Zero Crossing Detector: AoE 3rd Edition Exercise

[fatalelieberi]

Hi,

I stumbled upon this exercise in Art of Electronics 3rd Ed in which I have to design a zero crossing detector using several comparators to make sure it triggers exactly at 0V. It's Exercise 4.25:



Assuming the solution circuit is based on an example in the book as shown here:



I designed this circuit to achieve the goal from the exercise:



The concept for this design is when the R4 is connected, the circuit will trigger when the input rising to 0V. But, if R4 is unconnected, it will trigger when the input is falling to 0V. So, based on this behavior, I put a PNP switch to connect and disconnect R4 from the circuit. The PNP is driven by another comparator that turns it on when the input is rising to 50mV and turns it off when the input is falling to -50mV. In my opinion, it actually works as intended with about 10mV miss from the target of 0V. However, I have to remove the capacitors to achieve the goal. Also, there are some redundant components which I think can be reduced more but I don't know how to do it.

What do you guys think? Is there a better solution for it?