Common Emitter with emitter resistance small signal model

[Electrical_kid]

[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.

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

 

[Baluncore]

Welcome to PF.
Is this either coursework or homework ?

 

[Electrical_kid]

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?

 

[Baluncore]

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.

 

[NascentOxygen]

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?

V_be 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.

 

[Electrical_kid]

Should Rin be Rin = RB || (rpi + RE*(beta+1)) ?

 

[NascentOxygen]

Should Rin be Rin = RB || (rpi + RE*(beta+1)) ?

That looks better.

 

[Baluncore]

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) )

 

[Electrical_kid]

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)).