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

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SUMMARY

The overall voltage gain of two cascaded common-source (CS) amplifiers can be calculated by multiplying the individual gains of each stage. In this discussion, the first stage has a voltage gain of -20 V/V, while the second stage has a voltage gain of -10 V/V, resulting in a total gain of 200 V/V when multiplied together. The calculations involve parameters such as transconductance (gm), drain resistance (RD), and load resistance (RL). The assumption of infinite output resistance (ro) simplifies the analysis, allowing for straightforward gain calculations.

PREREQUISITES
  • Understanding of common-source amplifier configurations
  • Familiarity with MOSFET parameters, including transconductance (gm) and output resistance (ro)
  • Knowledge of voltage gain calculations in cascaded amplifier stages
  • Ability to analyze small-signal equivalent circuits
NEXT STEPS
  • Study the derivation of voltage gain for common-source amplifiers
  • Learn about small-signal analysis techniques for MOSFET circuits
  • Explore the impact of varying load resistance (RL) on amplifier performance
  • Investigate the effects of finite output resistance (ro) on overall gain calculations
USEFUL FOR

Electrical engineers, students studying amplifier design, and anyone involved in analog circuit analysis will benefit from this discussion.

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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.