Optimizing BJT Circuit Design: Solving for Rc and Vc

  • Thread starter Thread starter CDTOE
  • Start date Start date
  • Tags Tags
    Bjt Exercise
Click For Summary

Discussion Overview

The discussion revolves around solving an exercise related to BJT (Bipolar Junction Transistor) circuit design, specifically focusing on determining the values of the collector resistor (Rc) and the collector voltage (Vc) for a given transistor with a specified beta (β) range. The context includes theoretical and practical aspects of transistor operation in active and saturation modes.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks help to find Rc and Vc for a BJT circuit, referencing a textbook solution of Rc=1.5KΩ and Vc=0.3V to 4.8V.
  • Another participant emphasizes the importance of showing work and understanding definitions of active and saturation modes for BJTs.
  • Definitions of active mode and saturation mode are provided, with specific voltage conditions outlined for each mode.
  • Participants discuss the relationship between collector current (Ic), base current (IB), and beta (β) in determining Rc and Vc.
  • One participant proposes using β=150 to find the worst-case Ic and questions the calculation of Vc when β=50.
  • There is a suggestion to use Ohm's Law to relate Rc to the collector voltage and current, but uncertainty remains about the correct values to use.
  • Multiple attempts to calculate Rc and Vc are presented, with participants questioning the correctness of their approaches and calculations.
  • One participant concludes that their calculations may contradict the textbook's values, suggesting a potential error in the textbook.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correctness of their calculations and the textbook's values. There is no consensus on the final values for Rc and Vc, and multiple competing views on the correct approach to the problem remain.

Contextual Notes

Limitations include potential misunderstandings of definitions and assumptions regarding the behavior of the BJT in different operating modes. The calculations depend on the chosen values for β and the assumptions made about collector current and voltage.

Who May Find This Useful

This discussion may be useful for students studying BJT circuit design, particularly those preparing for exams or seeking clarification on the operation of transistors in different modes.

CDTOE
Messages
46
Reaction score
0
Hi, Everyone.

I have an electronics I exams tomorrow, and I'm looking for help in solving the following exercise if you don't mind.

2j6r12.jpg


The exercise tells that this circuit is to be fabricated with a transistor type whose β is in the range of 50-150. It asks to find the value of Rc, so that all fabricated circuits are guaranteed to work in active mode. It also asks to find the collector voltage range that the fabricated circuits may exhibit.

The answer, as it's provided in the textbook, is Rc= 1.5KΩ and Vc= 0.3V to 4.8V.

I have made a couple of attempts to solve it, but apparently I'm running out of time, so I need your help, experts!

Thanks in advance.


Update: My attempt in solving the exercise
 
Last edited:
Physics news on Phys.org
you need to show your own work and folks here will help you see where you are going wrong. We don't just feed you the answer. Read the forum rules.
 
Last edited:
How did your class define saturation mode and active mode for a BJT?
The answer to the question will fall out of these definitions.
 
es1 said:
How did your class define saturation mode and active mode for a BJT?
The answer to the question will fall out of these definitions.

Well, not the class, it's the textbook by Sedra&Smith. Talking about NPN BJT:

Active mode: as long as VBC<= 0.4V, in other words, VCB>= - 0.4V.
Saturation mode: as long as VBC>0.4V, in other words, VCB< - 0.4 V.

In either cases, it's always assumed that VBE=0.7 V, just to simplify the calculations. Also, it's assumed that VCE=0.2 V in saturation mode.
 
Last edited:
CDTOE said:
Active mode: as long as VBC<= 0.4V, in other words, VCB>= - 0.4V.
Saturation mode: as long as VBC>0.4V, in other words, VCB< - 0.4 V.
You have two pieces of information here that you need to juggle here. The first is the minimum collector voltage to stay within your definition of active mode: Vb is 0.7V and your definition of active mode requires that the drop from base to collector is less than 0.4V. That tells you [STRIKE]something about[/STRIKE] the minimum collector voltage. With that in mind, the second piece is the fact that the collector voltage is determined by how big the drop is over Rc. Use Ohm's law here for the worst case scenario (i.e. the biggest drop) to figure out the minimum value Rc must have.
 
