazing thing is that all this algebra is giving me flashbacks to
    high school math class. I keep hearing, "What's a zero and who cares
    about finding them?" I wonder who was saying that...
     
  9. rickman

    rickman Guest

    I can show my work if I have to. I flunked my first physics test at UMD
    because I didn't show my work. I was not a happy camper.
     
  10. josephkk

    josephkk Guest

    I can usually do 1 pole in my head. Two poles to 4 poles i can do with
    pencil and paper. Beyond that i don't bother, i use table based design or
    software. Never had to go past 8 poles, but that was a bitch to tune with
    10% parts.
     
  11. josephkk

    josephkk Guest

    A single peak is possible in theory. It is not likely to be realizable in
    production quantities. Doing it one off may be reasonably achievable.
    (How close do the peaks have to be before you cannot tell then apart? /
    How good is your measurement gear?)

    ?-)
     
  12. o pere o

    o pere o Guest

    It is easy, at least if you are not too stringent on the fractional
    bandwidth of the bandpass filter. If you want a narrow filter, with this
    approach you end up with unrealistic component values, and have to
    resort to the coupled-resonator approach.

    Pere
     
  13. josephkk

    josephkk Guest

    I'll bet you even still remember all the neat tracks that you can do with
    a complex Riemann sphere.
    My favorite filter system is inverse Chebychev.
     
  14. Fred Abse

    Fred Abse Guest

    If it has, pleas tell me how. I'm pissed off with having to use Berkeley
    Spice 3f to do PZ analysis.
     
  15. josephkk

    josephkk Guest

    I would literally try the same file in LTSpice. It may work. And you
    should get some possibly helpful diagnostic messages if it doesn't. This
    should work best from CL.

    ?-)
     
  16. josephkk

    josephkk Guest

    Gosh, you mean you didn't learn about interesting transforms of the
    complex frequency plane (rotations of the complex Reimann sphere before
    transforming back)? It can be handy for understanding going between s and
    z transforms.
    Well my favorite trick is placing the maximum attenuation notches just
    where i want the to block narrowband interfering signals. Like harmonics
    of power line frequencies. Then if needed another filter could restore
    much of the pass response in the stop band (initial design has to be low
    minimum stop band loss. They are also fairly good at approximating a
    brick wall filter with high minimum stop band loss. I think the phase is
    well behaved in the pass band as well.

    I would have to find my book of tables to setup some spice examples.

    ?-)
     
  17. Fred Abse

    Fred Abse Guest

    I did. It didn't.
     
  18. rickman

    rickman Guest

    I can see I'm going to have to separate Phil and Jim, but this isn't
    even *your* discussion! You will just have to stay after class in
    detention.

    Rick
     
  19. josephkk

    josephkk Guest

    Oh well. If it is not secret perhaps you could send me a copy of the file
    and let me tinker it a bit. I might figure it out.

    ?-)
     
  20. josephkk

    josephkk Guest

    For what it is worth, i remember it as rickman claiming only two peaks is
    possible. Please recheck the thread.
     
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