# How to calculate the current through the LEDs/the collector current in the BJT circuit

For this exercise I have to calculate the voltage Vce and the current through the LEDs. The LEDs have a knee voltage of 2 V, the transistor has one of 0.7 V. Beta has been given as very big.

To start I calculated the Vce simply by applying the voltage law. I did

Vce = 9 V - 4 V - 4.7 V + 0.7 V = 1 V.

Now I have to calculate the current through the LEDs, or in other words the collector current. Since I assume that beta is just infinity, I struggle with applying any formula I know to get to the answer, since I cant use $$Ic < Ib * Beta$$.

Any tips on how to continue with this exercise?

• Tell me this is an exercise and "9V" is a proper supply. The answer would be completely different if it was a PP3 battery.ps : you will find more accurate values of Beta in the transistor's datasheet (and you know what transistor is used, so that's easy to find)
– user16324
Commented Jun 16, 2022 at 11:27
• @user_1818839 I think its a proper supply yes, this is only my first electronics course! Commented Jun 16, 2022 at 11:43
• Just use Ohm's law. You know R7 voltage and resistance. Commented Jun 16, 2022 at 11:44
• I didnt know how to calculate the voltages. @Justme Commented Jun 16, 2022 at 11:47
• you will enjoy comparing your calculations with this simulator for many things. tinyurl.com/2o4euzf5 Commented Sep 4, 2022 at 14:42

## 1 Answer

Assume beta is large, base current is negligible.

Assume ideal zener diode: if current flows through it in reverse, it will deliver the voltage on the label.

So, there's 4.7V across the zener, and the current in R5 is (9V-4.7V)/R5. It is not asked in the question, but it's 2.15mA.

Knowing the voltage applied on the base (4.7V) then if the transistor is ON, and not saturated, then the emitter is 0.6V below, so 4.1V above ground.

So, the current in R7 is 4.1V/R7 = 87mA. LED current is equal to this minus base current.

The LEDs are ON, there's 2V across each, so calculate Vce like you did to confirm the assumption that the transistor is not saturated.

Then assume beta>100 and calculate maximum base current to validate the assumption that current actually flows in the zener diode.

Supposing beta>100, then base current is <0.87mA.

Basically:

• Make a bunch of assumptions (zener is conducting, and transistor is not saturated)
• Calculate circuit variables based on this
• Validate the previously made assumptions

For example in the last step if you found the transistor to be saturated, then the much lower resulting hFe would mean the zener would not have any current flowing through it, so the assumptions would be wrong, and you'd have to start over with different ones.

Note:

As far as current sources go, this one is pretty bad because it wastes lots of voltage heating the transistor and the resistor, only using 4V out of 9V to do something useful. Since everything is in series and the current is the same in the LEDs, the transistor and the resistor, and power P=V.I then power dissipated in each element is proportional to the voltage across it. So you want as much voltage as possible on the stuff that does something useful (ie, the LEDs) and as little as possible on the stuff that just makes heat.

In addition, if the 9V supply can vary, wasting less volts on the resistor and having higher Vce means it'll still work at lower supply voltage.

So here's an example simple current source with very low voltage drop. It's possible to go lower, but this one is hard to beat regarding price and simplicity.

This one uses feedback: if current through R1 (and the LEDs) increases, voltage across R1 increases, Q2 conducts more and steals base current from Q1, making it conduct less, that reduces current, and that makes a feedback loop. So Q2 regulates voltage on R1 to be equal to its own Vbe, which means it regulates current to the value Vbe/R1.

• In particular, once you know the approximate zener current, you can refine the zener diode voltage based on the I-V curves in its datasheet.
– user16324
Commented Jun 16, 2022 at 11:30
• Thank you for the explanation! I didn't think I had to assume values or modes but this is quite logical. Thanks Commented Jun 16, 2022 at 11:33
• For which purpose are you asking for the base current? You that the voltage across R7 is 1V. Hence, you have the emitter current - and it is by far exact enough to set Ic=Ie. This example clearly shows that that base current is an unwanted by-product and the emitter current is determined by Vbe only.
– LvW
Commented Jun 16, 2022 at 13:05
• @LvW you need the base current to make sure R5 passes enough current to power the transistor base and the zener, otherwise the zener wouldn't do its job and it wouldn't be a constant current source. Commented Jun 16, 2022 at 15:38
• @bobflux when the voltage across R5 is (9-4.7)=4.3 volts we have a current through R5 of app. 2mA. Do you really think that the base current plays such an important role ? In the task description we can read "beta has been given as very big"! More than that , why do you think the zener would be a "constant current source"? This surprises me.
– LvW
Commented Jun 16, 2022 at 17:33