Zener Diode Shunt Regulator

From the circuit given

                                                                 regulation = rz/(R +rz)

                                                                 regulation = - rz || R

Current in the network =(Vs - Vz0)/R +rz

                                                            Voltage across rz is

                                                                Vrz  =   Vz0  + (Vs - Vzo)rz/(R +rz) 

Thus Using Thevenin's Theorem

                                                Vo = Vz0 + (Vs - Vz0)rz/(R + rz) x    RL/(RL + R||rz)

                                                Thus R x (Sum Total current ) = Vsmin - Vzo - rzIzmin

                                Or

                                                  R = (Vsmin - Vz0 - rzIzmin)/(Izmin + ILmax)