Wrong? Unless the transistor is in saturation then it is absolutely, positively, correct.
Now, if the transistor is in its active region and if you drive the base with a current source then you've got control of its base current. However, this is not a common situation.
Bob
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Your voltage divider and the input signal define a 'load line', and you can graph the I/V characteristic of this combination.
The transistor base (with emitter grounded) also has an I/V characteristic, which has some perhaps non-negligible temperature dependence. Graph that.
Overlay the graphs. Where they intersect, is the base current so high that the transistor will burn up? Is it so low that the transistor will not switch on?
Since the input is a 'signal', it has both high and low excursions; look at the low excursion and graph the load line for that case. Overlay the graphs, and determine if the base is reverse biased beyond the spec sheet limits (usually about -5V). Is the base current low enough to really switch the transistor OFF in this condition?
The answers to these questions, if satisfactory, will tell you that the divider is going to switch the transistor. The exact values of the components can influence ANY of these multiple tests, there is no single right combination.
You can eliminate R1 values that, ignoring R2, don't deliver enough current. You can eliminate R2 values that would dissipate excessive heat at transistor turn-on voltages.
Various transistors have various saturation betas, but many datasheets will use a beta factor of 10 as their assumed "saturation case" partly because it is a commonly used value (well recognized) and the factor of 10 works most places. You can go to the datasheet itself to check, though.
For example, if you look for a spec on the collector-emitter voltage (labeled as Vcesat, often), you will see that they often specify it with an Ic that is 10 times the Ib. That's a clue that you may want to use that value. If you see it specified with an IC that is 5 times the Ib, you should take that as a clue to use 5, not 10. For most small signal BJTs I've looked at (not so many, really), 10 is the common factor used. But if you examine, for example, the datasheet from OnSemi for the 2N3055, you will see two entries -- one for a beta of 10 (Ic=4A, Ib=0.4A) and a beta of 3 (Ic=10A, Ib=3.3A). This should be a clue to think a little more about it.
Beta is a slippery thing and none of this means you must use 10 (or 5) for a saturation beta. Actually, depending on what you can tolerate for Vce in your application, you might actually want to use a larger number for the beta because the Vce you actually get may be quite fine. So now go over to the "Collector Saturation Region" curves, if you can find them included in the datasheet. For example, in the
2N2222 sheet from OnSemi I'm looking at right now, there are four curves for a fixed Ic -- 1ma, 10mA, 150mA, and 500mA. The y-axis will be Vce and the x-axis will be a log-scale of Ib. I find that at a Vce=0.2V, which might be acceptable to me, that at an Ic=10ma, Ib=55uA-- that's a beta of about 180!! So using a beta of 10 might be overkill. Of course, the curve is for the "typical case" so you need to keep that in mind, too. So here, I might choose a beta of 30 instead of 10 or 180. Just to be safe, yet not require quite so much base current.
This can an important thing to think about when a microcontroller is driving things. The pins may be only able to sink or source some particular level of milliamps with any guarantee of the output voltage being in a well-defined range. And you may be forced into using two BJTs to get the desired Vce when switched on if you assumed a beta of
10 as an absolute rule, when in fact you would find out you can get away with one BJT if you only had looked at an actual curve.By the way, on that curve of Ic=10mA, a beta of 10 suggests Vce=30mV. So you can see that using a smaller beta assumption means achieving a really low (well, low for most of us normal humans) Vce. But typically only a difference of 170mW between a beta of 180 and 10. You may not need that kind of extreme difference in Vce.
The datasheet has a lot of stuff and you should spend a little time familiarizing yourself. Gradually, it will make increasing sense what to look for and where to look for it.
Also, different manufacturers make different things even when they use the same number. The 2N2222 comes in Vceo of 40V and 60V, but from different manufacturers. Different processes and topologies, I guess. (I'm a hobbyist, not a professional, so I don't need to know exactly why.) So it helps, in getting a "feel" for the 2N2222 to examine a variety of datasheets to see where they seem alike and where they seem different enough to notice.
Jon
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