Understanding a regulator circuit with MOSFET and Zener-Diode

[Emin]

My professor used this circuit in a exam in 2016. This is a regulator with a zenerdiode D and a MOSFET. The transistor has a constant gate-source voltage equal to 4V. The voltage Vin = 24 V and we want the output voltage to be Vout = 19V when IL is constant equal to 1A.



My question is 1) What is the zenervoltage which gives the output voltage Vut = 19V. I know the solution is Vz = 15V. But what i dont understand is, why and how is it 15V?

2) Assume the current in zenerdiode is 5mA. Find R1.
- I know we have to use ohm's law here, which i did. But again, my professor used R1 = Vgs/5mA = 4V/5mA. Why did he use the gate-source voltage?

If anyone could help me to understand this, i would really appreciate it! Thank you.

 

[Harald Kapp]

I do sincerely hope thatthis is not your current assignment, that you ask for understanding only!?
Nevertheless I will not reveal the answer directly. Rather I will guide you to finding the answer(s) by yourself.

1) The answer to this question lies here:

The transistor has a constant gate-source voltage equal to 4V.

One has to assume that this is the threshold voltage. In a very simplified view, if the gate source voltage is less than 4 V, the MOSFET will be off. If the gate source voltage is higher than 4 V, the MOSFET will be gradually on. The higher the gate source voltage is, the lower is the drain-source resistance.
For the sake of simplicity assume that the zener diode is ideal, such that for a voltage less than Vz across the diode the current through the diode is 0 A. For any voltage higher than Vz, the current will increase exponentially. The current through the zeneer diode in turn will create a voltage drop across R1. This voltage is the gate source voltage controlling the MOSFET.
Now check the sum of branch voltages from source to gate and from gate to drain (via the zener diode). You should now immediately see the zener voltage required for a 19 V output voltage.

2) Look at how R1 is connected to the MOSFET. The voltage across R1 is equivalent to which voltage across the MOSFET?`

It may be easier to spot the required identities when you label S, G D on the MOSFET in the diagram and also draw lines or arrows with the repective lables on them for the various voltages in question.

 

[Emin]

I do sincerely hope thatthis is not your current assignment, that you ask for understanding only!?
Nevertheless I will not reveal the answer directly. Rather I will guide you to finding the answer(s) by yourself.

1) The answer to this question lies here:
One has to assume that this is the threshold voltage. In a very simplified view, if the gate source voltage is less than 4 V, the MOSFET will be off. If the gate source voltage is higher than 4 V, the MOSFET will be gradually on. The higher the gate source voltage is, the lower is the drain-source resistance.
For the sake of simplicity assume that the zener diode is ideal, such that for a voltage less than Vz across the diode the current through the diode is 0 A. For any voltage higher than Vz, the current will increase exponentially. The current through the zeneer diode in turn will create a voltage drop across R1. This voltage is the gate source voltage controlling the MOSFET.
Now check the sum of branch voltages from source to gate and from gate to drain (via the zener diode). You should now immediately see the zener voltage required for a 19 V output voltage.

2) Look at how R1 is connected to the MOSFET. The voltage across R1 is equivalent to which voltage across the MOSFET?`

It may be easier to spot the required identities when you label S, G D on the MOSFET in the diagram and also draw lines or arrows with the repective lables on them for the various voltages in question.

Thank you for the fast reply! This is not my homework or assignment. I am just doing old exams to learn and get ready for the upcoming exam in 2 months.

For 2) The reason the voltage across R1 is equivalent to gate-source is because top and bottom is connected to the mosfets gate and source, right?

Your answer helped me alot! Thank you!!

 

[(*steve*)]

For 2) The reason the voltage across R1 is equivalent to gate-source is because top and bottom is connected to the mosfets gate and source, right

No, it's due to feedback.

 

[Harald Kapp]

No, it's due to feedback.

Sorry Steve, but Emin is right. At this point no feedback has to be taken into account. Look again at the circuit in post #1.

 

[(*steve*)]

But there is feedback.

As the voltage across R1 increases, Q1 increases it's conductance causing R to drop more voltage, reducing the voltage across R1.

D is the reference. The voltage across R1 is compared to the threshold voltage of the MOSFET which acts as an error amplifier which effectively controls the regulating element (R).

 

[Harald Kapp]

No doubt there is feedback, that's what causes the regulation of the output voltage.
Concerning the relationship between the voltage across R1 and VGS the obvious answer is they are equal because R1 is connected from gate to source of the MOSFET.

 

[(*steve*)]

Aaah, I see.

I assumed that the Vgs which appears in the formula is a calculated value (possibly read from a graph).

I interpreted the question to be more along the lines of why does the circuit work and why does the voltage across R1 stabilize at some particular Vgs.

If the question is as simple as why is there voltage across R1 = Vgs (where Vgs is not a particular value) then yeah, because it's connected from gate to source is a pretty good reason

 

[Audioguru]

Maybe Emin does not know which pin is the drain or the source?

 

[Harald Kapp]

I don't think so. He's given the correct answer in post #3.

 

[fawad928]

You have to apply voltage divider rule here, The output voltage of zener is 15V and the overall output is 19V, so 19-15 = 4V left at gate voltage.

 

[Harald Kapp]

@fawad928 : You do realize that this is an old threat from 2017 and is not likely to be observed by anyone else?

 

[hevans1944]

@fawad928 : You do realize that this is an old threat from 2017 and is not likely to be observed by anyone else?

Well, I guess plenty of folks are likely to observe the thread now that newbie @fawad928 has gone and bumped it. Why do these old threads keep re-appearing so often? I've been "burnt" many times responding to an outdated thread, simply because i failed to notice the dates of the previous responses before adding in my two cents.

 

[Tha fios agaibh]

Old, doesn't mean it's not of value.

I for one, enjoyed its resurrection.

 

[Martaine2005]

I for TWO enjoyed it TOO. TO read old or new threads with math involved helps me heaps..
My ‘discombobulation’ will one day drop the ‘dis’ to ‘bobulation’.
I spend hours reading old posts while commuting on the train.

Martin