Finding output values in a circuit with a zener diode in parallel with a resistor

Question

Find Vout for all possible values of Vin. In this problem, Vf is the forward voltage drop across the diode and Vr is the reverse voltage drop across the diode. (You must break the problem into 3 ranges)

^{simulate this circuit – Schematic created using CircuitLab}

I know the ranges are when Vin is positively large enough so that there is a voltage drop across R1=Vf, when Vin is negatively large enough so that there is a voltage drop across R1=Vr, and when Vin is between these two ranges. How would you express Vout in terms of Vin and the resistor values?

Answer 1

The result is going to be a piecewise function. The basic idea with this sort of a problem is to write out an equation assuming the diode is in each operating mode (cutoff, forward bias, and reverse bias), figure out where the transitions between operation regions are in terms of Vin, then write a piecewise function that selects the proper equation under the proper conditions.