Calculating Minimum Power Source for Zener Diode Shunt Regulator

[dimpledur]

Homework Statement

A zener diode D1 is specified to have Vz=3.8V and a knee current of 100 microamps. It is used as a shunt regulator where the minimum load resistance is 6.2k. What is the minimum power source that ensures that the shunt regulator remains regulated?

Homework Equations

Vz=(Vzo)+(Iz)(Rz)

The Attempt at a Solution

I have spent the last hour trying to solve this one, but regardless of how I approached it I could not determine what Vz0 is. If a diode is spezified at Vz=3.8V, and the current its specified at is not given, do we assume this is the knee voltage, or what?

 

[rude man]

Homework Statement

A zener diode D1 is specified to have Vz=3.8V and a knee current of 100 microamps. It is used as a shunt regulator where the minimum load resistance is 6.2k. What is the minimum power source that ensures that the shunt regulator remains regulated?

Homework Equations

Vz=(Vzo)+(Iz)(Rz)

The Attempt at a Solution

I have spent the last hour trying to solve this one, but regardless of how I approached it I could not determine what Vz0 is. If a diode is spezified at Vz=3.8V, and the current its specified at is not given, do we assume this is the knee voltage, or what?

As usual in these device modeling situations, I don't know what model you were given for the zener. Was it really your above equation? Where's the knee current appear in your equation? Vz is at what current level?

 

[berkeman]

Homework Statement

A zener diode D1 is specified to have Vz=3.8V and a knee current of 100 microamps. It is used as a shunt regulator where the minimum load resistance is 6.2k. What is the minimum power source that ensures that the shunt regulator remains regulated?

Homework Equations

Vz=(Vzo)+(Iz)(Rz)

The Attempt at a Solution

I have spent the last hour trying to solve this one, but regardless of how I approached it I could not determine what Vz0 is. If a diode is spezified at Vz=3.8V, and the current its specified at is not given, do we assume this is the knee voltage, or what?

Unless your textbook is specifying something different, that Zener voltage you are given would be at the test current of 100uA. That's generally how Zener diodes are specified:

http://www.google.com/url?q=http://www.diodes.com/datasheets/ds18007.pdf&sa=U&ei=FqigTuu_O43TiAKui71J&ved=0CCIQFjAI&usg=AFQjCNHYCwT2NkxMH7wsIWLUi4UvskjESQ

So you know that the Zener voltage will be 3.8V at 100uA, so what do you need to set Vs at to get at least that minimum Zener current?

 

[dimpledur]

@rude_man, there is no model number. That equation I provided is the equation provided by my textbook. Also, the question is word for word from a midterm that my professor gave us from last year to study. There's no additionally information.

@Berkeman, normally when Vz is specified at that current, it specifically states "Vz=3.8V at a current Iz=100uA". Often times these are just coordinates and you have to determine what the intercept is actually via the equation I provided.

 

[dimpledur]

Anyways, if the question is indeed as you stated, then I think it is rather simple.

The current going through the zener diode will remain at 100uA, and the voltage across it and the load resistor will be 3.8V. Thus I can determine the current through the load resistor as follows,

i=(3.8V)/(6200 ohms)

I can then take this result to determine Vs as follows,

Vs-(i+100uA)(1000 ohms)=3.8

and after carrying out the calculations Vs must be greater or equal to 4.513 V.

If it were lower, it would not provide sufficient current to the zener to provide 3.8V across the resitor.

Hows that?

 

[berkeman]

Anyways, if the question is indeed as you stated, then I think it is rather simple.

The current going through the zener diode will remain at 100uA, and the voltage across it and the load resistor will be 3.8V. Thus I can determine the current through the load resistor as follows,

i=(3.8V)/(6200 ohms)

I can then take this result to determine Vs as follows,

Vs-(i+100uA)(1000 ohms)=3.8

and after carrying out the calculations Vs must be greater or equal to 4.513 V.

If it were lower, it would not provide sufficient current to the zener to provide 3.8V across the resitor.

Hows that?

That's how I would interpret it. Is there a way to check the answer?

 

[dimpledur]

Unfortunately not. He posted the exam for students to practice, but with no solutions. Which is essentially useless, hence why I came here in hopes someone could perhaps ensure that I was interpreting his wording correctly, as it is not the same used in my textbook.

