Common Emitter with emitter resistance small signal model

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Discussion Overview

The discussion revolves around the small signal model of a common emitter amplifier circuit, focusing on the calculation of voltage gain (Av) and input resistance (Rin). Participants are attempting to derive these parameters using the pi model and are addressing specific circuit configurations and formulas.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses frustration in calculating Rin, despite having derived Av, and seeks clarification on the correct formula for Rin.
  • Another participant questions whether the problem is related to coursework or homework, indicating a potential concern about academic integrity.
  • There is a suggestion that the emitter resistance might be incorrectly placed or that there could be a typo in the Rin formula provided.
  • Participants discuss the measurement of Rin, noting that it is frequency dependent due to a capacitor in the base circuit.
  • One participant proposes a formula for Rin as RB || (r_pi + R_E*(beta + 1)), while another later agrees that this formulation looks better.
  • Concerns are raised about the dimensional consistency of the proposed formulas for Rin, with emphasis on ensuring that all components have appropriate units of resistance.
  • A participant reflects on a previous professor's explanation that supports the formula Rin = RB || (r_pi + R_E*(beta + 1)), indicating a potential source of confusion in the provided answer.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct formula for Rin, with multiple competing views and formulations being discussed. There is uncertainty regarding the placement of the emitter resistance and the dimensional consistency of the proposed equations.

Contextual Notes

Limitations include potential missing assumptions regarding circuit configuration, the dependence of Rin on frequency due to capacitive elements, and unresolved questions about the definitions of certain variables like beta and R_base.

Electrical_kid
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[Mentor's Note: Thread Moved from EE Forum]

This link has the picture, for some reason it wasnt showing in this post. http://i.imgur.com/TYlb32t.jpg
Here is my problem, I am supposed to use this circuit and solve for Av and Rin. My problem is that I have solved for Av but I can't solve for Rin no matter what I use. Its very frustrating. I need to use the pi model.

Here is my work for the Av gain.

i2yiMT6.jpg


Please let me now if this is correct and then a tip on how I can solve for Rin which should be Rin = RB|| r_pi (R_E(1+B)). Is Vbe only across r_pi or r_pi and R_E?

Av = -B(R_C||R_L)/(r_pi) which is what I have in my work in the upper right middle
 
Last edited by a moderator:
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Welcome to PF.
Is this either coursework or homework ?

small_circuit.png
 
Last edited:
Baluncore said:
Welcome to PF.
Is this either coursework or homework ?
Its homework, do you think there is a typo in the Rin given? Or is the emitter resistance in the wrong place?
 
I shrank and posted the circuit.
Rin is shown as an indeterminate arrow, Is it measured at Vs of at the base terminal ?
Rin is frequency dependent because of the series C in the base circuit.
Re will appear higher resistance to Rin because it is seen through the base current gain, beta.
 
Electrical_kid said:
Please let me know if this is correct and then a tip on how I can solve for Rin which should be Rin = RB|| r_pi (R_E(1+B)). Is Vbe only across r_pi or r_pi and R_E?
Vbe is always the voltage across the active b-e junction; it doesn't embrace voltage across externally placed resistors.

Your formula for Rin looks awkward. The expressions on each side of the "||" symbol should have units of Ohms.
 
Should Rin be Rin = RB || (rpi + RE*(beta+1)) ?
 
Electrical_kid said:
Should Rin be Rin = RB || (rpi + RE*(beta+1)) ?
That looks better.
 
NascentOxygen said:
Your formula for Rin looks awkward. The expressions on each side of the "||" symbol should have units of Ohms.
If R_pi has dimension ohms then your Rin = RB || r_pi (R_E(1+B)) has dimensions of ohm || ohm2
Where has your R_pi come from ?

See schematic in post #2
Do you think Rbase = R1 || R2 ?

How is beta defined ?
Maybe; Rin = Rbase || (Re * beta)
or; Rin = Rbase || (Re * (1+beta) )
 
Baluncore, I think the reason I was having trouble is because the answer they provided was missing the plus sign, a previous professor of mine provided me a pdf file explaining how they get Rin and it definitely shows that it should be Rin = RB || ( rpi + RE(beta +1)).
 

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