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The basic problem with this circuit is that the load current (through R1) is much too high. The Zener stabiliser only works well in a circuit like this if the Zener current is comparable to the load current.

In your circuit, with your choice of resistors, the load current is 53mA ant the Zener current is 3nA. The Zener might just as well not be there.

These Zeners are characterised at about 5mA. If your load current is bigger than 5mA, the Zener will become increasingly ineffective, and it's the wrong circuit. You would be better just using a regulator.

If you change R2 to 100Ω, it will just work, but the ripple will still be significant.

You can estimate out the maximum value of Rs for it to work at all.

For the output voltage to be stabilised at ~7.5V, Rs should drop no more than 16 - 7.5 ~ 8.5V. At an output voltage 7.5V the load current current will be 75mA. If the Zener current is even just 5mA, then 80mA flows through R2, so it's value must be ~8.5/80m = 106.25Ω.

Realistically, there is also a minimum value for Rs. The maximum dissipation for the Zener is 350mW. Therefore, the maximum Zener current is 0.35/7.5 = 46.6mA. Therefore the current through Rs will be 75mA + 46.6mA ~122mA. So Rs(min) = 8.5/0.122 = 69.7Ω. I don't recommend operating any device at the maximum rating!

Note, that this resistor will dissipate ~1.04W.

You don't need LTspice to work out all this.

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