 

[berkeman]

Unfortunately not. He posted the exam for students to practice, but with no solutions. Which is essentially useless, hence why I came here in hopes someone could perhaps ensure that I was interpreting his wording correctly, as it is not the same used in my textbook.

Does he have office hours? It's reasonable for you to run your solution past him, and ask about the terminology differences...

 

[dimpledur]

Cooincidentally he is out of town until next week. He posted the midterm examination just before he left. He has a sub in for us tomorrow when we write out exam.

 

[rude man]

Anyways, if the question is indeed as you stated, then I think it is rather simple.

The current going through the zener diode will remain at 100uA, and the voltage across it and the load resistor will be 3.8V. Thus I can determine the current through the load resistor as follows,

i=(3.8V)/(6200 ohms)

I can then take this result to determine Vs as follows,

Vs-(i+100uA)(1000 ohms)=3.8

and after carrying out the calculations Vs must be greater or equal to 4.513 V.

If it were lower, it would not provide sufficient current to the zener to provide 3.8V across the resitor.

Hows that?

My final potshot is that zeners are not typically rated at their knee current. "Knee current" is in fact not a typical zener spec at all. The term instead implies an ideal zener model with i-V charateristic such that i = 0, Vz < Vz0, and i = unbounded, Vz >= Vz0. Which is why I wondered about the model. SOMEONE must have given dimpleur the equation Vz = Vz0 + izRz, then they would surely also have given Rz in a problem set, assuming Vz0 = Vz(i=100uA).

 

[dimpledur]

That formula is in my textbook. It is NOT provided with the question, nor is the incremental resistance. ^^^^^^^^^^^ that is the screen shot of the question if you have any doubts.

 

[rude man]

Yeh, but texdtbooks have text as well as problems. What did the text say about zeners?

 

[sandy.bridge]

The texbook always provides the incremental resistance. For example, "A 9.1 V zener diode exhibits its nominal voltage at a test current of 28 mA. At this current the incremental resistance os specified at 5 -ohm...". From this point we would normally calculate Vzo, which is the point where the line intersects the x-axis, and is usually the "knee" voltage.

Additionally, the textbook always converts the zener diode into a dc voltage source and a resistor rz. The value of the the voltage source is determined from Vz=Vzo+(rz)(Iz), and is equal to Vzo.

I don't see how its possible to use this formula to model the zener in this way. The question on the midterm is poorly worded as it doesn't specify that it is 3.8 V AT 100uA...

 

[rude man]

I agree. What they should have done is specified Vz at 100 uA, then everything else would not have mattered.

 

[sandy.bridge]

Hmm. Hopefully I don't get a question like this, although I most certainly am expecting a question like this considering he wouldn't post solutions... idk what ill do hahaha

 

[rude man]

Hmm. Hopefully I don't get a question like this, although I most certainly am expecting a question like this considering he wouldn't post solutions... idk what ill do hahaha

Just assume Vz = Vz0 @ whatever current he cites.. And have another beer.

 

[sandy.bridge]

Alright, thanks for the help! If I do run into this problem or one similar during the exam, would it be logical to get up and ask the TA what their take on it was?

 

[rude man]

Certainly. He should know that zeners are always modeled in circuit analysis, & that those models should be clearly delineated before posing problems to students. Furthermore, no zener model is particularly accurate in the first place. For example, low-voltage zeners like around 3.3V look more like 4 or 5 regular diodes in series, with very weak knees (low di/dV and d^2i/dV^2 on an i-V plot). Higher-voltage ones, like around 15 or 20V, have much sharper knees. A voltage source in series with a resistor is actually a poor model. It falls apart totally at low currents, obviously. Zeners are not batteries! Zeners should, and are, specified typically at a current so as to give a power dissipation of around 30-50 mW, i.e. P = i*Vz.

 

[dimpledur]

Just looked at another question off the midterm. I think it's safe to say that he is assuming Vz=Vzo. I guess he's not too worried about accuracey. The other question I saw stated the following: Assume ideal op amps are used. Using a zener diode with a breakdown voltage of 5.6 V, design the circuit to produce an output voltage of 10 V. Assume the input voltage is 12 V and the zener diode current is 1 mA.

The other question just isn't very clear with his english...

 

[rude man]

Here we go again. The question again is, what is Vz at 1 mA? Your guess is as good as mine.

The rest of the problem should be trivial, just an exercise in setting up the correct op amp gain ...