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[Homework] Resonance and capacitor values.

Discussion in 'Electronic Basics' started by Daniel Pitts, Feb 17, 2013.

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  1. Daniel Pitts

    Daniel Pitts Guest

    So, I have a circuit:

    ___ |
    D1 \,/ S
    ===== S
    | S
    VR ----+ S 2 mH inductor
    | S
    ===== S
    D1 /^\ S
    --- S
    | |

    D1 and D2 are Varactors. I'm supposed to find the value of D1 and D2
    for a resonance of 1MHz.

    I went with 1MHz = 1/(2Ï€*2mH*C) which results in C=50.6pF

    So, I'm not entirely sure if that is the entire capacitance of the
    circuit, or the capacitance of of each of D1 and D2.

    This homework exercise is about varactors, but I have skipped the
    "Introduction to AC" class, so my basic understanding of the above
    circuit as an LC circuit is lacking. If I understood that much of it, I
    know I'd understand the varactor part.

    Any hints, help, suggestions would be appreciated.

  2. amdx

    amdx Guest

    I was surprised when I found 2.2mH inductors with a SRF of 1.9Mhz and
    1.7Mhz, that's only 3 or 4 pf. I'm not argueing against your "2 mH is a
    pretty big inductor to use at 1 MHZ" I agree. I was just surprised by
    the high SRF of 2.2mH inductors.

  3. Take out the varactors, and replace with regular capacitors. Then figure
    what's needed for resonance. Keep in mind that the two capacitors will be
    in series, so study the pertinent section of the book about capacitors in

    Then put back the right value varactors. Keep in mind that your homework
    as you present it doesn't say anything about tuning range, so you can only
    pick a varactor that tunes the coil to the 1MHz, rather than figure out
    how much range it should have. It also leaves out what voltage range is
    available for tuning the varactors, so you can't pick varactors either
    since you don't know if you have a good range of voltage available, or
    have to use some of those special varactors that have a high max to min
    capacitance range with a small control voltage.

  4. Fred Abse

    Fred Abse Guest

    Poorly stated problems, and inappropriate values are symptomatic of
    teachers who have no practical experience. Nothing new there.
  5. Fred Abse

    Fred Abse Guest

    It's f=1/(2*pi*sqrt(L*C))

    That's not the easiest way to remember it:

    Just remember that 2*pi*f*L=1/(2*pi*f*C) at resonance....(1)

    From which you can derive everything you need for whatever circumstance.

    There's a further trick. 2*pi*f crops up so many times, that we allocate a
    symbol to it, actually the lower case Greek omega, which I will type as a
    lower case "w", here. That means you only have to do a single pi
    approximation for the whole calculation, which improves precision.

    Like wL=1/wC (same as (1) above)

    Hence wC=1/wL

    and C=1/w^2*L

    giving 12.6651pF for the combination. The varactors are in series, so the
    effective capacitance, assuming both are equal, will be half that of each.
    I leave it to you to do the multiplication;-)

    There's no point stuffing your head with lots of formulas, which you can
    remember wrongly. Just remember one, and derive the others with a bit of
    mental algebra.
  6. Jamie

    Jamie Guest

    Ok, but since "w" omega is kind of not a constant, because you still
    need to define it at the start, may I add the part there to even shorten it

    w= Ï„*f

    Most likely the tau symbol didn't come out but some where in my math
    history it once represented 2 * PI.

    for some reason I can't find the lower case Omega (Ω ) in my chart.

  7. Daniel Pitts

    Daniel Pitts Guest

    Oops I wrote the formula wrong in here.
    Running through it the second time, I get the same answer you do. Not
    sure where I messed up, but such is arithmatic.
    VR provides the reverse bias on the diodes which "sets" the capacitance,
    no? Or am I not understanding?
    That was my error. Each one should have been labeled separately. D1 and D2
    Perhaps, though that is what the problem states.

  8. Daniel Pitts

    Daniel Pitts Guest

    This is straight from the text book:
    Electronic Devices (Conventional Current Version) (9th Edition), Thomas

    Frankly, my teacher has perhaps too little theoretical experience. You
    may have seen my previous thread about a different question. I tried to
    go over the calculus approach to solve the Average Power problem, but he
    said it really wasn't that important, and he alluded to the fact that he
    doesn't really remember calculus very well.
  9. I'm always just taking 2*pi = 10, (for approximations)
    It's the metric system for frequencies... 1 cycle = 10 radians :^)

    George H.
    (I then remember there's a factor of ~1.6 floating around)
  10. Only one?
    I didn't read the whole thing, and I don't know much about
    But I'd rather it read 'at DC only a very small reverse bias current
    flows' rather than 'no current flows'.

    What didn't you like?

    George H
  11. You must have heard about the dyslexic agnostic with insomnia...

    He stayed up all night wondering if there really is a dog.
    George H.
  12. Daniel Pitts

    Daniel Pitts Guest

    Yup, after I reworked it, that is exactly what I got.
    "About 25 pF" was the correct answer for this problem. I'm not sure how
    the lower diode is shorted, since it is reverse biased.
    My bad, D1 is the upper, I meant to label the bottom diode D2.
  13. It still does:
  14. Fred Abse

    Fred Abse Guest


    Usenet doesn't necessarily support 8-bit extended character sets (of
    which there are a few). Better to stick to standard ASCII.

    That goddamn Greek mu screws up LTspice listings over Usenet, if you
    don't watch out for it, for example.
  15. Fred Abse

    Fred Abse Guest

    "1meg" works fine, though. It's been like that since Berkeley Spice
    started, and it was all on punch cards and Teletype.

    Heck, we still talk about model "cards".

    Spice was always *supposed* to be non-case-sensitive.
  16. Bill Bowden

    Bill Bowden Guest

    Yes, I discovered that. Also the LTspice default value for resistance
    of an inductor is 1 milliohm and so the Q is too high. I'm playing
    with a couple LC tank circuits for IR 36KHz use (6.8mH and 2700pF) and
    need the rise and fall times to be only a couple cycles out of 32.
    What sort of inductor Q would you recommend?

  17. Bill I'm not sure I understand your question. But it will take about
    Q cycles for an oscillator/ filter to either build up or decay back

    George H.
  18. Bill Bowden

    Bill Bowden Guest

    The problem is to receive 32 or 64 cycle bursts of 36KHz from a hand
    held IR remote control and output a DC level representing the time
    duration of the bursts, either 890uS or twice that of 1.778 mS. It
    looks like a tradeoff between gain and response time. If the Q of the
    LC circuit is low, the response time will be fast with low gain, and
    visa versa. How do I approximate the Q of the inductor for a
    reasonable compromise of gain and response time?

  19. Bill Bowden

    Bill Bowden Guest

    Yes, could do that. But I want to roll my own input circuit and
    receive weak IR signals from 10 feet or so using a regular IR LED. So,
    the idea is to amplify weak signals and provide varying DC time
    lengths to a processor for decoding. I realize there are (3 terminal)
    IR receiver modules to do the job, but I wanted to roll my own using
    tuned circuits.

  20. Jamie

    Jamie Guest

    You have back ground IR to worry about, sun light contributes to ~50%
    of IR out side. Being inside you have other sources that can saturate
    the detector.

    If you put a detector in operation in a linear state, you can see a
    lot of this noise on the scope. If you have a scope with FFT on it you
    can also locate or should be able to, signals from a remote.

    I suppose one could make a regenerative oscillator with the IR
    detector element as part of the circuit in the gain loop.

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