It's the zener current which, except for the base current, is the same as the current in Rz. With a Darlington having a current gain of 3000, we can pretty safely neglect the base current in the face of almost any reasonable zener current.

 

It's the zener current which, except for the base current, is the same as the current in Rz. With a Darlington having a current gain of 3000, we can pretty safely neglect the base current in the face of almost any reasonable zener current.

huh, that's not good!

Obviously I haven't detected that Darlington transistor. We have just mentioned it in classes but we have not studied it. So, to me they were only 2 simple transistors!

What if the gain was not that high and we couldn't neglect the base current of T1? Could we use the same method to find Rz min and Rz max?

 

The circuit you analyzed in this thread uses a Darlington, which is nothing more than a particular arrangement of two BJT transistors. The effective current gain is the product of the individual gains.

Yes, if you had to take into account the base current you could use the same approach -- it is just a bit uglier, that's all.

 

The circuit you analyzed in this thread uses a Darlington, which is nothing more than a particular arrangement of two BJT transistors. The effective current gain is the product of the individual gains.

Yes, if you had to take into account the base current you could use the same approach -- it is just a bit uglier, that's all.

Ok, so using the equations we previously evaluated I got these 2 values for Rz min and Rz max.

Rz min = 160 Ω -> this should return the 90% of Iz MAX which I named Iz max (Iz max = 90% of Iz MAX, just to distinguish them)
Rz max = 540 Ω -> this should return the 10% of Iz MAX which I named Iz min...

Do you think this is correct?

I tried to do this:

Pz = Rz*Iz² = 160 Ω * (40.2 mA)² = 257 mW which goes over the Zener limit power dissipation given by the problem statement!

 

Ok, so using the equations we previously evaluated I got these 2 values for Rz min and Rz max.

Rz min = 160 Ω -> this should return the 90% of Iz MAX which I named Iz max (Iz max = 90% of Iz MAX, just to distinguish them)
Rz max = 540 Ω -> this should return the 10% of Iz MAX which I named Iz min...

Do you think this is correct?

Why are you using Iz max ? (In other words, why are you now setting a limit at 90 % of Iz MAX? Not saying that this is bad, but just wondering why the change. Also, is it a change that the grader will approve of).

If you are going to hedge the upper end of the range, you should probably hedge the lower end and use, perhaps, 20% of Iz MAX instead of 10% (since the claim seems to be that a zener current below 10% may not provide adequate regulation and so you want to stay noticeably away from that 10% level).

 

Well, the 10% and 90% were values that we learned last year from our teacher! So we've been using those values as the safe values to the zener to work properly!

What would you suggest to be a more reasonable limits? 20% and 85%???

 

Well, the 10% and 90% were values that we learned last year from our teacher! So we've been using those values as the safe values to the zener to work properly!

What would you suggest to be a more reasonable limits? 20% and 85%???

No, if the 10% and 90% values were given as safe values, then you are probably okay to use them. The question is whether they are meant as hard limits (meaning that your design should not exceed them even due to device tolerances) or if they were picked specifically as soft limits that you can target for the nominal case and live with them being exceeded slightly due to tolerances.

 

No, if the 10% and 90% values were given as safe values, then you are probably okay to use them. The question is whether they are meant as hard limits (meaning that your design should not exceed them even due to device tolerances) or if they were picked specifically as soft limits that you can target for the nominal case and live with them being exceeded slightly due to tolerances.

Well, as you know, these are just theoretical problems. They are not intended to be built on a breadboard or PCB or whatever. So, these discussions are recurrent. We accept the values given by the teacher and he also is not thinking about practical circuits. I know this is probably wrong, but it's the way teacher is lecturing... And we accept things as they are! That's why I see your point, and I know it is the correct one that works for theoretical problems and for practical problems, and that's why I asked what would be reasonable values for the limits!

