Electronic – zero cross detector missing zero cross

Why not use an optocoupler? Vishay's SFH6206 has two LEDs in anti-parallel, so it works over the full cycle of the mains voltage. If the input voltage is high enough the output transistor is switched on, and the collector is at a low level. Around the zero crossing, however, the input voltage is too low to activate the output transistor and its collector will be pulled high. So you get a positive pulse at every zero crossing.

The most important parameter for an optocoupler must be its CTR or Current Transfer Ratio, which gives you the ratio between output current and input current. You can compare it with the \$H_{FE}\$ of a common BJT. But while \$H_{FE}\$ for a small signal transistor is often higher than 100, CTR is low. So low that it's expressed in %, like 20%. That's not 20, that's 0.2.
A CTR of 0.2 means that you have to drive the input LED(s) with 1mA to get a mere 200\$\mu\$A out. Usually that's not a problem, since the output is often only used to get a logic level, which will connect to a high impedance input. In that case a high value pull-up resistor can be used, like > 27k\$\Omega\$ in a 5V system. Then the 200\$\mu\$A is sufficient to drive the output low.

Detailed calculations can be found here.

I have tested this that and found that there are something unstable over it. It develops a form of "noise" which disturb the signal. This takes place between every 30 seconds to 1 minute. (Perhaps my setup?)

This is a simple one

Opdate:

About the message "Simulation is not running in real time" here, try the following.

Select 'Set Animation Option' from the menu system and simply push the 'SPICE Options button'. Try to put [ABSTOL] down to, for example 1e-08 and see if it helped.

If it has not helped, try to go further down or if it helped, try to go one up by one until the error recurs, then go one down.