Yes, values need a change!
The original circuit from National shows some remarkable features: Negative voltages are suppressed by an offseting technique which works ratiometric, means where changes of supply voltages have no influence on precision, and where no voltage drop of diode is part of the cancellation network. This will result in a very stable zero cross detection. But it still needs two things to work properly: A comparator providing low and stable offset, which isn't realized with the LPC9xx comparator, probably, and low leaking diodes, which is no problem with higher supply voltages, but with +3V as in your case.
The inital offset can be adjusted, that's no problem. The question is, how much the offset will drift. And there's no data in the datasheet...

The problem with diodes is, that they must surely limit unsane voltages to the LPC9xx, but on the other hand must not leak with the potentials being applied, when the signal goes through zero. Otherwise the offseting circuit would be mistuned and phase errors would develop. So, I would recommend the use of two small signal Schottky diodes and a red LED, which is much steeper than a simple zener diode or standard diodes (two 1N4148, put in series to form a 1.4V "zener" diode):



The red LED is used here as ultra low leakage zener diode: At 1V less than 1nA flows through it!! A standard diode like 1N4148, on the other hand, lets a current of 1µA flow at 0.25V!

How to calibrate the circuit?
Connect the transformer to the input, as if you would want to run the circuit, but don't connect the primary side to mains. Now, carefully turn the 1k cermet trimmer (20 turns!) up to the moment, where the comparator flips. Now, turn the trimmer to opposite direction. Again, the comparator will flip. Finally, turn the trimmer just to the middle point of this range.

Two further comments:

1. Hysteresis with shown values is in the 10mV range. You might want to have a smaller hysteresis. Then, increase the feedback resistor to 10MOhm.

2. Schematic assumes that +3V is clean. If it's not, insert a RC low pass filter of about 100Ohm + 100nF, or so.

Prahlad, this circuit will work nicely. But precision suffers from unpredictable drift performance of LPC9xx. A better approach would use a precision comparator fed by a bipolar supply voltage (+-15V), but would cost much more components, of course.

Kai