# Voltage gain of an emitter follower (BJT Common-Collector)

1. Oct 21, 2013

### bznm

1. The problem statement, all variables and given/known data
I'm trying to find a relation for the voltage gain of an emitter follower.

For an emitter follower the voltage gain is given by \$A_v=\frac{r_o|| R_L}{(r_o|| R_L)+r_e}\$, where \$r_o\$ is the output resistance of the transistor and \$r_e\$ is the intrinsic resistance of the emitter. This result is obtained without considering internal capacitances of the BJT.

What should I obtain, if I do a graphic (modulus and phase) with the response of the amplifier to the frequency?

2. Relevant equations

3. The attempt at a solution
The formula that I have written on the top gives me only one value... so I think that I have to use one that depends on frequency, (and so in this formula have to "appear" the internal capacitances of the BJT) but I don't know how I can obtain it...
If I have correctly understood, the emitter follower needs to the T-model for small signal, but I have seen the internal capacitances only for a hybrid-pi model and for high-frequency. So I don't know how to go on. If you can help me, I'll be so grateful!

2. Oct 21, 2013

### Staff: Mentor

You'll want to investigate Depletion Capacitance and Diffusion Capacitance in conjunction with BJT's.

Datasheets will specify Input capacitance (variously CTE or Cib or Cibo)and Output capacitance (Cob, Cobo) . Look up a typical datasheet to see (the 2n2222 is pretty common). Values are generally small, on the order of a few pF for discrete transistors.

3. Oct 22, 2013

### bznm

In the datasheet I have found the values of Input capacitance and Output capacitance. And now what do I have to do?

4. Oct 22, 2013

### Staff: Mentor

You'll want to incorporate them into your small signal model for the transistor and re-analyze the circuit to obtain the transfer function.

This presumes that the goal is to see the effects of frequency on a more accurately modeled emitter follower. Is that the case, or do you simply need to recognize that the simple model without capacitances is unaffected by frequency?

5. Oct 22, 2013

### bznm

I've just started to study this argument. The book starts analysing the BJT amplifiers without internal capacitance and, for the emitter follower, gets the formula of voltage gain that I have written on the top.
Then it analyses the BJT internal capacitances and the high-frequency model of a BJT common emitter, but it says nothing about the voltage gain.
I'd like to obtain the formula of the voltage gain for the emitter follower, considering the internal capacitances...

6. Oct 22, 2013

### Staff: Mentor

If I recall correctly, a hybrid-$\pi$ model is preferred for high frequency work. Apparently its basic parameters are relatively independent of frequency over a wide range. So you'll have to incorporate the given capacitances into the hybrid-$\pi$ model and do the analysis.

I think that if you do a web search on "high frequency hybrid-pi" you'll turn up some relevant information to get you going.