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When we have an NPN transistor in forward active mode, why do we sometimes use this equation to find the collector current I_c (whereby V_be would be the voltage across the base emitter junction)?

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But then other times use I_c = B*I_b (whereby I_b is the current into the base of the NPN transistor)?

Thanks

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  • \$\begingroup\$ \$\beta\$ is used when it doesn't really matter that much. For example, when biasing a CE amplifier stage that uses a stiff biasing pair. There it is convenient to pick a number, knowing that this gets you in the ballpark and also knowing that if you are off by 50% then it's still in the ballpark. However, \$\beta\$ would be useless when working out the fact that 60 mV change in base-emitter voltage leads to a factor of 10 change in the collector current. There, you need the Shockley equation. Can you give a few divergent examples where you'd like to know which is better to use, or use at all? \$\endgroup\$
    – jonk
    Commented Apr 24, 2021 at 3:24
  • \$\begingroup\$ @tapeside, I understand your question - and the discussion shows that there are many, many misunderstandings and wrong assumptions regarding the problem as described in your question. If you are interested, I can give you several references (with excellent reputation) in which it is explained how and why the voltage Vbe is the only controlling parameter for the emitter and collector currents. A small current cannot control a current that is 100 times larger! That is physically impossible! \$\endgroup\$
    – LvW
    Commented Apr 24, 2021 at 13:45
  • \$\begingroup\$ @tapeside, I hope you were able to derive an answer to your question from the various answers and comments. Perhaps the following is also interesting for you. Here is what Prof. Hu from Berkeley Univ. writes in chap. 8.12 ( chu.berkeley.edu/wp-content/uploads/2020/01/…): (Quote) "VBE determines the rate of electron injection from the emitter into the base, and thus uniquely determines the collector current, IC. An undesirable but unavoidable side effect of the application of VBE is a hole current flowing from the base, ." (End of quote). \$\endgroup\$
    – LvW
    Commented Apr 25, 2021 at 16:22

3 Answers 3

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All models are wrong, but some are useful

Neither of the expressions you give is correct, as they ignore the collector voltage, β is not a constant, and the temperature sensitivity is rarely accurately known enough. However, they are both useful.

If the base is being substantially current fed, so from a high impedance, then the β model is most useful. If we are substantially controlling the base voltage, so driving it with a low impedance, then the diode equation can be easier to use.

When we design transistor amplifiers, we need to be able to tolerate the large changes in temperature and β that would otherwise upset the bias conditions, so these approximations are quite good enough to tell us whether we have a workable design. Any precision work needs feedback, and that's a different set of equations.

When I design a transistor amplifier, I tend to choose the working collector current of each stage, then work backwards with the β formula to what base current (to what range of base currents) that would require, and then see how much voltage drop is caused in my proposed biassing network or feedback divider by that current. If it's too high, or too variable, then I can reduce the bias impedances, or choose a higher β transistor configuration, or otherwise iterate the design to tolerate the range.

I don't find a need to use the base voltage formula. It's not predictive enough to use for setting up bias conditions. When I need to know the response of a transistor to base voltage variations, I use a gm model (basically the differential of that), or better still, S-parameters.

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  • \$\begingroup\$ You do not "find a need to use the base voltage formula"? Does this mean that you also do not find a need to use the transconductance gm for calculating the gain of a BJT stage? Remember that gm is derived from the slope of this base voltage formula. And what about the well-known current mirror? How do you derive the tanh-characteristic for a long-tailed pair? \$\endgroup\$
    – LvW
    Commented Apr 24, 2021 at 9:45
  • \$\begingroup\$ @LvW You'll notice I explicitly do use the gm model, check the last line of my answer. gm is derived from the slope, or differential as you say. Current mirrors are a good example of when you drive a base from a low impedance (check my third paragraph). However, I tend not to design current mirrors, but to look them up, so I tend not to need that formula. Current mirrors are a good example of where the temperature does not cause a problem, as it's easy to match the device temperatures. Note I gave a personal 'I tend not to', rather than a general 'one never needs to'. \$\endgroup\$
    – Neil_UK
    Commented Apr 24, 2021 at 11:10
  • \$\begingroup\$ Leading with George Box: +1 \$\endgroup\$ Commented Apr 24, 2021 at 11:30
  • \$\begingroup\$ Neil_UK, thank you for the addtional explanantion. But to me it is a kind of contradiction to say "I do not...use the base voltage formula" and at the same time to use the transconductance gm which is derived from this formula. This parameter gm is not a "mystic" term, but it is the main parameter which determines the voltage gain - and it only exists because of the physical dependence between Ic and Vbe. And THIS question touches the problem as described by the questioner (tapeside). As you know, this exponential formula contains Is which is the main reason for temperature problems. \$\endgroup\$
    – LvW
    Commented Apr 24, 2021 at 13:26
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The BJT is a physical device - and, of course, it is possible to describe how and why it works. It is not a problem to show that and why the BJT is a voltage-controlled device following the well-known exponential Shockley equation Ic=f(Vbe). That is not a "model", it is a description of physical properties - however, somewhat simplified because the Early effect is not yet included (base width modulation). Therefore, most of our principles and methods for designing BJT based amplifier stages are based on the voltage-control feature.

