BJT Common Collector Amplifier: Voltage & Current Gain Calculation

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In summary: Vin - Ib*Rin - Ib*(1+Beta)*Rout - Vout = 0In summary, the conversation discusses the calculation of voltage gain and current gain for a BJT common collector amplifier. The equations Ie = Iload = Ib + Ic and Vin = Ib*Rin + Ie*Rout are suggested, with the reminder to assume Vbe = 0 and βR_L/Rin >> 1. The conversation also mentions considering I Kirchhoff's law and II law, as well as doing KVL for the loop Vin - Ib*Rin - Ib*(1+Beta)*Rout - Vout = 0 to solve for Vout.
  • #1
gfd43tg
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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.
 

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  • #2
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
 
  • #3
I'm not quite following. What is I Kirchoff's law and II law?
 
  • #4
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
Here is my 2nd attempt, how does it look?
 

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  • #6
Wrong again

Vout = Iin*(1 + Beta)*Rout
and
Vin = Ib*Rin + Ib (1 + Beta)*Rout
So the gain
Av = Vout/Vin = ??
 
  • #7
how is it that Vin is not just Iin*Rin?
 
  • #8
Maylis said:
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?
 
  • #9
Maylis said:
how is it that Vin is not just Iin*Rin?
Try to do KVL for this loop
 

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FAQ: BJT Common Collector Amplifier: Voltage & Current Gain Calculation

1. What is the function of a BJT in a circuit?

A BJT (Bipolar Junction Transistor) is a type of transistor that is used to amplify or switch electronic signals. It consists of three layers of a semiconductor material, with two layers forming a p-n junction and the third layer acting as a control terminal.

2. What is the difference between voltage gain and current gain in a BJT?

Voltage gain refers to the ratio of output voltage to input voltage in a BJT, while current gain refers to the ratio of output current to input current. Voltage gain is typically measured in decibels (dB), while current gain is measured in units of amperes per ampere (A/A).

3. How do I calculate the voltage gain of a BJT?

The voltage gain of a BJT can be calculated by dividing the change in output voltage by the change in input voltage. This can be represented by the equation: Vout/Vin = ΔVout/ΔVin.

4. What factors affect the voltage gain of a BJT?

The voltage gain of a BJT can be affected by various factors, such as the type of BJT (NPN or PNP), the biasing of the transistor, the load resistance, and the frequency of the input signal. Additionally, the physical characteristics of the BJT, such as the material and dimensions of the layers, can also impact the voltage gain.

5. How can I increase the voltage gain of a BJT?

The voltage gain of a BJT can be increased by using an appropriate biasing technique, such as the common emitter configuration, and by selecting a suitable load resistance. Additionally, using a BJT with a higher current gain (β) and higher frequency capabilities can also result in an increased voltage gain.

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