Verify Is Math Correct? Assumptions Correct?

[Duave]

Can someone please tell me if I have solved the problem? Is the math correct? Were the assumptions correct?

Thank you in advance

Homework Statement

Show that:

I(B) = 44 uA
I(C) = 4.4 mA
V(CE) = 1.2 V

https://scontent-a.xx.fbcdn.net/hphotos-prn1/t1.0-9/1011057_10151937081760919_165466716_n.jpg

Homework Equations

V(B) - V(BE) = V(E)

I(B) = V(B)/R(B)

I(B) = [Beta][I(B)]

The Attempt at a Solution

The dotted lines were placed for clarity.


Part A

V(B) = 5V
.....
V(BE) = 0.6V
......
V(B) - V(BE) = 5V - 0.6V
........
V(B) - V(BE) = 4.4V
........
R(B) = 100 x 10^3(ohms)
........
I(B) = [4.4V/100 x 10^3]
........
I(B) = 44 uA
......
I(C) = [Beta][I(B)]
.....
I(C) = (100)(44 x10^-6)
.......
I(C) = (4.4 mA)
........
V(C) - [I(C)][R(C)] = V(CE)
........
10V - (4.4 x 10^3(A))(2000(ohms)) = V(CE)
............
10V - (8.8(V)) = V(CE)
......
1.2V = V(CE)
......

Part B

Find Beta

(Beta)[I(B)] = I(C)
.....
I(S){e^(V(BE)/V(T)] -1} = I(C)
.........
I(S){e^(V(BE)/V(T)] -1} = (Beta)[I(B)]
...........
Beta = [I(S)/I(B)]{e^(V(BE)/V(T)] -1}
..........
Beta = [{[V(CC) - V(CE)]/[R(C)]*[e^{V(BE)/VT]}/I(B)]{e^(V(BE)/V(T)] -1}
.............
Beta = [{[V(CC) - V(CE)]/[I(B)][R(C)]
........
Beta = [{[10V - 1.2V]/[44 x 10^-6(A)][2000]
.........
Beta = 100

 

[mfb]

Looks good. But why do you calculate beta (with something calculated in (A)), if you can use it in (A)?

 

[rude man]

Where do you assume beta = 100? It can't be calculated except by assuming the answers a priori.
.

 

[Duave]

Looks good. But why do you calculate beta (with something calculated in (A)), if you can use it in (A)?

@mfb

I made a mistake. I know that beta is unitless.

My question to you is, if I erase the (A), would the statement then be COMPLETELY correct?

Thanks again

 

[Duave]

Where do you assume beta = 100? It can't be calculated except by assuming the answers a priori.
.

@ Rude Man

I understand what you mean. I was to answer the question below:


Suppose that the circuit shown in this thread goes into saturation. What is the MINIMUM value of β which would cause saturation?


Do my calculations answer this question? Do my final answers in bold answer it or do I need to give additional information?

Thanks again

 

[rude man]

@ Rude Man

I understand what you mean. I was to answer the question below:


Suppose that the circuit shown in this thread goes into saturation. What is the MINIMUM value of β which would cause saturation?


Do my calculations answer this question? Do my final answers in bold answer it or do I need to give additional information?

Thanks again

In that case beta needs to be a bit more than 100.

I answered your other question by quoting your 1st post.

 

[rude man]

Can someone please tell me if I have solved the problem? Is the math correct? Were the assumptions correct?


V(B) = 5V
.....
V(BE) = 0.6V
......
V(B) - V(BE) = 5V - 0.6V
........
V(B) - V(BE) = 4.4V
........
R(B) = 100 x 10^3(ohms)
........
I(B) = [4.4V/100 x 10^3]
........
I(B) = 44 uA
......
I(C) = [Beta][I(B)]
.....
I(C) = (100)(44 x10^-6)

.

No. A beta of 100 will not saturate the transistor.

.......
I(C) = (4.4 mA)

No. See above comment.

........
V(C) - [I(C)][R(C)] = V(CE)

........
10V - (4.4 x 10^3(A))(2000(ohms)) = V(CE)

It takes more than 4.4 mA to saturate the transistor.

I'll leave it here for the time being ...

 

[mfb]

@Duave: All the confusion here comes from the missing problem statement.
Please post the full, exact problem statement here, otherwise we keep on guessing what you are supposed to do.