Last edited:
But to be able to use Ohm's law for the worst case scenario (the largest voltage drop across Rc), I must have the value of Ic. As shown in my pencil and paper attempt of solution (here), I used β=150, because it defines Ic in the worst case scenario since Ic=IB (β).

Please check the solution that I made in the link, and tell me if it's correct or not that way. Also, how would I be able to get the maximum Vc value that the circuit may exhibit, which is specified as 4.8V in the solution? I tried to use the best case scenario, when β=50 (to get the minimum voltage drop across Rc which has become known as 1.5KΩ), and I did all the calculations to end up with a Vc value of 6.775 V.
 
Last edited:
CDTOE,

Let's go back to your first attempt. You were going in the right direction and the work you did was correct. You determined that the collector current was 2.15mA at a beta of 50. How can we use that collector current to find the voltage at the collector?
 
I would be able to use the 2.15mA collector current to find the collector voltage, if I have the value of Rc. It's 10 - (2.15Rc), but Rc is a missing parameter, which has to be found, too.
 
Last edited:
  • #10
You can find RC using Ohm's Law. RC carries a maximum of https://www.physicsforums.com/images/icons/icon5.gif mA and has 10V at one end and how many volts at the other end of RC? https://www.physicsforums.com/images/icons/icon6.gif
 
Last edited by a moderator:
  • #11
Well, it's ( (10 - Vc)/ 2.15mA). Now, Vc is missing. So?
 
  • #12
I noticed I should not have used 2.15mA as the value of collector current here, so have edited my post.
 
  • #13
So, none of the attempts I made was going in the right direction. Is that it? Wouldn't be correct to take β=150 to get the highest possible value for Ic, and then assume that Vc=0.3V (the worst case scenario), and finally calculate Rc value?

Rc= ((10-Vc) / β (IB)) --> ((10-0.3) / 150(0.043mA))= 1.5KΩ

That was my second attempt, but is it correct this way? and what about the 4.8V for Vc (the highest value in the range of 0.3 to 4.8V)? how was it calculated?
 
  • #14
CDTOE said:
So, none of the attempts I made was going in the right direction. Is that it? Wouldn't be correct to take β=150 to get the highest possible value for Ic, and then assume that Vc=0.3V (the worst case scenario), and finally calculate Rc value?

Rc= ((10-Vc) / β (IB)) --> ((10-0.3) / 150(0.043mA))= 1.5KΩ
That looks like the right idea.

Now, keeping that as Rc, what is Vc when β is the lowest value expected?
 
  • #15
It's equal to ( 10 - ( β (IB) 1.5K)) --> ( 10 - ( 50 (0.043m) 1.5K)) = 6.775 V

So, it's wrong, or maybe I did it wrong. What's the problem here?
 
  • #16
CDTOE said:
It's equal to ( 10 - ( β (IB) 1.5K)) --> ( 10 - ( 50 (0.043m) 1.5K)) = 6.775 V
That's right.
 
  • #17
This means that it's the textbook's value that's wrong. If this is the case, then thanks everybody for help.
 

Similar threads

Engineering Designing a Bias Circuit for BJT with Optimal Ratio and Voltage Drop
  • · Replies 2 ·
Replies
2
Views
2K
Engineering BJT Transistor for Motor Control - PIC Microcontroller Interface
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Analyzing an RC Circuit: Solving for Time Constants and Resistance
  • · Replies 10 ·
Replies
10
Views
4K
MATLAB Exercises Help: Solve Series RC Circuit & Plot Circle
  • · Replies 1 ·
Replies
1
Views
3K
Engineering How can I design a transistor switch for a 10-Ohm load with a +5V supply?
  • · Replies 2 ·
Replies
2
Views
3K
Solve RC Circuit Problem: 45V -> 10V in 4.21ms
  • · Replies 4 ·
Replies
4
Views
9K
Solving Circuit Problem with PNP-Common BJT Transistor
  • · Replies 1 ·
Replies
1
Views
1K
  • Sticky
Physics Forums Global Guidelines
  • · Replies 2 ·
Replies
2
Views
506K