Dynamic Resistance

Discussion in 'Homework Help' started by xKael, Jun 30, 2010.

  1. xKael

    Thread Starter New Member

    Jun 30, 2010
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    I'm studying Electronics and the professor gave us this homework...

    As you may know, the formula for dynamic resistance is:
    [​IMG]

    r = resistance
    I = current


    Now, the question is, where did the "26mV" come from?

    Explain why there is a "26mV" there.

    Thanks to those who will help... :D
     
  2. retched

    AAC Fanatic!

    Dec 5, 2009
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    Its the thermal voltage, at room temperature, of the diode.
     
  3. Georacer

    Moderator

    Nov 25, 2009
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    1,266
    ...and is given by the formula
    V_{\small T}=\frac{k \cdot T}{q} where
    k is the Boltzmann constant k=1.38e^-23 joules/Kelvin
    T is the absolut temperature in Kelvin
    q is the electron charge q=1.602e^-19 coulomb

    This yields approximately a Vt of 25mV @ 20^{\tiny{o_C}} or
    26mV @ 25^{\tiny{o_C}}
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
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    It is derived from (Dr.) Shockley's Diode Equation and requires some relatively simple differentiation and algebraic manipulation.

    It's well known and (if interested) you'll find plenty of derivations of the dynamic resistance on the web.

    There's been some recent discussion recently on the forum - so try searching here.

    The dynamic resistance is routinely used for BJT small signal amplifier analysis.
     
  5. xKael

    Thread Starter New Member

    Jun 30, 2010
    24
    0
    Thanks to all!!! :D


    EDIT:
    So, you can derive the Thermal Voltage by differentiating the Shockley Equation right?

    Could someone show the detailed differentiation of Shockley's Equation to become the Thermal Voltage Equation...
     
    Last edited: Jun 30, 2010
  6. xKael

    Thread Starter New Member

    Jun 30, 2010
    24
    0
    Hi, sorry for double posting but, I found this...

    The derivation of emitter resistance is as follows: (Google "diode equation" for definitions of k, q, and T)

    I=Is(e^(qv/kT)-1)

    where kT/q=26mv at T~300 degrees Kelvin

    since Is<<I at normal bias currents,

    I/Is~e^(V/.026)

    V/.026~ln(I/Is)

    V~.026(ln(I)-ln(Is))

    Recall that R=dV/dI

    dV/dI=.026/I QED


    Could somebody explain it... :)

    What does "<<" mean?
     
  7. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    Which part is not clear to you?

    'Is << I' means 'Is "is very much less than" I'.
     
  8. mahdi firouzi_1436825059

    New Member

    Jul 13, 2015
    1
    0
    whats f mean in If?
    it mean forward bias?!!??
     
  9. Jony130

    AAC Fanatic!

    Feb 17, 2009
    3,957
    1,097
    I_f = forward current.
     
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