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

In summary, the voltage gain for an emitter follower 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. Internal capacitances of the BJT will affect the gain calculation, but the results are relatively independent of frequency.
  • #1
bznm
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0

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!
 
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  • #2
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
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?
 
  • #4
bznm said:
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?
 
  • #5
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
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.
 

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

What is the voltage gain of an emitter follower?

The voltage gain of an emitter follower, also known as a common-collector circuit using a bipolar junction transistor (BJT), is approximately equal to 1. This means that the output voltage will be nearly the same as the input voltage.

Why is the voltage gain of an emitter follower close to 1?

Since the emitter follower circuit has the emitter directly connected to the output, the output voltage follows the input voltage. Therefore, the gain is close to 1, making it act as a voltage buffer.

How is the voltage gain of an emitter follower calculated?

The voltage gain of an emitter follower can be calculated using the formula Av = (Vout/Vin). However, as mentioned earlier, the gain is approximately equal to 1, so this calculation will result in a value close to 1.

What are the advantages of using an emitter follower circuit?

One of the main advantages of using an emitter follower circuit is that it has a high input impedance and a low output impedance. This makes it useful for impedance matching, and it can also provide isolation between circuits.

Are there any disadvantages of using an emitter follower circuit?

While the emitter follower circuit has several benefits, it also has some limitations. One of the main disadvantages is that it has a low voltage gain, which means it cannot amplify the input signal. Additionally, it has a high power dissipation due to the biasing resistor between the collector and the emitter.

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