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Need help with the process for finding input resistance of atransistor ??

Discussion in 'Electronic Basics' started by [email protected], Sep 19, 2008.

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  1. Guest

    I have been trying to follow along with a books calculation for the
    input resistance of a transistor which they define as Rin = delta
    (Vbe) / delta (Ib) or Rin would be 1 / (slope of the diode curve) or
    1 / (derivitive of the diode curve) . Doing the math and assuming
    that KT/Q = 26 mv and assuming that (Is) the reverse saturation
    current is negligible, I get the desired Rin = 26 mv / Ib.

    My question is why is Rin = delta (Vbe) / delta (Ib) and not just
    Vbe / Ib . My some how flawed reasoning is that if you look at ohms
    law E = IR, then R = I/E and therfore Rin should be Vbe / Ib . Why
    is Rin equat to the change in current divided by the change in
    voltage?

    Any help would be greatly appreciated. Thanks
     
  2. It may be better to think of this as:

    rin = hie = rbb' + (1 + hfe).re

    where rbb' is the base resistace, usually of the order 10-500 ohms, and
    re=1/(40.IC) = 1/gm

    The fundamental reason is:

    del_y = f'(x).del_x

    if del_y, and del_x are small, as a general math result, from differential
    calculus.

    For small signals, i.e., when an input signal only changes a small amout
    about a fixed bias point, what is the resulting change in the output, about
    a fixed bias.

    rin, is a small signal resistance. It is not equal to VINDC/INDC. Since the
    inputs and outputs that are wanted are the small signal changes, than one
    needs the small signal resistance, not the large signal resistance. If one
    actually wanted large signal values, than one would use such values
    throughout.

    Kevin Aylward

    www.kevinaylward.co.uk
     
  3. Interesting point. The resistance does not follow ohm's law, so in that
    sense is not ohmic. However, it does have characteristic similar to ohmic
    resistors but not similar inductors and capacitors. That is, the current and
    voltage are independent of time, i.e not +/-j

    For DC conditions, the actual value of V/I may be important, especially for
    values of Vdc of around 0.5 to 1V.
    Well... technically one can actually define the large signal resistance as
    V/I.

    So that:

    R = Vd/I = (Vd/Io).exp(-Vd/Vt)

    And using the results of
    http://www.kevinaylward.co.uk/ee/widlarlambert/widlarlambert.html, for the
    Lambert W() function

    One can obtain the inverse relation;

    Vd = -Vt.W(-R.Io/Vt)

    I will leave it as an exercise for the reader to deduce formulas expressing
    R in terms of I, and I in terms of R:)

    Kevin Aylward
    www.blonddee.co.uk
    www.anasoft.co.uk
     
  4. neon

    neon

    1,325
    0
    Oct 21, 2006
    NO such a thing as input resistance. but there is inpedance. and using boltzman constant you can find it . it is a function of current
     
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