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Input impedance of BJT amplifier

  1. Jan 21, 2012 #1
    1. The problem statement, all variables and given/known data
    Find input resistance of the ckt (see attached)


    2. Relevant equations



    3. The attempt at a solution
    Q2 is diode connected, so I replaced Q2 with VBE resistance (rbe or r∏).
    So, Rin is rbe1+(β+1)rbe2

    But the answer is somewhat different, it's rbe1+ (β+1) (rbe2||1/gm2)
    Where did 1/gm2 come from?
     

    Attached Files:

  2. jcsd
  3. Jan 21, 2012 #2

    vk6kro

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    Science Advisor

    Q2 is also a transistor and it draws collector current as well as base current.

    So, this affects the total resistance of Q2 in this circuit.
     
  4. Jan 22, 2012 #3
    I tried to draw an equivalent diagram and solve. see attachment.
    Basically, rbe and gm*vbe are both shorted (because of collector base short of Q2).

    I attached a test source Vx to determine the input impedance of just Q2. So impedance will be Vx/ix.
    After solving, I got 1/gm (assuming β>>1).

    From the equivalent ckt,
    Vx=Vbe
    ix = Vbe/rbe +gmVbe

    ix=Vbe (1/rbe+gm)

    ix = Vx (1/rbe+gm)

    Rin = Vx/ix = 1/(1/rbe+gm)

    rbe = β/gm

    Rin = 1/(gm/β +gm)
    Rin = 1/gm((1+β)/β))

    if β>>1, then (1+β)/β = 1

    Rin = 1/gm
     

    Attached Files:

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