How Do You Calculate the Overall Voltage Gain of Two Cascaded CS Amplifiers?

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Discussion Overview

The discussion revolves around calculating the overall voltage gain of two cascaded common-source (CS) amplifiers. Participants explore the theoretical framework, mathematical relationships, and practical implications of cascading amplifier stages, including circuit diagrams and gain calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a homework problem involving two identical CS amplifiers and provides initial calculations for parameters such as transconductance (gm) and output resistance (ro).
  • Another participant requests a circuit diagram to better understand the configuration of the amplifiers.
  • A participant acknowledges an error in their initial gain calculation for the second stage, suggesting a gain of -10 V/V based on the formula -gm * (RD || RL).
  • There is confusion regarding the multiplication of gains from the two stages, with one participant questioning whether it is valid to multiply the gains of the first and second stages to find the total gain.
  • Another participant asserts that multiplying the gains is appropriate, as the output of the first stage serves as the input to the second stage, supporting the correctness of the provided answer.

Areas of Agreement / Disagreement

Participants express differing views on the calculation of gains and the validity of multiplying them. While some agree with the multiplication approach, others question the correctness of the initial calculations and the resulting total gain.

Contextual Notes

Participants reference various assumptions, such as the infinite output resistance (VA) and the conditions under which the gain calculations are made. There are unresolved aspects regarding the accuracy of the initial gain values and the implications of cascading amplifiers.

Who May Find This Useful

This discussion may be useful for students and practitioners interested in amplifier design, particularly in understanding the behavior of cascaded common-source amplifiers and the associated calculations for voltage gain.

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Homework Statement


two identical CS amplifiers connected in cascade. 1st stage fed with vsigand Rsig=100k ohm. load RL= 10k ohm connected to drain of 2nd stage. each MOSFET biased at ID = 0.25mA and VOV=0.25V. assume VA is very large. Each stage has RD=10k ohm.

a) sketch equivalent circuit of two-stage amplifier
b) find overall voltage gain Gv

Homework Equations


ID = (1/2)*kn*(VOV)2 <-- sat.
gm = knVOV
ro = |VA|/ID
GV=AV=-gm*RD || RL = -gm*RO
Vo = -(gmvgs)(RD||ro)

The Attempt at a Solution


i sketched the small signal circuit on paper but I'll probably show it later. solving for kn i get 8mA/V2. and gm=2mA/V. If VA is infinite then ro is infinite, and RO=ro||RD=RD. I get for 1st stage AVo1=GVo1=-20V.

To find the relationship for 2nd stage I did Vo1=Vi2=-(gmVi1)(RO) and Vo2=-(gmVi2)(RO)=(gm)2(RD||ro)2Vi2 then GVo2=Vo2/Vi2=400V. but is that right? I get a positive gain so I think i did it wrong.
 
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I wasn't thinking, and i did it wrong xD
the gain for 2nd cascade stage, would actually be -gm* RD|| RL = -2 * 10||10 = -10 V/V. what I don't get though, how they get an answer of total gain of -20 V/V (1st stage) * -10 V/V = 200 V/V. are you allowed to multiply them like that?

sorry, here's the image for 2 stage cascade CS amplifiers
http://postimg.org/image/cnqur1y6h/
 
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I guess from what you wrote that gm = 2 mA/V.
If I have two amplifier in cascade as you have, why should you not be able to multiply their gains? The input to the 2nd stage is the output of the 1st stage.
The answer they give is correct.