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How regions (modes) of operation are defined and correctly named? The most controversial thing is the so named “saturated region/mode”. It is defined differently, sometimes radically different, in various sources. The discrepancy surfaced several times at electronics.SE, e.g. here and here, but wasn’t acted upon by experts. BTW, are “mode” and “region” equivalent in this context?

Definitions of “saturation” that can be found include:

  1. Both junctions are forward-biased. En.Wikipedia, but popular on this site too, and quoted e.g. here.
    Variant: both junctions are on – implicated to be the same as the above by ru.Wikipedia, but “forward-biased” and “on” are not synonyms.
  2. “minimum voltage drop between collector and emitter”.
    Variant: \$V_{\mathrm{CE}}\$ reaches some [low] value.
  3. \$I_{\mathrm C} ≈ I_{\mathrm E}\$. We can infer that they suppose that \$I_{\mathrm B}\$ is negligible. Spanish Wikipedia isn’t anywhere near a trusted site, but they made changes to en.Wikipedia text they stoletranslated, which indicates some doubt about the original.
  4. \$I_{\mathrm C}\$ is less than \$I_{\mathrm B}\$ times the current gain of the BJT (Ignacio Vazquez-Abrams; see comments below).
    Variant: no increase in \$I_{\mathrm C}\$ when \$I_{\mathrm B}\$ increases.

Note that any of 2.–4. fully or partially is a part of the Wikipedia’s “active”. Imagine a common base scheme without a load, but with a slightly reverse biased base–collector junction; say, for 0.1 V. The condition 2. holds manifestly, whereas for \$I_{\mathrm B}\$ sufficiently large we can meet the condition 4. and the transistor will not burst in flames. The base–collector junction is reverse biased by construction. The base–emitter junction is forward biased since we have a significant \$I_{\mathrm B}\$ – it’s definitely not a cut-off, so we are in Wikipedia’s “forward-active”.

Is would be also nice to trace the origin of aforementioned English Wikipedia definition.

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  • \$\begingroup\$ "Active" and "saturated" are certainly two distinct modes of operation, based on the device curves alone. \$\endgroup\$ – Ignacio Vazquez-Abrams Aug 26 '16 at 21:27
  • \$\begingroup\$ @Ignacio Vazquez-Abrams: what is your definition of “saturation”? \$\endgroup\$ – Incnis Mrsi Aug 26 '16 at 21:30
  • \$\begingroup\$ When the base current is high enough that the collector current exceeds supply. \$\endgroup\$ – Ignacio Vazquez-Abrams Aug 26 '16 at 21:34
  • \$\begingroup\$ @Ignacio Vazquez-Abrams: What means “a current exceeds supply”? You don’t look like a guy unaware of the Kirchhoff’s current law. \$\endgroup\$ – Incnis Mrsi Aug 26 '16 at 21:39
  • \$\begingroup\$ I wasn't specific enough. When I said "collector current" I meant "base current times the current gain of the BJT". \$\endgroup\$ – Ignacio Vazquez-Abrams Aug 26 '16 at 21:41
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There is a precise definition and a sloppy one for saturation. I'll start with the precise one.

enter image description here

That's pretty much it. The saturation region is precisely defined here.

The sloppy one comes about because the practical behavior of different parameters of the BJT don't all neatly fall so perfectly on those lines. Besides, those voltages aren't the only thing that is important. Temperature certainly has a large effect on some parameters, so you could imagine extending a 3rd axis, in and out of the paper here, to add in that dimension. And then mapping the practical details onto that new view would be even more complex.

The sloppy idea of saturation is a practical one. If you are considering operating the BJT as a switch, you have already made the decision to operate in some part of the saturation region in the chart. But you also will be operating with a substantial forward biased \$V_{bc}\$ and not close to zero and certainly not reverse biased. This isn't a precise definition and different people will use different thresholds. So part of that region isn't useful. If you are considering operating the BJT as an amplifier, then you probably want to keep \$V_{bc}\$ reverse biased and perhaps add a small margin to that, as well. So once again, varying ideas of "out of saturation" will apply here for an amplifier. And once again, it doesn't fall precisely on the chart as shown.

EDIT: The distinction shown in the above chart is an arbitrary demarcation using the difference value of \$0V\$ as the place to draw lines, but it is also an objective, measurable, quantitative, and exact one. Whether or not it is a physical one depends on the physical parameters you care about, I suppose. But if you seek some physical point of demarcation, such as was found for Pluto vs the other planets where 5 orders of magnitude in natural demarcation was found based upon some well-reasoned physical ideas, then we'd have to get into a discussion about what physical ideas you think are appropriate. Only then could anyone attempt to decide about where these points of demarcation occur. And I don't believe that kind of discussion is appropriate here.

