To be fair I was using googles AI Gemini app to find a way of achieving 3.4uF when no caps were available. The answer I got is below Quote!
Yes, you can use two 6.8µF 450Vac capacitors connected in series to replace a single 3.4µF 650Vac capacitor for a 131W SOX lamp, provided they are non-polarized motor-run type capacitors suitable for AC use. The series connection will result in the correct capacitance and a sufficient voltage rating.
Technical Details Connecting capacitors in series is a standard method to achieve a lower total capacitance and a higher combined voltage rating.
Capacitance Calculation (Series): For two identical capacitors in series, the total capacitance is half the value of a single capacitor
(C_total = C / N, where N=2).
6.8µF / 2 = 3.4µF
This precisely matches the required 3.4µF capacitance for the SOX lamp circuit.
Voltage Rating Calculation (Series): When capacitors are connected in series, "the voltage rating increases." The total voltage rating is the sum of the individual ratings (assuming identical capacitors and proper voltage balancing).
450Vac + 450Vac = 900Vac
This 900Vac combined rating is significantly higher than the original 650Vac requirement, providing a good safety margin for the lamp's inductive circuit.
Important Considerations
Capacitor Type: Ensure the 6.8µF capacitors are AC-rated (e.g., motor-run or power factor correction capacitors, likely made of film) and not general-purpose electrolytic DC capacitors. The circuit uses AC power, and DC capacitors used in AC circuits can fail catastrophically.
Voltage Balancing: In practice, using a high-value balancing resistor in parallel with each capacitor is recommended to ensure the voltage divides equally between the two, compensating for slight manufacturing tolerances or leakage current differences.
Physical Fit: Verify that the two capacitors will physically fit within the ballast enclosure or mounting area of the existing single capacitor.
end quote.
I always try to be as helpful as I can and I think the ultimate solution to our conundrum might be here:
https://capacitorfilm.en.made-in-china.com/product/LmPYuRgObCVy/China-Cbb65-80UF-Motor-Running-Capacitor-Start-Capacitor-for-Air-Conditioner-AC-660V-540V-450V-440V-370V-250V-50-60Hz-5-.html?pv_id=1jfo65loa13c&faw_id=1jfo65qv59a2&bv_id=1jfo6g4vne51&pbv_id=1jfo65g4p738This seller offers caps in low volumes and there appears to be a range of voltages up to 660v and a range of capacitance. All we need do is pop the question and see what happens.