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Formula for gain?

Discussion in 'Electronic Basics' started by little billy, Aug 5, 2004.

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  1. little billy

    little billy Guest

    How do I find the gain for the High Gain Amplifier
    in the manual of the lm317 page 16

    http://www.national.com/ds.cgi/LM/LM117.pdf

    Assuming we have a load RL from the output to ground
    can we say the following:

    IL = Vo/RL where Vo = output current, IL = load current

    Denote the constant current of the regulatror as C

    C = Ic + IL , where Ic = collector current

    Ic = Ib * beta hence Ic = Vi/R1 * beta where Vi = input voltage

    all of this gives us

    (Vo/RL) + (Vi/R1)*beta = C

    what is the gain ?
     
  2. The LM117 and the R2 together, is a current source provides the same current
    whatever voltage on the "output".
    Idealy, the gain is infinite, because you shouldn't be able to make an
    input current so precise so that the outpot voltage stays stable (even for a
    short time) between maximum and minimum. (not considering rise/fall time).
     
  3. Active8

    Active8 Guest

    I was working on a proper derivation but ended up with an extra term
    and couldn't divide through by Vin to get Vout/Vin.

    The above approach has errors and beta, which I wouldn't use isn't
    specified for that transistor, though there is a g_m curve.

    For a current source load, gain is limied by the early voltage. I
    think the proper approach is to select a current for the 117 and use

    Ic = g_m*Vin - Vin being Vbe and

    I_R2 = Ic + I_L

    to get the load current and thus the voltage. It's an approximation
    IMO, but It's quick.
     
  4. Keep in mind that the 'transistor' is an integrated circuit, LM195.
     
  5. Active8

    Active8 Guest

    Right. THat's why the transconductance isn't 40Ie and oops, I said
    Vbe which isn't right.

    I hit the dead end when I got to:

    1.25/R2 = g_m*Vin + Vout/R_L
     
  6. little billy

    little billy Guest

    We can't isolate Vo/Vi so there is no gain because
    gain is defined as Vo/Vi. Not all circuits have
    gain, this one doesn't, which is very strange
    considering the title.
     
  7. Active8

    Active8 Guest

    Too bad thr spec doesn't list hfe :-0
     
  8. colin

    colin Guest


    Vout = Vin/Rin*hfe*RL (asuming rin >>rb)

    Colin =^.^=
     
  9. little billy

    little billy Guest


    o.k. guys, thanks for the response.

    Gain is gm * RL and from the graph we see that gm
    is about 3, so 3RL, so for an 8R speaker we get
    Av=24. For a 64R speaker, about 200.

    l.b.
     
  10. Active8

    Active8 Guest

    Can we make this simplification with a current source load? i.e.
    treat Rc as infinity (theoretical R of current source) in parallel
    with R_L? Even with R2 going to Vcc?

    [sotto voce] I guess.
    And a ton of distortion. Don't fergitcher output cap :)
     
  11. colin

    colin Guest

    true, it doesnt, it does show a graph of the relationship between ib and ic
    tho and its not like an ordinary transistor at all, like i asumed it was.
    from the graph delta hfe goes to infinity and then goes negative. hardly
    much like a bipolar transistor at all its not realy a transistor anyway, its
    even got a pnp input stage.

    i think the circuit would be highly unstable. im not sure i cld think of any
    use for it that actualy needed such high gain but could cope with the
    instability.

    although thinking about it again as bias curent is so low the 10k input
    resistor hardly has any efect. so my original asumption i stated doesnt
    hold.

    however it does show colector curent versus colector voltage for various
    base voltages..
    eg, at IC = 0.825 Amp, vb = 0.825 @ vc 12.5 and vb =0.75 @33

    therfore gain at that Ic seems to be 280, asuming infinite colector
    reistance.

    Colin =^.^=
     
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