We have been using the 10% and 90%. I'm ok with it and I also have in mind that this should be more carefully looked into when it comes to real life. I'm also ok if you tell me something like: "it's ok to use 20% and 80% or even 50% for more conservative circuits" as you already said...

So, I'm ok with either. After all it's just numbers when it comes to find the final values!

 

Yep -- the big thing is to understand what the numbers mean and what the considerations are. I have no problem with problems that live in an ideal world, particularly when illustrating basic concepts. At some point, real-world considerations need to start being factored in, but that doesn't have to happen immediately -- crawl, walk, run.

Bottom line is to use your understanding of your instructor as your guide. If they are going to mark you down for not following exactly their approach, the exactly follow their approach (while asking yourself what might be more reasonable, if necessary). If they are going to look favorably on a more practical and/or complete approach, then go for it.

 

I will remember this when I want to go breadboard anything...

For these problems, I'll stick to my teacher's notes and use the 10% and 90% values...

So, getting back to the problem, where were we??...

Do you want to re-answer my post #24???

Why am exceeding the given limit of the Zener's dissipation power??

 

PsySc0rpi0n said:
.....
Pz = Rz*Iz² = 160 Ω * (40.2 mA)² = 257 mW which goes over the Zener limit power dissipation given by the problem statement!
.....
You have calculated the power resistor. Power Zener is 40.2mA*5.6V=225.12mW

 

PsySc0rpi0n said:
.....
Pz = Rz*Iz² = 160 Ω * (40.2 mA)² = 257 mW which goes over the Zener limit power dissipation given by the problem statement!
.....
You have calculated the power resistor. Power Zener is 40.2mA*5.6V=225.12mW

Yes, I know about that but if I use P = R*I² = 160 Ω * (40.2 mA)² = 257mW which exceeds the power dissipation limit given by the problem statement!

 

I would not bother. I would take the value of the resistor
Rz=(Rzmax*Rzmin)^0.5=(180*540)^0.5=311.769
The closest nominal of 300 ohms.
Imax=(12-5.6)/300=21.33mA
Imin=(8-5.6)/300=8mA
P = Rz*I²=300*(21.33e-3)^2=136.5mW
Pzener< 21.33mA*5.6V=119.448mW

 

Ok, so using the equations we previously evaluated I got these 2 values for Rz min and Rz max.

Rz min = 160 Ω -> this should return the 90% of Iz MAX which I named Iz max (Iz max = 90% of Iz MAX, just to distinguish them)
Rz max = 540 Ω -> this should return the 10% of Iz MAX which I named Iz min...

Do you think this is correct?

I tried to do this:

Pz = Rz*Iz² = 160 Ω * (40.2 mA)² = 257 mW which goes over the Zener limit power dissipation given by the problem statement!

It would really help if you showed the calculation you did to get the 160 Ω and the 540 Ω, instead of making use guess or reverse engineer your work. If you show your work we can usually spot whether you are doing it right and, if not, where you are going wrong at first glance. But when you don't show your work, you force use to work the problem from scratch so that we can compare our answer to yours and, at the end of the day, all we can say is yes you are right or no you aren't. That's a lot of work to not be able to provide more feedback. Doesn't it seem reasonable that YOU should put forth the effort to make it easier for the people that you are asking free help from to provide more meaningful feedback?

So, in line with the information you provided, No, I don't think this is correct.

If you want to provide more detail about how you got these limiting values for Rz, I can provide more meaningful feedback on where and how you went wrong.

 

@WBahn , hope your festivities went all well... Hope Santa was generous to you and your beloved ones! Merry Christmas and Happy New Year!

Regarding the calcs, I just used your equation and the values for Vin_min and Vin_max...

had to change the 'tex' code by an image... It was not rendering properly!

 

PsySc0rpi0n said:
.....
Pz = Rz*Iz² = 160 Ω * (40.2 mA)² = 257 mW which goes over the Zener limit power dissipation given by the problem statement!
.....
You have calculated the power resistor. Power Zener is 40.2mA*5.6V=225.12mW

I missed this reply!! Sorry!

