BJT Common Collector Amplifier: Voltage & Current Gain Calculation

[gfd43tg]

Homework Statement

The circuit below is a BJT common collector amplifier. Find both the voltage gain (AV = Vout / Vin) and the current gain (AI = Iout/Iin). As with Problem 1, this may seem hard to parse at first, but it is actually pretty straightforward. Carefully replace the BJT symbol with the model for a BJT we used in class, making sure the base (B), emitter (E), and collector (C) terminals are connected properly, then use any method you want to solve for Vout!
For this problem, you can assume Vin ≫VBE.

Homework Equations

The Attempt at a Solution

I'm not sure if my connections are right. Also, with a BJT, if current and voltage are amplified (according to my solution), what is being reduced? I don't think you can get these gains with no losses incurred.

 

[Jony130]

Your answer is not correct. You simply forget about I Kirchhoff's law and also about II law.
Ie = Iload = Ib + Ic and if we assume Vin>>Vbe then we have
Vin = Ib*Rin + Ie*Rout

 

[gfd43tg]

I'm not quite following. What is I Kirchoff's law and II law?

 

[rude man]

Or yyou can work backwards:
Vout = Iout*Re
Iout = βIb
Ib = ?
finish the set of equations yourself to get Vout. Remember to assume Vbe = 0.
I would also assume βR_L/Rin >> 1 but your prof may or may not agree.

 

[gfd43tg]

Here is my 2nd attempt, how does it look?

 

[Jony130]

Wrong again

Vout = Iin*(1 + Beta)*Rout
and
Vin = Ib*Rin + Ib (1 + Beta)*Rout
So the gain
Av = Vout/Vin = ??

 

[gfd43tg]

how is it that Vin is not just Iin*Rin?

 

[rude man]

how is it that Vin is not just Iin*Rin?

V = iR means: the voltage ACROSS the resistor = the current thru the resistor times the resistance of the resistor.

Is Vin the voltage across Rin?

 

[Jony130]

how is it that Vin is not just Iin*Rin?

Try to do KVL for this loop