Why Do Equations Remain Unchanged Across Different Transistor Operating Regions?

[noamriemer]

Hi there! I'm having trouble understanding the transistor circuit analysis. Hope you could help me :)

First I need to find the active region of the transistor. What I saw in the solutions was an assumption that the transistor is in saturation region and then:

VBB=IbRb+Vbe+IeRe
Vcc=IcRc+Vce+IeRe

Why did the solver assume the transistor is in saturation mode, when he is supposed to find the active region?

Next, I have to calculate the minimal RE needed for the transistor to be active.
This time, they did refer to it as in active region. But, the equations remained the same. I thought that in Active region, it is supposed to reverse:

VBB=IbRb+Vbe+IeRe
Vce-IcRc-Vcc=IeRe

Why isn't there any change in the equations ? the BC diode is supposed to be in reverse mode, isn't it ?

Thank you!

 

[NascentOxygen]

First I need to find the active region of the transistor. What I saw in the solutions was an assumption that the transistor is in saturation region and then:

VBB=IbRb+Vbe+IeRe
Vcc=IcRc+Vce+IeRe

Why did the solver assume the transistor is in saturation mode, when he is supposed to find the active region?

There is nothing here to indicate an assumption of saturation. Those equations hold for both regions of operation, active and saturated.

Why isn't there any change in the equations ? the BC diode is supposed to be in reverse mode, isn't it ?

Yes, and that condition is implicit in setting V_CE = 0. (Explanation: If V_CE = 0 and V_BE = 0.6, then it follows that V_CE = -0.6)

[PLAIN]https://www.physicsforums.com/images/icons/icon2.gifAlso, may I point out that you should not be using lower-case subscripts here, as they mean something different from the capitals subscripts. For DC or average values, use upper-case subscripts.

 

[rude man]

Hi there! I'm having trouble understanding the transistor circuit analysis. Hope you could help me :)
View attachment 50224

First I need to find the active region of the transistor. What I saw in the solutions was an assumption that the transistor is in saturation region and then:

VBB=IbRb+Vbe+IeRe
Vcc=IcRc+Vce+IeRe

Why did the solver assume the transistor is in saturation mode, when he is supposed to find the active region?

Next, I have to calculate the minimal RE needed for the transistor to be active.
This time, they did refer to it as in active region. But, the equations remained the same. I thought that in Active region, it is supposed to reverse:

VBB=IbRb+Vbe+IeRe
Vce-IcRc-Vcc=IeRe

Why isn't there any change in the equations ? the BC diode is supposed to be in reverse mode, isn't it ?

Thank you!

The first set of 2 equations is correct irrespective of values of the R's or power supply voltages. The second set is garbage.

A quick check shows that this configuration IS in saturation. Approximately,
i_e = (3V-0.7V)/0.5K = 4.6 mA which when multiplied by R_c = 3K gives V_cc - V_c = 13.8V, exceeding even the V_cc power supply.

(How did I do that? I just assumed β = ∞, a reasonable approx. with the low value of R_b).

To get your answer, you need 3 more equations:

Obviously,

i_e = i_c + i_b

and i_c = βi_b.

Then you need one more. Hint: what is the current i_b thru R_b? And if you know V_e do you automatically also know V_b?

That's 5 independent equations and 5 unknowns: the three currents plus emitter and collector voltages. Set V_c - V_e = 0 and solve for R_e.

 

[noamriemer]

Thank you both for your great help!