 

[Duave]

I have to solve for I(B), I(C), and V(CE)

@Duave: All the confusion here comes from the missing problem statement.
Please post the full, exact problem statement here, otherwise we keep on guessing what you are supposed to do.

The whole problem statement for Part (a) is Literally:

"
Show that:

I(B) = 44 uA
I(C) = 4.4 mA
V(CE) = 1.2 V
"

I have to show calculations that prove that I(B) = 44 uA, that I(C) = 4.4 mA, and that V(CE) = 1.2 V.

Seriously, that's all that I was given.


The whole problem statement for Part (b) is Literally:

"Suppose that the circuit shown in this thread goes into saturation. What is the MINIMUM value of β which would cause saturation?"

Thanks again

 

[rude man]

The whole problem statement for Part (a) is Literally:

"
Show that:

I(B) = 44 uA
I(C) = 4.4 mA
V(CE) = 1.2 V
"

I have to show calculations that prove that I(B) = 44 uA, that I(C) = 4.4 mA, and that V(CE) = 1.2 V.

Seriously, that's all that I was given.


The whole problem statement for Part (b) is Literally:

"Suppose that the circuit shown in this thread goes into saturation. What is the MINIMUM value of β which would cause saturation?"

Thanks again

OK, we caw summarize this as follows:
part (a) beta = 100 and your computatiuons are correct.
part (b) did you ever find the minimum beta?

 

[Duave]

OK, we caw summarize this as follows:
part (a) beta = 100 and your computatiuons are correct.
part (b) did you ever find the minimum beta?

@rude man

Thank you so much for your response:

Right now β = 100

i_C/i_B = β
.........
i_C = 4.4 mA
.........
i_B = 44 uA
.........
4.4 mA/44 uA = β
.........
100 = β
.........

if V_C drops to V_CE then,
............
V_C = 1.2V
.........
I_C(1.2V) = V_C/R_C
.............
I_C(1.2V) = 1.2V/2000(ohms)
.............
I_C(1.2V) = 0.6mA
.............
if I_B is fixed, then
.......
I_C/I_B = β
..........
0.6 mA/44 uA = β
......
13.64 = β
......

So, the minimum β = 13.64

Is this correct or am I still missing soemthing? Thanks again.

 

[Jony130]

For this circuit Ib = (Vin - Vbe)/Rb = (5V - 0.6V)/100k = 44μA
The maximum collector current is equal to
Ic_max = (Vcc - Vcs(sat))/Rc ≈ Vcc/Rc ≈ 10V/2K ≈ 5mA

So if BJT current gain Hfe (β) will be larger than 5mA/44μA = 114 the BJT will enter saturation region.

 

[Duave]

For this circuit Ib = (Vin - Vbe)/Rb = (5V - 0.6V)/100k = 44μA
The maximum collector current is equal to
Ic_max = (Vcc - Vcs(sat))/Rc ≈ Vcc/Rc ≈ 10V/2K ≈ 5mA

So if BJT current gain Hfe (β) will be larger than 5mA/44μA = 114 the BJT will enter saturation region.

Thanks Jony130

I can understand the max value you that you calculated, but does my minimum look okay or do I need to fix that?

 

[Jony130]

but does my minimum look okay or do I need to fix that?

But what this minimum Hfe value will represent? Because if you want Ic = 0.6mA for fixed base current (44μA), then you need to use a BJT with a Hfe equal to 13.64.

 

[Duave]

But what this minimum Hfe value will represent? Because if you want Ic = 0.6mA for fixed base current (44μA), then you need to use a BJT with a Hfe equal to 13.64.

Jony130,

So does the collector branch always determine the minimum Hfe (β) that will cause saturation? That's right isn't? In this circuit, The collector determined the minimum saturation value.

 

[Jony130]

How do you define a saturation? Do you understand what saturation is ?
Please read this
https://www.physicsforums.com/showthread.php?t=703097&highlight=saturation (post 4 and 6)

 

[rude man]

Part b assumes eveything in the circuit stays the same except beta can rise.

So to compute the min. needed for saturation, use the same base current, multiply by beta, and let that product = the collector current needed to reduce the collector voltage to zero. Then solve for beta.