How to find the range of load resistance in voltage ragulator circuit
Answers
Answer:
Explanation:
Look over the following two schematic conditions:
schematic
simulate this circuit – Schematic created using CircuitLab
Your value of RiRi must be small enough to support a load current of 100mA100mA (which implies a load of 12V100mA=120Ω12V100mA=120Ω.) You also have to support the minimum needed current through D1D1 at this time, as well. For a typical zener like this, that value can span over some range. But for good regulation, you probably want Iz≥10mAIz≥10mA. And RiRi must do all of this while the voltage supply is at its minimum value of 15V15V. So:
Ri≤15V−12V100mA+10mA≈27.27Ω
Ri≤15V−12V100mA+10mA≈27.27Ω
A standard value of 27Ω27Ω would do.
Note that I had to place this circuit at the extremes in order to make sure that RiRi was having to cope with the worst possible supply circumstance (minimum) it might experience when trying to deal with the worst case load circumstance (maximum.)
Now that we know that Ri=27ΩRi=27Ω, the second schematic allows us to change things up in order to compute the worst case power in RiRi (and in D1D1.) The power in RiRi will be the same, regardless of the load current. But I'm setting the load current to a minimum now, while setting the supply to its maximum, in order to see the worst case for D1D1 (whose power does depend on the load current.)
In this case, the current through RiRi is:
IRi=20V−12V27Ω≈300mA≈2.5W
IRi=20V−12V27Ω≈300mA≈2.5W
The power in RiRi is then about 27Ω⋅(300mA)227Ω⋅(300mA)2
Since only 20mA20mA of that is going through the load, the remainder, or 280mA280mA, is left to go through D1D1. So the power required by the zener diode is 12V⋅280mA≈3.4W12V⋅280mA≈3.4W.
That covers (a) and (b) pretty well.
Now the problem is about (c). Before I engage that issue, I want to say that the datasheet for the 1N4742A says that when using 21mA21mA, Rz=9ΩRz=9Ω. This would tend to mean that if someone is telling me that Rz=3ΩRz=3Ω, the value I used for the minimum Iz=10mAIz=10mA wasn't enough. It should be much higher. And this would tend to mean that I didn't compute RiRi correctly. However, your problem doesn't require this particular zener and so I can't debate or argue the facts, as given. The problem also didn't state a minimum zener current to use. So this allows me to keep my calculations and just move on.
Since the dynamic resistance of the zener is given as Rz=3ΩRz=3Ω, and since I can see that the dynamic change in IzIz, from minimum to maximum, is 300mA−10mA=290mA300mA−10mA=290mA, I can multiply these two to get 870mV870mV variation at the zener. Or, if I'm lucky with the zener, I may get 12V±440mV12V±440mV at the output over all design circumstances (excepting thermal drift and aging and part variation, which also don't seem to be part of the problem here, but would be in the case of a real circuit.)
But let's do this a different way. We can insert RzRz into the circuit:
schematic
simulate this circuit
Now, that's not an exact reality. I just picked an arbitrary 11.55V11.55V for the ideal zener value in order to make things work out to center on 12V12V at the output. The reality will be different. Worse, the dynamic range of current through the zener is a factor of 30! There is no possible way that Rz=3ΩRz=3Ω for such a dynamic range of current. It might be valid had I chosen a minimum Iz≥100mAIz≥100mA, perhaps. Which would have resulted in a different value for RiRi. But the problem doesn't care, so I don't care. Had it listed a specific part where I could examine a datasheet, a more accurate idea might have developed from here.