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!

 

[rezeew]

I would first like to clarify that transistor circuit analysis is a complex and multi-faceted topic, and it is not possible to fully explain it in a short response. However, I will try my best to address your questions and provide some guidance.

To begin with, the solver may have assumed the transistor to be in saturation mode because it is a common assumption in circuit analysis. It simplifies the equations and makes them easier to solve, especially for introductory or basic circuit analysis problems. However, it is important to note that this assumption may not always hold true in real-life scenarios and may need to be revisited in more advanced analyses.

Moving on to your second question, the equations do not change because they are still valid in the active region. In the active region, the transistor is biased such that both the base-emitter and collector-emitter junctions are forward biased. This means that the transistor is conducting and the equations still hold true. The reverse-biased BC diode does not affect the equations as it is essentially acting as an open circuit in this case.

Finally, to calculate the minimal RE needed for the transistor to be active, one needs to consider the operating point of the transistor. This is determined by the biasing circuit and can be found by solving the equations you mentioned. Once the operating point is known, the value of RE can be chosen to ensure that the transistor remains in the active region.

I hope this helps clarify some of your doubts. However, I would highly recommend seeking further resources or consulting with a knowledgeable individual for a better understanding of transistor circuit analysis. It is a fundamental concept in electronics and understanding it thoroughly is crucial for any scientist or engineer in this field. Best of luck with your studies!