For the seminal paper which provides the mathematical models and expresses them using exactly the two axes I show above, see: J. J. Ebers and J. L. Moll, "Large-Signal Behavior of Junction Transistors," Proc. IRE, Vol. 42, pp. 1761-1772, December 1954. The earliest publication I happen to have on the shelf, showing the above chart, is "Modeling the Bipolar Transistor," by Ian Getreu, 1976. It appears in the first few pages of the book. His book was the result of his working at Tektronix in their STS (semiconductor test systems) group in the late 1960's and early 1970's and was initially published by Tektronix. It is currently available via Lulu.

If you want to see the original Ebers-Moll equations, which use \$V_{bc}\$ and \$V_{be}\$, then I conveniently posted them here, "Why is Vbc absent from bjt equations?," as a response to that question. You don't have to go back to the original paper if such a summary is okay. Also, if your question is an historical one, I could attempt to re-contact Ian and see if he remembers where he got his chart. He may recall.

EDIT AGAIN: I'm adding a chart taken from a 1979 edition of Jacob Millman's "Microelectronics: Digital and Analog Circuits and Systems." This is from the top of page 61, Section 3-2:

Page 61, Section 3-2, Jacob Millman, "Microelectronics," 1979

Hopefully, that helps more. Such a chart should be readily available in nearly any introduction text on semiconductors.

You now have both a quantitative description that you can get from this post where I provide three separate, but equivalent, quantitative DC views of the BJT and also a qualitative description in the above diagram, as well, which illustrates both minority and majority carriers. It doesn't get more complete than that in a post on EE.SE.

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  • \$\begingroup\$ Reference, please? Not en.wikipedia, of course. \$\endgroup\$ – Incnis Mrsi Aug 26 '16 at 22:01
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    \$\begingroup\$ @IncnisMrsi: The reference here is: J. J. Ebers and J. L. Moll, "Large-Signal Behavior of Junction Transistors," Proc. IRE, Vol. 42, pp. 1761-1772, December 1954. \$\endgroup\$ – jonk Aug 26 '16 at 22:34
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    \$\begingroup\$ @IncnisMrsi: I probably can't help you trace things. If this is a serious historical question and you want something that is well-researched, I can only help by contacting Ian (I know him) and asking him where he got his chart for his book back in the mid 1970's. But this is way out of my pay grade, if so. Otherwise, I honestly can't seem to figure out what you want to know. \$\endgroup\$ – jonk Aug 26 '16 at 23:05
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    \$\begingroup\$ @IncnisMrsi: Regarding your comment about \$V_{bc}\$ not being forward biased when the BJT is used as a switch, I'm not going to belabor this because I'm not going to go argue with a web page. If you like the page, that's fine. But I've no need to go look at it or care. I was speaking accurately, regardless. (A BJT does, or used to have symmetries [see the reverse active region], so the he-says, she-says argument could spend way too much time working over the meaning of meaningless words.) \$\endgroup\$ – jonk Aug 26 '16 at 23:11
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    \$\begingroup\$ @jonk: I am also confused about his very skeptical mindset as well. There is nothing mysterious about BJT fundamentals. It was pretty much fully understood just a couple years after it was built. There are two diodes in the BJT. Just like the diagram he shows (where the origin is really around 0.6V imo), there are four possible combinations for these two diodes when broken into on or off. The only reason the Vce saturation voltage is not 0V is because they dope the emitter more heavily than the collector, so it comes out to be ~0.2V usually. \$\endgroup\$ – jbord39 Aug 27 '16 at 0:28
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Definition of Saturation in Bipolar Transistors

In reality it depends on your application for high linearity ( low THD without feedback ) or low saturation Vce(sat) (In some high current switches Vce exceeds Vbe as a switch)

For linear operation in moderate currents, we consider Vce <2V to be non-linear @ midrange currents and significant rounding of the sine peak below Vce=2V. i.e. distortion

In between Vce(sat) specs (rated Ic:Ib ratios @load) for operation and the non-linear grey zone for Vce <2V such as for common emitter amplifiers there is the transition zon. This is where the effects of saturation change linearity and are largely unspecified. (except in below example datasheet)

For example. see fig 3&4 comparing effects of saturation and non-linear operation below 2V get worse with rising current for this 100mA part.

