# BJT voltage/current gain

1. Feb 20, 2014

### Maylis

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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.

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• ###### 3.7 attempt 1.pdf
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2. Feb 20, 2014

### Jony130

Ie = Iload = Ib + Ic and if we assume Vin>>Vbe then we have
Vin = Ib*Rin + Ie*Rout

3. Feb 20, 2014

### Maylis

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

4. Feb 21, 2014

### 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.

5. Feb 21, 2014

### Maylis

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

#### Attached Files:

• ###### 3.7 attempt 2.pdf
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6. Feb 21, 2014

### Jony130

Wrong again

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

7. Feb 21, 2014

### Maylis

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

8. Feb 21, 2014

### rude man

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?

9. Feb 23, 2014

### Jony130

Try to do KVL for this loop

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