Differential Mode Gain and 1/2 circuit

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perplexabot
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Hey all! I have been trying this problem for a while and can't seem to get the same answer as the solution. If someone can tell me where I am going wrong, that would be much appreciated. I am very close to the solution, but I am missing a term in the denominator. Everything is shown below! Thank you for your time.

Homework Statement


Schematic of a BJT differential amplifier: two NPN transistors Q1 and Q2 with collectors tied to +VCC through RC and RL, emitters joined through RE and each fed by a current source IEE returning to -VEE, inputs vi1 and vi2, outputs vo1 and vo2.


Homework Equations

(the solution from the solution manual)[/B]
Handwritten derivation of a differential-mode half-circuit of a BJT differential amplifier, with formulas for Rc_eff, Re_eff, Adm, Rid and a common-mode half-circuit sketch.


The Attempt at a Solution


Handwritten differential-mode analysis of a BJT differential amplifier: a half-circuit with RE/2 and RC//RC/2 and a derivation of Vo/Vi = gm(RC//RC/2) / (1 + RE/(2 rπ)), with the final denominator shown as 1 + RE gm/(2β).


I am getting stumped. Please help : /
Thanks for reading.
 
Since the two halves are coupled both at the emitters and collectors I would not try to use the "1/2 d.m. model" at all. Write the usual equations, I would go with kvl (actually I just sum currents to zero at every dependent junction which is basically the same set of equations.)

If you HAVE to use the d.m model I cannot be of help.
 
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rude man said:
Since the two halves are coupled both at the emitters and collectors I would not try to use the "1/2 d.m. model" at all. Write the usual equations, I would go with kvl (actually I just sum currents to zero at every dependent junction which is basically the same set of equations.)

If you HAVE to use the d.m model I cannot be of help.
Hmmm, ok. I will consider trying without half circuits. I don't have to use the 1/2 crkt model, I just thought it would be easier.

Thank you
 
perplexabot said:
Hmmm, ok. I will consider trying without half circuits. I don't have to use the 1/2 crkt model, I just thought it would be easier.
Thank you
It would have been except for RL and RE.
I will keep the answers to myself until you come up with your answers, then let you know how they look.
 
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pallidin said:
I agree with Integral. This scheme involves no more than a power distribution network, and a very poor one at that.
To "charge" the Earth with any measurably useful non-local extracting force would require a placement of an earth-charging generation device likely to boggle the imagination, and likely far surpassing any ability we have.
Furthermore, what would be the point?
A considerable amount of energy would be required to charge the earth, for one, and the Earth's exceptionally poor conductivity would create current losses far exceeding the rationality of efficient distribution.
In my opinion, the idea is dead from the start.
Ok, thank you. I'm in the middle of finals week, I will post an answer, just not too soon. I appreciate your help.
 
perplexabot said:
Ok, thank you. I'm in the middle of finals week, I will post an answer, just not too soon. I appreciate your help.
?
Different thread.
 
rude man said:
?
Different thread.
Lol, I wonder where that quote came from?! That is weird, I was trying to quote your previous reply. My reply is still valid, except the quote is wrong. Let me try and remove it. I apologize for that.
 
perplexabot said:
Lol, I wonder where that quote came from?! That is weird, I was trying to quote your previous reply. My reply is still valid, except the quote is wrong. Let me try and remove it. I apologize for that.
No prob.
Actually a pretty involved analysis. 7 equations, 7 unknowns.
For c.m. gain a hint: consider symmetry!
 
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The main problem I see is that you have calculated the voltage across RE/2 using the voltage divider formula applied to the input voltage Vi. But the current into RE/2 isn't just the current flowing down through rπ; you also have to include the current flowing down from the dependent current source, so you can't just use the voltage divider formula.
 
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