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My question is with regard to establishing regulation using values taken off the characteristic curve. I have \$I_{kn}\$ = 1.8mA and \$V_z\$ = -8.2V. How can I determine the minimum input voltage for regulation to be established?

schematic

Do I have to calculate \$R_z\$? I am not sure what I need to calculate in order to figure this out.

Thanks.

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You want to avoid operating at Izk. That is the point where breakdown begins and there is noticeable change. A good place to operate at is the Izt (zener test current) which is usually provided in the datasheet.

Anyways...

This problem is going to depend on what you current limiting resistor is. If we assume you are operating at Izk (no load) then you first need to figure out what value resistor you are going to be using. If we assume 0.25W resistor, then

$$ P_{resistor} > R_{max}*I_{zk}^{2} $$ $$ R_{max} < 77.16k $$

In this case, it doesn't matter a whole lot because the resistance is just high. But its a good check to do !

Now that we have that, we can just plug in the values

$$ I_{zk} = \frac {V_{in} - V_{z} } {R}$$

If you plug in a high value of R ( R closer to R_max, you'll find that Vin tends to be quite high and if you use a low value R, then Vin tends to be close to Vz.

However this will probably only apply to the no load configuration. As soon as you throw a load on, there will be less current going into the zener. This is also why I suggested you avoid working at Izk, because if you are at boundary between reverse bias and breakdown ( a zener is only useful when its in breakdown), and you throw a load, you can put your zener back into reverse bias region.

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  • \$\begingroup\$ I'm sorry, I've taken a great tip from your answer, but I don't see the answer to the actual question: how to calculate the minimal voltage at which stabilization is achieved? \$\endgroup\$ – Violet Giraffe Feb 10 '16 at 18:22
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Well you've at least got 1.8 mA across R1, even if the load (not shown) is infinite.

Try sticking some load resistors on the output.
(then you've got look on the spec sheet and see what happens when I-zener decreases.)

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