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

 

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)

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.

 

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

I think the question mentions that the stages are 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.

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

 

"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."

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.

 

@AD633

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

Re-check your solution.

 

Have you considered that under some conditions it might be true that AT=A1*A2, and what those conditions might be?

 

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!!