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The Emitter Follower

  1. Mar 16, 2014 #1
    Thank you for any help that you can offer.

    Did I answer all of the questions correctly and thoroughly? Can you please find any errors, and point them out to me so that I can fix them?

    1. The problem statement, all variables and given/known data

    (a) Confirm these quiescent values:

    VB = 8.2V
    IE = 1.0 mA

    (b) show that Zin for the bias network alone is 50K.
    (c) Show that for high frequency ac signals Zin measured at point P2 is 500k.
    (d) Show that for high frequency ac signals Zin measured at point P1 is 45.5K.
    (e) show that f3dB for the entire circuit is ~ 165Hz


    https://scontent-a.xx.fbcdn.net/hphotos-prn2/t1.0-9/1901740_10151937081755919_967279941_n.jpg

    2. Relevant equations

    {R110k/(R110k + R91k)} x VCC = VB
    ...................................................................................................
    VB - VBE = VE
    ............................................................................................
    VE/RE = IE
    ....................................................................................................................
    Zbias network = (R91k)(R110k)/(R91k) + (R110k)
    ............................................................................................
    Zin,P2 = hFE{(re)^' + (re)}
    ............................................................................................
    Zin,P1 = (Zbias network)(Zin,P2)/{(Zbias network) + (Zin,P2)}
    .....................................................................................................................
    f3dB = 1/(2)(pi)(ZP1 - 7.5k||15k){(C0.033uF)(C0.1uF)/{(C0.033uF + (C0.1uF)}}
    .....................................................................................................................................



    3. The attempt at a solution


    (a)1 Confirm this quiescent value:

    VB = 8.2V
    .......................................................

    {R110k/(R110k + R91k)} x VCC = VB
    .........................................................................................
    110k/(110k + 91k) x 15V = VB
    .......................................
    8.2V = VB
    ........................................


    (a)2 Confirm this quiescent value:

    IE = 1.0 mA
    ...........................

    VB - VBE = VE
    .......................................................
    8.2V - 0.6V = VE
    ...........................
    7.6V = VE
    .....................
    VE/RE = IE
    ...........................................
    7.6V/7.5mA = IE
    ...........................................
    1.03mA = IE
    ...........................................
    1.00mA ~ IE
    ...........................................


    (b) show that Zin for the bias network alone is 50K.

    Zbias network = (R91k)(R110k)/(R91k) + (R110k)
    ............................................................................................
    Zbias network = (91k)(110k)/(91k) + (100k)
    .....................................................
    Zbias network = 49.8k
    ...............................................
    Zbias network ~ 50.0k
    .............................................



    (c) Show that for high frequency ac signals Zin measured at point P2 is 500k.

    Zin,P2 = hFE{(re)^' + (re)
    ......................................................................
    Zin,P2 = hFE{(25mV/(IC) + (R7.5k)(R15k)/(R7.5k + R15k)}
    ...........................................................................................................................
    IC = IE
    ..............................
    Zin,P2 = hFE{(25mV/[(VB - VBE)/RE] + (R7.5k)(R15k)/(R7.5k + R15k)}
    .............................................................................................................................................................
    Zin,P2 = hFE{25mV(RE)/[(VB - VBE)] + (R7.5k)(R15k)/(R7.5k + R15k)}
    .............................................................................................................................................................
    Zin,P2 = 100{(25mV[(7.5k)/{(8.2V - 0.6V)]) + (7.5k)(15k)/(7.5k + 15k)}
    .................................................................................
    Zin,P2 = 100{24.671(ohms) + 5k(ohms)}
    .................................................
    Zin,P2 = 502.4k(ohms)
    ................................
    Zin,P2 ~ 500.0k(ohms)
    ................................



    (d) Show that for high frequency ac signals Zin measured at point P2 is 45.5K.

    Zin,P1 = (Zbias network)(Zin,P2)/{(Zbias network) + (Zin,P2)}
    .....................................................................................................................
    Zin,P1 = {(49.8k)(502.0k)/{(49.8k) + (502.0k)}
    .........................................................
    Zin,P1 = 45.3k
    ..........................



    Z7.5k||15k = (7.5k)(15k)/(7.5k + 15k)
    .............................................
    Z7.5k||15k = 5k(ohms)
    .............................................
    Zin,P1 - Z7.5k||15k = ZP1 - 7.5k||15k
    ..................................................................
    45.3k - 5k = ZP1 - 7.5k||15k
    ......................................
    40.3k = ZP1 - 7.5k||15k
    ......................................

    (e) show that f3dB for the entire circuit is ~ 165Hz


    f3dB = 1/(2)(pi)(ZP1 - 7.5k||15k){(C0.033uF)(C0.1uF)/{(C0.033uF + (C0.1uF)}}
    ............................................................................................................................................
    f3dB = 1/(2)(pi)(40.3k){(0.033uF)(0.1uF)/{(0.033uF + 0.1uF)}}
    .........................................................................
    f3dB = 1/[(2)(pi)(40.3k){2.48x10-8}}]
    ..................................................
    f3dB = 159.17 Hz
    .............................

    I can see answer (e) is not 165 Hz. Where is the error? Are answers (a) - (d) correct? If not, where are the errors located?

    Thanks again for your help.
     
  2. jcsd
  3. Mar 17, 2014 #2

    gneill

    User Avatar

    Staff: Mentor

    For part (e), assume that the emitter follower itself is a buffer amplifier (high input impedance, low output impedance, gain very close to unity). You then have a cascade of two isolated low pass filters...
     
  4. Mar 17, 2014 #3
    gneil,


    I will make corrections to (e) based on your comment. I am not asking for the answer, but does (a) - (d) look as though I have answered the questions?
     
  5. Mar 17, 2014 #4

    gneill

    User Avatar

    Staff: Mentor

    I didn't go over the math in fine detail, but they look okay to me after a short perusal.
     
  6. Mar 17, 2014 #5
    In this circuit we have two first order filter.
    The first one
    Fd1 ≈ 0.16/(Cin * Zin) = 0.16/(33nF * 45.5kΩ) = 106.5Hz
    And the second one
    Fd2 ≈ 0.16/(Cout * RL) = 0.16/(100nF * 15KΩ) = 106.6Hz

    And as you can see in our case Fd1 = Fd2 and because of this the dominant lower cutoff frequency is increased by a factor of [itex]\LARGE \frac{1}{\sqrt{ 2^{\frac{1}{n}}-1}}[/itex]
    http://202.191.247.221/courses/imag..._Analysis/Resources/Multistage_AMplifiers.pdf

    In our case n = 2 so we have [itex]\frac{1}{\sqrt{ 2^{\frac{1}{2}}-1}} = 1.55377[/itex]

    And finally

    Fc = 106*1.55 = 164.3Hz
     
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