Cut off frequency at a emitter circuit

Discussion in 'Homework Help' started by Tobias Hildebrandt, Jan 24, 2016.

  1. Tobias Hildebrandt

    Thread Starter Member

    Jan 1, 2016
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    0
    Capture42.PNG

    Hello,

    This is the information provided on top of the page: A sine shaped signal with a frequency of 100 Hz and an amplitude of 1.5V is put in the circuit. The current amplification of the transistor is B = 200. A SPICE simulation proivdes for Ic(Q1) a current of 18 mA. Provide your calculations down to four significant figures.

    a) Calculate the cutoff frequency (fc).

    This is my question. Where does the 20.1 kOhm coming from? He calculate "little re" as 25.8 mV / 18 mA = 1.433 Ohm. Now, this is what I did next, I added "little re" to R4 and multiplied it by 200 ( (1.433 Ohm + 100 Ohm) * 200) and got as a result 20286.6 Ohm, rounded this is 20.3 kOhm.

    So, what is wrong with my approach?

    Tobias
     
  2. Jony130

    AAC Fanatic!

    Feb 17, 2009
    3,957
    1,097
    The input impedance for this amp is
    Rin = R1||R2||RinT where

    RinT = (β+1)*(R4 + r'e) and because r'e<<R4 we can use ≈ (β+1) * R4 = 20.1kΩ
    Why (β+1) ??
    Because the emitter current is Ie = Ic + Ib = β*Ic + Ib = (β + 1)*Ib
     
    Tobias Hildebrandt likes this.
  3. MrAl

    Well-Known Member

    Jun 17, 2014
    2,418
    488
    Hi,

    I thought we talked about this before. The more correct way is (B+1)*R4 not B*R4 but sometimes B*R4 is acceptable. If it is shown on the text then they want you to use (B+1)*R4 this time.

    Little re is the internal transistor emitter resistance, which in this case is very small (about 0.15 percent of external R4) so it can be neglected as Jony said.
    Little re is more important sometimes but not for this circuit. The idea probably is that you should calculate the approximate little re (as they show) and determine for yourself if it is significant or not. Little re times (B+1) is around 300 ohms, while R4*(B+1) is 20.1k, so the combined total is 20.4k which isnt that different than 20.1k so it only makes a little difference.
     
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  4. Tobias Hildebrandt

    Thread Starter Member

    Jan 1, 2016
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    0
    Thanks to both of you! Yes, we went over this before, but I got puzzled when I saw the "little re" calculation in his solution.

    So, I can ignore "little re" when << R4. Good!
     
  5. BramLabs

    Member

    Nov 21, 2013
    98
    5
    If i applied small signal analysis :

    an.PNG

    Rin = R1//R2//RinT

    And applied KVL for finding RinT =
    V at hie + V at R4 = VinT
    hie*ib + (hfe*ib+ib) * R4 = VinT
    because hfe = B, then :
    hie*ib + (B+1) * ib* R4 = VinT
    (B+1) * ib * (R4+hie) = VinT
    Then : VinT / ib = RinT = (B+1)*(R4+hie)
    And if hie at least 10 times less than R4, we can say :
    RinT = (B+1)*R4

    CMIIW (Correct Me If I'm Wrong)
     
    Last edited: Jan 25, 2016
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