# Why does a BJT enter saturation? I'm a beginner in EE, learning about the forward active mode of transistors. The equation, Ic = Ib * BETA, and Ic=Ie * ALHPA, are referred to as the ways to figure out what base resistor you should have when running forward active mode. What is Ic and Ie? Do these mean the amount it lets in, or some ratio?

Along with this, how do I use these numbers? On this site, https://learn.sparkfun.com/tutorials/transistors they give an example where they say Ic is 100mA. From my understanding, that means that if it hooked straight up to the positive and negative terminals it passes 100mA. But what if there are resistors in series? What effect does this have?

Thank you very much. I'm sorry if there is a term for this I don't know, by all means give me something to google.

-edits-

Thank you for the name suggestion.

• @andrews_favorite_jfet I don't see what you mean. The link I provided says Ic=Ie*a, as well as this wikipedia page: en.wikipedia.org/wiki/Bipolar_junction_transistor , and some random other link I found just to make sure that the wikipedia article wasn't wrong: learningaboutelectronics.com/Articles/… – Evan K Jul 4 '17 at 2:34
• "What is Ic and Ie?" Not sure where to start, for npn, Ic is current into the collector terminal and Ie is current out of the emitter terminal. – sstobbe Jul 4 '17 at 2:39
• @sstobbe Ok, let's say there is a 9v power source, with a 450 ohm resistor preventing the current from going above 20 mA. The Ic I calculate ends up around 110 mA. As far as I know 110 mA wouldn't be possible since the resistor is limiting the current, so what does the 110 mA mean? – Evan K Jul 4 '17 at 2:41
• – The Photon Jul 4 '17 at 3:28
• Regarding saturation of a BJT, where it's base-collector junction becomes forward biased, it's not a property of the BJT itself but of the BJT as part of a surrounding circuit and operating point. See: electronics.stackexchange.com/questions/276146/… – jonk Jul 4 '17 at 4:15

## 2 Answers

The equation, Ic = Ib * BETA, and Ic=Ie * ALHPA, are referred to as the ways to figure out what base resistor you should have when running forward active mode. What is Ic and Ie?

$I_c$ is the collector current. That is, the amount of charge flowing in to the collector per unit of time.

$I_e$ is the emitter current. In a circuit theory class, this will be the amount of current flowing in to the emitter terminal. But in every-day usage, we might define it to be the current flowing out of the emitter terminal as that is more likely to be a positive number. A good source will provide a schematic with arrows indicated the direction to be considered positive for every current they want to talk about.

Do these mean the amount it lets in, or some ratio?

$I_c$ and $I_e$ are currents. $\beta$ and $\alpha$ are ratios.

Usually in EE a variable named $I$ will be a current.

When talking about BJT's, the important ratio is $I_c/I_b$. This is often designated by $\beta$ or $h_{fe}$. ($\alpha$ might sometimes also be important but it's much more rare for it to come up in a practical circuit solution)

On this site, https://learn.sparkfun.com/tutorials/transistors they give an example where they say Ic is 100mA. From my understanding, that means that if it hooked straight up to the positive and negative terminals it passes 100mA.

If they say the current is 100 mA, they mean the current is 100 mA in whatever circuit they're talking about. If that circuit has the collector connected directly to the power supply, that's what they mean. If they're talking about a circuit with resistors, then they mean the current flowing in to the collector in that circuit.

But what if there are resistors in series? What effect does this have?

If there's a resistor (and nothing else) between the power supply and the collector, then any current into the collector will have to flow through that resistor to get to the transistor. Ohm's law will tell you what the voltage drop must be across the resistor for that current to flow.

• In your answer it doesn't address the direct thing I'm confused about (though I thank you for the greatly detailed answer I did learn quite a bit. And maybe it does, and I just don't see it.) When I said the current is 100 mA, I mean Ic evaluates to 100 mA. If the current flowing is only 20 mA, but the transistor's Ic is at 100mA, does that basically mean 20 mA will be allowed through? How does this act as amplification? – Evan K Jul 4 '17 at 3:44
• Usually $I_c$ is the current flowing into the collector. If the current is 20 mA, the current is 20 mA, not 100 mA. If the current is 100 mA, then it's 100 mA, not 20 mA. It can't be 20 mA and 100 mA at the same time. So that part of your question is unclear --- I don't know how to answer it because it doesn't make any sense to me than if you asked "If my weight is 50 kg and how much I weigh is 70 kg, how much do I weigh?" – The Photon Jul 4 '17 at 3:47
• Ah, I see where the confusion is hitting. Let me back up. In the site, they say to calculate for Ic, as this is the current that will be passed through the transistor. Then, it was said that it would be 100 mA. I'm confused now what it means when it isn't possible for 100 mA to be flowing, as a resistor is limiting it down to 20 mA. Am I getting confused about the purpose of forward-active mode? I thought it was for current amplification. – Evan K Jul 4 '17 at 3:51
• I guess I am asking how to solve for what current is actually flowing. In the circuit diagram provided, what is the current through the LED? Is it evaluated by a simple ohm's law equation, or is the equation more complicated? When I made a circuit representing it, changing R2, even though the Ic was well above the amperage supported by R1 every time, the LED's brightness changed. – Evan K Jul 4 '17 at 3:54
• You do it like a diode---first guess what operating mode it's in and solve under that assumption. Then check whether the pre-requisites for that mode are held ($V_{ce}>0.2 V$, for forward active). If not, guess again about the operating mode, solve, check. And so on (if you have multiple BJTs in the circuit you have to consider different combinations of modes for the different BJTs). – The Photon Jul 4 '17 at 4:15

The main point to takeaway is the relation $I_C = \beta I_B$ is a model of how a BJT behaves when operating in forward-active mode. As an extreme example, one cannot simply apply a negative current to the base of an NPN BJT and expect negative $\beta I_B$ current to flow in the collector.

The actual reason current flows in a BJT is extremely complicated and only described by modern solid state physics. However the models that have been developed to describe their behavior are in most cases "good enough" when applied within their regions of validity.

I have simplified your schematic slightly to illustrate the concept of saturation.

Take for example the following schematic, Here the current into the base terminal is set by an ideal current source (only for convince in a Spice simulator) in a real circuit a resistor is often close enough to set the base current by ohms law.

The following figure is the simulations reults of a DC sweep of the current source injecting into the base terminal. The x-axis is base-current. The left y-axis is the collector voltage. The right y-axis is the collector-current. We can see that when the collector-emitter voltage is greater than ~0.2V the forward-active relation holds true, namely, $I_C = \beta I_B$. As more base-current is applied more collector-current flows. However as more current flows more voltage is being dropped across R1 and the collector-emitter voltage is dropping. Eventually when the collector-emitter voltage becomes small enough the BJT is no longer in forward-active but in forward-saturation.

The textbook definition of forward-saturation for an NPN BJT is when Vbe is positive and when Vbc is also positive.

In saturation the BJT, loosely speaking it looks like a switch between collector and emitter. Slightly more complete model is a small mV level voltage source with low series resistance.

So when the NPN is behaving as a switch (saturated) it is the circuit around it that dictates what current will flow, in your case R1.