Cascade Amplifiers

Discussion in 'Homework Help' started by AD633, Jul 22, 2013.

  1. AD633

    Thread Starter Member

    Jun 22, 2013
    96
    1
    Hi,

    I was looking for some information on how to calculate the total gain of a circuit with two cascade voltage amplifiers.
    I need to prove analiticaly that the total gain (AT) of an amplifier circuit with 2 cascade amplifiers, is not equal to the product of the individual gains (Av1*Av2)
    For this i need the equivalent model for an voltage amplifier right?

    So the voltage amplifiers have a input and output resistances( R_i_n,R_o_u_t and  A_v and a gain associated with them.

    So the voltage Vi across the  R_i_n_1 of the first amplifier would be:



    Thanks
     
    Last edited: Jul 27, 2013
  2. LvW

    Active Member

    Jun 13, 2013
    674
    100
    AD633, at first you (we) have to clarify what is the meaning of "individual gain":
    With or without the second stage connected?

    As far as I could follow your calculation you did consider the input impedance of the 2nd stage in calculating the gain of the 1st stage.
    In this case, of course the total gain is indeed the product of both individual gains.
     
  3. AD633

    Thread Starter Member

    Jun 22, 2013
    96
    1
    I think the question mentions that the stages are connected..

    What the question says exactly is :

    "Show analiticaly that the total gain  A_T of two voltage amplifiers A1 ( Av_1,R_i_n_1,R_o_u_t_1 ) and A2 ( Av_2,R_i_n_2,R_o_u_t_2 ) conected in cascade is not equal to the product of the gains AT=Av1*Av2
    Deduce the correct expression of the total gain."

    Thanks
     
  4. LvW

    Active Member

    Jun 13, 2013
    674
    100
    OK - I see.
    That means: Av1 and Av2 are the gains of both stages in case they are NOT connected. Otherwise, the question makes no sense, because you are requested to prove that a simple product Av1*Av2 is NOT correct.
    The difference between both approaches is clear: The input impedance of the second stage must be taken into consideration by calculating the gain of the 1st stage.
    If the signal source has an internal source resistance, the input resistance of the 1st stage reduces the gain of the first stage - as you have calculated in your first posting.
     
    Last edited: Jul 22, 2013
  5. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    @AD633

    The obvious deficiency in your final answer is that there is no reference to Rin2 or Rout1.

    Re-check your solution.
     
  6. The Electrician

    AAC Fanatic!

    Oct 9, 2007
    2,281
    326
    Have you considered that under some conditions it might be true that AT=A1*A2, and what those conditions might be?
     
  7. LvW

    Active Member

    Jun 13, 2013
    674
    100
    AD633 - to answer your basic question: No, your result is not correct.
    * Why are formulas in the 2nd and 3rd line equal?
    * Rout,2 is already contained in Av2. Thus, it cannot appear again in your formulas.
    * By the way: What are the definitions for Av,1 and Av,2 you are using?
    * Please, distinguish between static resistors (R) and dynamic resistances (r)
    * A circuit diagram would be VERY VERY helpful!!
     
Loading...