How to find common-mode voltage gain of a Differential Amp

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Discussion Overview

The discussion revolves around calculating the common-mode voltage gain of a differential amplifier, including considerations of various parameters such as thermal voltage, beta, and the impact of non-ideal circuit conditions. Participants explore theoretical equations and practical implications related to the amplifier's performance.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether Ro can be considered zero given that Va is infinite, suggesting that this leads to Acm=0 and an infinite CMRR, which seems incorrect.
  • Another participant asserts that the common mode gain is indeed zero due to the 'tail' being a pure current source, assuming no transistor asymmetries are present.
  • There is confusion regarding two different gain values presented by one participant, prompting a clarification about which value corresponds to Gm and which to Ad.
  • A participant corrects their own calculation of g_m, indicating that it should be 0.029 A/V, and discusses how this affects the overall gain calculation.
  • One participant introduces a non-ideal aspect of the circuit related to current biasing and presents a calculated value for Ro, which is contested by another participant who argues that Ro should be infinite due to the Early voltage being infinite.
  • There is a suggestion to ensure consistent units when performing calculations to avoid confusion.

Areas of Agreement / Disagreement

Participants express differing views on the value of Ro and its implications for the common-mode gain, with some asserting it should be infinite while others present calculations suggesting a finite value. The discussion remains unresolved regarding the impact of current biasing on the circuit's ideality.

Contextual Notes

Participants reference various assumptions, such as the ideal behavior of the current source and the implications of the Early voltage, which may not be universally accepted or clarified. The calculations presented depend on specific definitions and interpretations of circuit parameters.

DODGEVIPER13
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Homework Statement


Beta=100,Thermal Voltage=0.026 Volts, Va=infinity, and Vbe=0.75 Volts for the differential amplifier. Please look at the upload for a clearer picture.


Homework Equations


Ad=betaRc/2(rpi+Rb)
Acm=-gmRc/(1+(2(1+beta)Ro/(rpi+Rb)))

The Attempt at a Solution


I have uploaded my attempt but I am wondering if Ro is really zero I mean Va is infinity so I would think so but this would cause Acm=0 and CMRR= infinity this seems incorrect what am I doing wrong?
 

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I think what you did was correct.
The 'tail' in this diff amp is a pure current source (Ic3) and so not changed by a common mode input voltage.
Thus, the common mode gain, absent any transistor asymmetries of which none are specified, is indeed zero and the CMRR is infinity.

For Ad you seem to have two answers: "Ad = 73.169 = 28.846". What gives with that? Anyway, I got close to your the second number by approximating as
i = is exp(V/VT), ∂i/∂V = is (1/VT) exp(V/VT) = (1/VT) i = (1/.026)0.75e-3 = 34.7
so your number of 28.846 looks about right since my approx. will come in high.
 
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Well darn the 28.846 is actually my Gm the 73.169 is my gain I need to check that
 
I myself goofed in computing g_m. It should have been 0.029 A/V.
That times the 8K resistor gives A_d = 232 but that ignores beta, r_pi and the 2K base resistor so the actual gain will be somewhat less.
 
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Sweet thanks again man!
 
Hey I had one last question I had a friend bring up the point that the circuit is not ideal due to current biasing. So I resolved for R0 by running a kvl from 12 to Vec3 soI got 12-Ib(2)-0.7=Vec=IcRo and Ro=7.54 k ohms
 
DODGEVIPER13 said:
Hey I had one last question I had a friend bring up the point that the circuit is not ideal due to current biasing. So I resolved for R0 by running a kvl from 12 to Vec3 soI got 12-Ib(2)-0.7=Vec=IcRo and Ro=7.54 k ohms

I don't quite understand this. Ro is due to the Early voltage VA which is given to you as infinite, so Ro should also be infinite.

" the circuit is not ideal due to current biasing "?? Every transistor circuit is current biased, or maybe there is an interpretation here I don't know about. I realize the "tail" is a constant-current source = 1.5 mA.

Maybe you can elaborate on your equation.
 
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Alright man appreciate it well that kind of sums it up Ro=infinite
 
OK viper. One last suggestion - watch your units, like mixing mA and Ohms etc. It's probably best if you change everything to ohms, amps and volts before computing numbers.
 

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