And you're correct, of course!

For the Zener I would have to find it's "internal" resistance to be able to calculate it using that R*I² expression!

 

Ok, so next I did:

(160 Ω + 540 Ω) / 2 = 350 Ω for an intermediate Rz value...

Then I re-calculated the current, yet ignoring Ib, for this resistor which turned out to be 18.29 mA. This results in a dissipated power on the zener of around 102.4 mW which looks just perfect, no???

 

When you show work, you should provide enough detail so that the reader can verify the approach without doing any calculations except to verify your results. For instance, in this case you use two different values for Iz, so you should show where those come from. Something like:

Iz_MAX = 250 mW / 5.6 V = 44.64 mA
Iz_min = 10% Iz_MAX = 4.464 mA
Iz_max = 90% Iz_MAX = 40.18 mA

Notice that I carry an extra sig fig on results that are going to be used as intermediate steps (I actually usually carry two extra).

159.3 Ω < Rz < 537.6 Ω

While a choice of 160 Ω for Rz_min satisfies this constraint, a choice of 540 Ω for Rz_max violates them.

So let's check the power and the Iz_min limits.

At max Vin and 160 Ω: Iz = (12 V - 5.6 V) / 160 Ω = 40 mA => Pz = Iz·Vz = 224 mW

At min Vin and 540 Ω: Iz = (8 V - 5.6 V) / 540 Ω = 4.44 mA = 9.96 % Iz_MAX. Is this acceptable? (in practice, the answer is likely yes, on an exam?)

Note that the Pz you calculated is the power for the resistor, not the diode. So what size resistor should you use if you use a 160 Ω Rz?

What further constraints would you have if your Rz needs to be a 1/4 W resistor that you don't want to exceed 50% of it's power rating and you need to use a standard 5% tolerance resistor (i.e., the E24 sequence)?

 

Ok, so next I did:

(160 Ω + 540 Ω) / 2 = 350 Ω for an intermediate Rz value...

Then I re-calculated the current, yet ignoring Ib, for this resistor which turned out to be 18.29 mA. This results in a dissipated power on the zener of around 102.4 mW which looks just perfect, no???

It's probably quite reasonable, except good luck finding a 350 Ω resistor. How much power is being dissipated in Rz? What wattage rating would you choose for this resistor?

Another option is to use the geometric mean of sqrt((160 Ω)(540 Ω) = 293.9 Ω => 300 Ω

Although the 5% code includes a 300 Ω resistor, most people prefer to use the E12 code (it minimizes the number of resistor values they must stock), which forces a choice between 270 Ω and 330 Ω. No driving reason to choose one over the other (based on the available specs). The smaller the value the better the regulation (in terms of variations due to load fluctuations) but the greater the power consumption. The larger the value the opposite is true. You might also need to look at what value nominally puts you the closest to the desired 5.6 V for the Zener voltage, which is something you would need the data sheet for the Zener diode to determine.

 

Well, so for the larger resistor I should use a lower value... I got that! A lower value will grant a larger current which means that it's larger than the minimum acceptable current for the zener to hold his working mode (zener mode).

Also I saw it later that the power that I have calculated was for the Rz and not for the zener. I mentioned it after I saw @Bordodynov 's post that I think I missed!

I'm not sure what is the answer for this question of yours:

So what size resistor should you use if you use a 160 Ω Rz?

But I presume that you mean that I need to choose a resistor capable of dissipating more than 1/4 W... Probably 1/2 W but I don't know if these resistors has a specific name or not!

What further constraints would you have if your Rz needs to be a 1/4 W resistor that you don't want to exceed 50% of it's power rating and you need to use a standard 5% tolerance resistor (i.e., the E24 sequence)?

I also don't know that E24 sequence... What constraints are you referring to? Like, what current should I have if I couldn't use 1/2 W resistors?