Core-less transformer for Zero-crossing detection

Question

If possible, what are calculations and precautions involved in making a simple transformer without core? The only purpose of this transformer is to trigger an opto-coupler for zero-crossing detection of mains supply.

^{simulate this circuit – Schematic created using CircuitLab}

Answer 1

Since you said that it didn't need to be isolated, maybe something like this would work:

Output looks like this:

If you are on 120Vac, then change the 2.2k to ~1.1k.
Again, beware that the left hand side is not isolated from the mains.

Source: https://circuitdigest.com/electronic-circuits/zero-crossing-detector-circuit-diagram

UPDATE: Per the other answer, looks like some caveats are in order to the sourced circuit as given.

1. As pointed out, the power will be quite high in the 2.2kΩ resistor. Since the input waveform is NOT filtered with a capacitor The correct equation for the current is the average of the peak voltage divided by the resistance: $$ I=\frac{230V*\sqrt{2}*63\%}{2.2kΩ} = 94mA$$ The power is then $$P=94mA^2*2.2kΩ=19W$$ This is quite high for most circuits. It does work, but we can do much better.
   
   The opto coupler is well specified down below 1mA, so: $$ I=\frac{230V*\sqrt{2}*63\%}{200kΩ} = 1.0mA$$ The power is then $$P=1mA^2*200kΩ=214mW$$ Much better!

2. As for the time that the input voltage can cause an output pulse: The forward voltage drop at 1mA is 0.9V, so $$325V*sin(2\pi*50*t) \text{ where} -8.82us < t < +8.82us$$ Thus 17.6us is the time the pulse is output. Plenty of time to detect it! And will look very very similar to the wave form image above.

Answer 2

The above circuit by Aaron is NOT possible! The sine wave graph is also not correct!!

Reason, simple.

current at 2.2K resistor is 230*√2/2200 =0.1478496 A
Heat produced at 2.2K resistor is 0.1478496^2 * 2200 =48 WATT !!!

The graph of zero cross is not correct either, because diode generally drops 0.75v, at positive cycle of AC zero cross will occur at 0.75v earlier and negative cycle will zero cross 0.75v later.

The time can be calculated as (0.75/((230x√2x2x3.14x50)=7.34 micro second

Since it is about zero crossing, so it does not work. And it's devastating for a novice.