Nowhere in a semi. datasheet does it define saturation limit as Vc=Vb for a grounded emitter.. This is the real analog world where there are partial effects of saturation.

Just as all logic uses analog thresholds with a grey zone in between guaranteed levels of saturation for reasons of noise margin and thermal offset.

http://obrazki.elektroda.pl/6808765000_1472252095.png

Note the limit of Vce(sat) is under Vbe. (good) but the drop in hFE and rise in leakage, due to change in gaps and slope of these curves in the linear region. The device linearity >2V is very flat and not shown here.

This supports my argument that there are different thresholds for saturation depending on requirements for Switch or Linear operation.

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  • \$\begingroup\$ In short, do you claim that today’s en.Wikipedia definition of the forward-active region is non-standard and too weak (lax)? Respectively, it would suggest that their definition of the saturation is too narrow. \$\endgroup\$ – Incnis Mrsi Aug 26 '16 at 23:34
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    \$\begingroup\$ I think that the en-Wiki definition is a simplification for conceptual understanding by saying when Vce =Vbe is a clear and accurate boundary for saturation. It depends on the doping levels, Ic:Ib ratios, current, temp. and many other factors. But for a simple approximation,,it is ok. For the advanced user it could be greatly improved. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Aug 26 '16 at 23:35
  • \$\begingroup\$ Do you see any evidence of saturation in Fig 4 bottom left where Vce is < Vbe such as 0.4V and 0.05mA . The curve is flat , ie linear yet Vce<Vbe we can prove. I rest my case. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Aug 27 '16 at 0:02
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    \$\begingroup\$ @IncnisMrsi: Why do you think the definition is non-standard and weak? Forward active is when the base-emitter diode is forward biased and the base-collector diode is forward-biased. The regions of operation are not a mysterious thing; they have been around for 50+ years. \$\endgroup\$ – jbord39 Aug 27 '16 at 0:30
  • \$\begingroup\$ @jbord39: Watch your vocabulary, please. A diode is an electronic device with two terminals. Ī̲ don’t claim there is a mystery. Ī̲ claim there was some negligence in papers and textbooks. \$\endgroup\$ – Incnis Mrsi Aug 27 '16 at 6:56
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“Saturation” is a generic term for regions that are useless for an amplifier (i. e., are strongly non-linear on \$I_{\mathrm B}\$ or have β less than 1), but are far from cut-off. Most authors don’t apply due efforts to formulate a usable definition. There exists at least one English book not negligent on the matter:

E. Ramshaw (Google Books info) or R. S. Ramshaw (as written on the cover)
Power Electronics Semiconductor Switches
Springer Science & Business Media, 2013

The book specifies a distinct quasi-saturation region, that is non-linear (meets “4.”), but still fits to en.Wikipedia’s “forward-active” and the collector current flows in a healthy direction. After \$V_{\mathrm{BC}}\$ passes through zero (≈ “2.”), a hard saturation mode develops, that meets the definition “1.”. Ī̲’d call it “on–on region”.

Also, Ī̲’d characterize the region immediately before switching B–C on as “(forward) low-voltage”, having low (but positive) β. For details, see comments and my answer in Why does the collector current direction remain the same in saturation and active region? and the Common base circuit with zero supply voltage thread (with some simulation in CircuitLab).

What about the en.Wikipedia definition (as of today) of regions? It can be traced to various sources where authors were unwilling to get into details of these marginal modes. Quasi-saturation is close to the hard saturation region on the voltage–voltage plane (albeit operates in a different way), and many authors were satisfied with the simplistic picture presented in @jonk’s answer. What about the stuff from es.Wikipedia under “3.”? It’s just incompetent rubbish.

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  • \$\begingroup\$ The most precise model (that correlates closely to measured data) is (as mentioned) the Ebers-Moll large signal equation. In terms of terminology, perhaps active is best defined as where varying Vce has little effect on Hfe. Outside of that the device is either in cutoff or in saturation to some degree. \$\endgroup\$ – Peter Smith Aug 29 '16 at 16:07
  • \$\begingroup\$ @Peter Smith: A mathematician’s quibble: saying “ varying … has no effect on …”, one must specify which parameters are held constant. If you are going to clarify, then this ought to be a stand-alone answer. \$\endgroup\$ – Incnis Mrsi Aug 29 '16 at 16:12
  • \$\begingroup\$ I can accept that quibble. I need to think through the specifics of the answer so it is very clear; perhaps in the morning. \$\endgroup\$ – Peter Smith Aug 29 '16 at 16:26

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