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

[bznm]

Homework Statement

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?

Homework Equations

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!

 

[gneill]

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

Datasheets will specify Input capacitance (variously C_TE or C_ib or C_ibo)and Output capacitance (C_ob, C_obo) . 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.

 

[bznm]

So many thanks for your answer, gneill!

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

 

[gneill]

So many thanks for your answer, gneill!

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

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?

 

[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...

 

[gneill]

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.