For example, we use a low-resistive voltage divider at the base for providing a bias voltage as "stiff" as possible (as much as possible independent on the base current) and we use an emitter resistor for providing current-controlled voltage feedback.

We know that the voltage gain depends on the collector current only (and its associated transconductance gm) - and not on the base current. Hence, two gain stages with different beta values will have the same voltage gain (same DC operational point provided). Different beta values have an influence on the input resistance only (determined by the base current).

Nevertheless, in some specific cases (switching applications) it might be helpful and easier to use a model based on the equation Ic=beta*Ib and some proven simplified design rules. However, a good engineer is always able to discriminate between practical formulas and physical laws. He knows the physical background of simplified design rules.

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  • \$\begingroup\$ isn't a bjt current controlled device? The bjt is controlled by the current which is the side-effect of the applied voltage across BE. controlling V_be can control collector current, but the main controller is the base current, isn't it? We apply voltage to vary the base current only. \$\endgroup\$
    – Sayan
    Commented Apr 24, 2021 at 11:02
  • \$\begingroup\$ In other words voltage is the "indirect" controller of bjt. \$\endgroup\$
    – Sayan
    Commented Apr 24, 2021 at 11:11
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    \$\begingroup\$ @Sayan Chill, LvW has an obsession with BJTs being voltage-controlled devices, to the exclusion of any other view. This is of course nonsense, there is no 'main' controller. If you apply Ib, you get a base voltage, if you apply Vbe, you get a base current. The only difference is which is the more useful model when you're designing stuff. If you design current mirrors, then voltage controlled is more useful. If you want to bias general purpose transistor amplifiers, then current controlled is more practical. \$\endgroup\$
    – Neil_UK
    Commented Apr 24, 2021 at 11:15
  • \$\begingroup\$ Neil_UK, may I recommend something to you: Before using terms like "obsession" and "nonsense" it would be better to start thinking. Or what about asking me for some proofs or evidence? Are you aware that "applying a current like Ib" is nothing else than a kind of "labor jargon"? YOU CANNOT APPLY or INJECT a CURRENT! That is physically wrong! So, may I ask you something? At first, what is wrong in my answer and my examples, Secondly, have you one single proof for current control? I have several proofs for voltage control. I am really curious if you are willing to answer these two questions. \$\endgroup\$
    – LvW
    Commented Apr 24, 2021 at 13:04
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    \$\begingroup\$ +@LvW I asked you to link to the proofs you were saying existed, not to replay three totally irrelevant factoids, which though they are correct in themselves, have no bearing on whether Ib can cause Vbe. I haven't spotted the two questions you wanted me to answer, what are they? \$\endgroup\$
    – Neil_UK
    Commented Apr 24, 2021 at 15:57
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Technically, this is not an answer, but an extended comment. It would be superfluous to add one more answer: @Neil_UK gave a comprehensive answer.

The aphorism 'All models are wrong, but some are useful' is enlightening, and Wikipedia has a more straightforward article related to the subject matter, Bipolar junction transistor.

The paragraph Voltage, current, and charge control directly addresses the OP's quesion:

Detailed transistor models of transistor action, such as the Gummel–Poon model, account for the distribution of this charge explicitly to explain transistor behaviour more exactly. The charge-control view easily handles phototransistors, where minority carriers in the base region are created by the absorption of photons, and handles the dynamics of turn-off, or recovery time, which depends on charge in the base region recombining. However, because base charge is not a signal that is visible at the terminals, the current- and voltage-control views are generally used in circuit design and analysis.

