Transistor how to find total amplification

[kliker]

[PLAIN]http://img43.imageshack.us/img43/9491/47613590.jpg

find Aus which is Vout/Vs = Vout/Vi * Vi/Vs

where Vi = ib*β*re and Vout = VL in this case

also we know that

Rc=2kΩ , Rb=430kΩ , Rs=1kΩ, RL=4kΩ, Vcc=10V, β=100.

MY ATTEMPT FOR A SOLUTION

Vout = ic*rL

where rL = RL||Rc

also Vi = ib*β*re

but we know that ic = β*ib

hence

Au = Vout/Vi = (β*ib*rL)/ib*β*re = rL/re

as i said rL = RL||Rc = 8000/6000 = 1.34 KΩ

I need to find re know, we know that re = 25mV/IE

BUT we don't know IE, I should analyze the dc circuit in order to find IE

in the DC circuit we have

10 - 0.7 = Ib*430000

hence Ic = β*(9.3/430000) = 2.15mA which is almost equals to IE since β is large enough

we know IE now

so

re = 25mV / 2.16mA = 11.57 Ω

hence Au = rL/re = 1340/11.57 = 115.8

now I need to find Vi/Vs

taking the ac circuit I get that Rs is in series with β*re||Rb

hence we have a voltage devider here and

Vi = Vs*(β*re||Rb)/(β*re||Rb+Rs)

hence

Vi/Vs = (β*re||Rb)/(β*re||Rb+Rs)

β*re||Rb = 1157||430000 = 1153 Ω

hence Vi/Vs = 1153/(1153+1000) = 0.53

so Aus = 0.53*115.8 = 62

am I correct?

thanks in advance

 

[anathema]

Yes, your solution is correct. Good job! Just a small correction, the value of re should be 11.57 Ω instead of 115.7 Ω in the last calculation. Keep up the good work!