RLC circuit - radio tuner

Discussion in 'Homework Help' started by lll, Apr 25, 2012.

  1. lll

    Thread Starter New Member

    Mar 7, 2012
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    I'm not even sure I know how to approach this problem. I really don't know anything about radios, and the book doesn't cover them at all.

    I tried setting the resonance frequency equal to 89.1 MHz (pure guess), and solving for C, but I didn't get the right answer.

    The correct answer is 3.2pF. How?
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    You have to use the exact resonance formula

    \omega_o=\sqrt{\frac{1}{LC}-\frac{R^2}{L^2}}
     
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  3. lll

    Thread Starter New Member

    Mar 7, 2012
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    That didn't work. :(

    I keep geeting 125 pF.

    I'm thinking that maybe I'm supposed to use wd (damped resonance frequency) instead of w0. But I don't know how to calculate the neper frequency since the circuit is neither in series nor parallel.
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    It does work - your maths has let you down. C=3.1904pF is the answer or 3.2pF is close enough.
     
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  5. lll

    Thread Starter New Member

    Mar 7, 2012
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    Ok, I found a mistake in my previous calculation, so now I'm a little closer to the answer, but it's still off by a factor of 3, no matter how many times I double check. Here's the calculation:

    8910000=\sqrt{\frac{1}{10^{-6}C}-\frac{5^2}{{(10^{-6})^2}}}
    \frac{1}{C}=(8910000^2+\frac{5^2}{(10^{-6})^2})(10^{-6})
    and that gave me C=9.57964pF
     
  6. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    You need to convert 89.1MHz to an equivalent value in radians/second. It's ωo not fo that you need.
     
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  7. lll

    Thread Starter New Member

    Mar 7, 2012
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    Thank you! Finally got it.
     
  8. atferrari

    AAC Fanatic!

    Jan 6, 2004
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    89.1 MHz = 89100 KHz = 89100000 Hz, right?
     
  9. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    That's correct.
     
  10. mlog

    Member

    Feb 11, 2012
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    I got approximately 3.19 pF and had <0.01% error by neglecting the (R/L)^2 term.
     
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