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Every one may be familiar with zener diode function in positive voltages but I don't know how to use them in negative voltages.

For example in the schematic below, if we use a 10v zener and the input voltage is around 12v, we can expect a rather 10v output, but if we reverse it for a negative voltage as in schematic number 2 ( ground is now a positive voltage compared to -12v), all we get is power dissipation ( because it tries to bring down the ground voltage and as it is impossible, the diode just starts getting hot). What is the correct design for using a zener for negative voltages?

1- Positive Voltage:

Positive Volatge:

2- Negative Voltage:

enter image description here

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If you use your first diagram, substitute -12V for the +12V source and turn the Zener diode around the other way, you'll get a regulated -10V at the output node.

With your second diagram, the output node will be regulated to 10V above the -12V source, for a net value of -2V, which is probably not what you intended.

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To amplify Dave Tweed's correct answer, note that the second diagram can be redrawn as:

schematic

simulate this circuit – Schematic created using CircuitLab

But, you want the output voltage to be taken from across the zener diode (after all, the voltage across the diode is what is approximately constant!) and not the resistor.

The correct circuit is, as Dave Tweed remarks:

schematic

simulate this circuit

Now, the output voltage is across the zener diode and is equal to \$ -V_Z \$

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