# Find the Min Value of R in a Zener-Transistor Regulator

It's my first time here, and i'm starting asking a question, but I hope I can help some people in the future.

So, my Teacher showed this exercise to us and i'm wrapping my mind around it without sucess. So he asked us to find the minimum acceptable value for R and the tension in the zener diode so that the Vout (Regulated) is equal to 5 V.

He said that the transistor is a basic silicon one, and the max power of the zener is 500 mW.

$V_{in}$ is 12 V with a variation of +25%.

I found that the voltage of the Zener is 5.6 or 5.7 V (I'm not sure if Vbe should be 0.6 V or 0.7 V for this particular transistor) with this formula:

$V_Z = V_L + V_{BE}$

Also found that the Maximum Current on the zener is 89 mA using this formula:

$P_Z = I_{Z(max)} \cdot V_Z$

But after this, I don't know what to do, and I don't even know if this is the right steps.

I'm having a hard time analyzing this regulator circuit in general.

If someone can spare some of their time to help me, I would be glad.

Thank you :)

• Take the current you've calculated and (taking into account the input variation) calculate the resistor you would need to generate this current. Give it a try :) 5.6V is a common zener voltage, so that's fine. Nov 15, 2017 at 15:58
• Thanks for you input, you meant to use ohms law to do it? I gave it a try and ended up with R = 12/0,089 (Min Tension) that equals to 134,83 Ohms and when using R=15/0,089 (Max Tension) it equals to 168,53 Ohms. I think the result should be 110 Ohms Nov 15, 2017 at 16:06
• WOW. It's teachers like this that make the old adage "People who can, DO. People who can't, TEACH!" Nov 15, 2017 at 16:10
• He is a terrible teacher indead Trevor, but he's a good Electrical Engineer. He leaves their students to learn stuff for their own, and when he tries to explain something in the classroom he ends up confusing everybody even more. I solved other circuits like this, but this one is giving me trouble because of the lack of information i'm used to. Nov 15, 2017 at 16:14
• @marquesini You need to account for the zener diode's voltage as well. Subtract the zener voltage from the input voltage. Nov 15, 2017 at 16:15

Consider the case when load is open circuited. This the case when we have maximum current flow through the zener. Now we have to make sure that this current is below the absolute maximum current through the zener.

$$I= Pmax/Vz= 100mA$$

This current is limited by the series resistor R. So now there should be some minimum value for this Resistor, to make sure that it limits the current to 100 mA.

Now, Input Voltage can go upto $$12x125/100 = 15V$$

So our exterme condition is when $$Vin = Vmax$$

therefore R should be such that,

$$(Vmax-Vz)/R < 100 mA$$

i.e., R should be greater than 100 ohms. $$Rmin = 100 Ohms$$

• You can see that, when we open circuit the load, that transistor has no role here. Nov 15, 2017 at 16:16
• Except at max current Vz <> 5.7V. OP's assignment is b.s. in the first place, Nov 15, 2017 at 16:18
• Is that so ? Maybe ideally it is 5.7 V. We were taught to solve like this in classes. Nov 15, 2017 at 16:23
• @MITURAJ you seem to be right, the answer he gave us was 110 Ohms and 5,6V. But still, Trevor is right about the temps. I too think that this is calculated in ideal situations where we don't account for temperatures and other variables of the real world, which is a shame imo. Nov 15, 2017 at 16:27
• @MITURAJ Thanks for your input, it really brighten up this circuit for me. Nov 15, 2017 at 16:33

WOW. It's teachers like this that make the old adage...

"People who can, DO. People who can't, TEACH!"

In truth the answer to "Find the minimum acceptable value for R and the tension in the zener diode so that the Vout (Regulated) is equal to 5 V." is ...

"You did not give me enough information to calculate that."

You have no way to tell from this information what the zener current needs to be so it produces the 5.6V voltage you need to get 5V at the output.

You can NOT calculate that current from the wattage of the ZENER. That value is just how far you can over-stress it before it melts. At that current the ZENER will not be giving you anywhere close to 5.6V even when cold, and it will not stay cold for long at max current.

EDIT

The answer given is 100R... lets look at that.

At 12 + 25% Rail and the diode at 5.6V that's nominally 526.4mW on the diode, so you are already out of spec.

For a typical 5.6V 500mW zener 1N5232, the junction will be close to 175C and Vz will 5.7% higher at 5.92V...

The spec for said diode calls for 20mA to regulate at 5.6V, not 100mA.

Even with that number though, the output will only be at 5V under a very specific set of conditions. That is, almost never.

• The answer he gave to us is, 110 Ω and 5,6 V. I think you're right about that, considering the temps, it would not regulate well or at all. But i guess, it's the only way to arrive at those answer he gave us. Nov 15, 2017 at 16:21
• @marquesini sometimes, the question and answer given are as much about making the student think as it is going through the mechanics of it. If this is for a hand in assignment, adding the information I have highlighted, and showing you understand the question better than it was written, is to your credit. Nov 15, 2017 at 17:29