Hi,
let´s assume the capacitor is discharged to near zero voltage at zero cross.
* the mains voltage rises and current is flowing through the resistor.
* the same current is flowing through the capacitor and thus the voltage across the capacitor rises.
Assuming the capacitor is charging slowly...
* Then with rising mains voltage the voltage across the resistor rises
* the current through resistor and capacitor rises.
* the voltage_steep at the capacitor rises
* after the mains voltage peak (90°) the voltage drops and thus the current drops.
* While the voltage_steep decreases it is still positive, menas the voltage at the capacitor still rises (until the mains voltage drops below capacitor voltage.
* so there is a critical phase angle where it is impossible to tirgger the triac.
Some calculations:
Lets assume the diac triggers at 30V capacitor voltage (depends on diac VBO and triac gate volatge)
* 230V AC mains voltage means 325V peak voltage
* calculate critical phase angle: means when 230V sine voltage meets 30V: sin(phi) = 30V/325V --> phi = 5.29° symmetric: 180°-5.29° = 174,7°
(good, we are far away with the desired 120°)
* raw estimation of average mains voltage 0°, 30°, 60°, 90°, 120° => 0V, 162V, 281V, 325V, 281V => average about: 210V
* time for 120°: 360° = 20ms, --> 120° = 20ms/3 = 6.7ms
* average capacitor voltage dring 120°: 0V to 30V (but slowly rising at the end makes the average a bit higher that 15V.) Lets assume 17V.
***
Now I´ll take a 10nF capacitor. If the value is good or not, we will se later.
Calculate the average current that is needed to charge a 10nF capacitor from 0V to 30V within 6.7ms:
C = I * t / V => I = C * V / t = 10nF * 30V / 6.7ms = 44.8uA
calculating R: average voltage across R / I: (210V -17V) / 44.8uA = 4.3MOhm.
****
I just started a LTSpice simulation. (I recommend you to use it. It´s free)
It says 30V after 6ms,
and 34V at 120°
So my raw estimation was no too bad.
********
Result:
I´d choos a larger capacitor: maybe 10 times. Means 100nF.
Then the resistor needs to be 1/10 of the calculated value. = 430k
According reliabilty of the results:
I´d say we are very close, because the capacitor will start with a negative value, not at zero. Therefore it will take longer to reach 30V.
How much depends on the diac, and triac data.
But I think the values are a good point to start.
Klaus