I would even take courage to expand on the cited aphorism. The utility of the scientific model depends on 1) its ability to be extended and 2) its compatibility with other models. As research proceeds in the area, there arises an hierarchy of models, a more complex and true models comprising earlier efforts. The Gummel-Poon model of charge control supersedes both the current control model (\$I_c = \beta_F I_b\$) and the voltage control model (for example, Ebers-Moll) providing more precise calculation results, but it does not oust the earlier models from practical design, where these models can be applied for adequate scenarios. The next paragraph, Transistor characteristics: alpha (α) and beta (β), specifies some of these scenarios:

Beta is a convenient figure of merit to describe the performance of a bipolar transistor, but is not a fundamental physical property of the device. Bipolar transistors can be considered voltage-controlled devices (fundamentally the collector current is controlled by the base-emitter voltage; the base current could be considered a defect and is controlled by the characteristics of the base-emitter junction and recombination in the base). In many designs beta is assumed high enough so that base current has a negligible effect on the circuit. In some circuits (generally switching circuits), sufficient base current is supplied so that even the lowest beta value a particular device may have will still allow the required collector current to flow.

The Gummel-Poon model not only enhances the calculation precision; it handles the effects which the earlier models cannot, as generation of minority carriers in the base region by the absorption of photons and the dynamics of recovery time.

So, although all models are equal (in that they are only approximations to reality), some are more equal (in that they approximate the phenomena more close and comprise more aspects of the "reality").

For a deeper understanding of the concurrent views of the cause-effect relations in the BJT operations pay attention to the low-level injection effect mentioned in the cited article:

The collector–emitter current can be viewed as being controlled by the base–emitter current (current control), or by the base–emitter voltage (voltage control). These views are related by the current–voltage relation of the base–emitter junction, which is the usual exponential current–voltage curve of a p–n junction (diode).3

The explanation for collector current is the concentration gradient of minority carriers in the base region.[3][4][5] Due to low-level injection (in which there are much fewer excess carriers than normal majority carriers) the ambipolar transport rates (in which the excess majority and minority carriers flow at the same rate) is in effect determined by the excess minority carriers.

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  • \$\begingroup\$ VVT, thank you for your contribution - nevertheless, I have the following question: Is the BJT such a "mysterious" component that it is not possible to clearly describe its physical operation - unlike all other components we are using in electronics? I ask this because your post talks so much about models and I find statements like: "charge control view", "current and voltage control view", "BJTs can be considered...", "concurrent views", "...can be viewed as...current-control or...voltage-control".. What is your opinion? \$\endgroup\$
    – LvW
    Commented Apr 25, 2021 at 8:55
  • \$\begingroup\$ (continued): As I have stated very often - from the practical engineering viewpoint - I do not know one single BJT application circuit which could be explained on the basis of current-control only. Do YOU know such an example? ´But in the contrary, I know many circuits, effects and applications which can be explained with voltage-control only. I repeat again: I do not speak about models and not about carrier physics. I speak only about practical measurements, observations and commonly applied design methods. Can you help me? (By the way: Wikipedia is not always the best knowledge source) \$\endgroup\$
    – LvW
    Commented Apr 25, 2021 at 9:04
  • \$\begingroup\$ Not quite clear what do you want and how can I (or some other poster on the forum) help you. Back to the original question, the OP is confused with two seemingly alternative equations for BJT's collector code. The first answer dissolved this confusion aptly indicating that these are equations derived from two transistor models, or, rather, derived in different ways from possibly one model. The application areas for these equations partially overlap but mainly it is the utility matter what equation to use. \$\endgroup\$
    – V.V.T
    Commented Apr 25, 2021 at 10:26
  • \$\begingroup\$ As for your inquiry, you can ask the question about the specific "physical operation" of BJT that you find "mysterious", but the matter is extensive and I recommend you better take the course from the engineering school of your choice, something like Physical Principles in Semiconductor Devices or Semiconductor Devices and Device Simulation. \$\endgroup\$
    – V.V.T
    Commented Apr 25, 2021 at 10:26
  • \$\begingroup\$ I can recommend the courses of which I have access to their course materials: courses.physics.illinois.edu/ece340/sp2021, they offer a Remote Learning feature; myplan.uw.edu/course/#/courses/E%20E531; gonzaga.edu/catalogs/current/undergraduate/…. The Gonzaga's EE303 course notes on BJT Physics (web02.gonzaga.edu/faculty/talarico/EE303/HO/BJTPhysics.pdf) is an attractive teaser for students interested in physical principles of basic device operation. \$\endgroup\$
    – V.V.T
    Commented Apr 25, 2021 at 10:27

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