The discussion focuses on the delta-star conversion formula for capacitors, specifically how to find equivalent capacitance using this method. Participants highlight the importance of treating capacitors as impedances, using the formula ##\displaystyle \frac{1}{j\omega C}## to facilitate the conversion. The quick approach involves applying the delta-star transformation to the impedances and then converting back to capacitance, while the slower method relies on first principles. Key insights include the cancellation of frequency (ω) during calculations to simplify the process.
PREREQUISITESElectrical engineering students, circuit designers, and professionals working with capacitive networks who need to understand delta-star conversions for capacitors.
Curious3141 said:The slow way to do it is from first principles.
The quick way is to use the AC impedance of a capacitor, which is ##\displaystyle \frac{1}{j\omega C}##, which can be treated like a resistance, then apply the delta-star conversion formula to it and see what you end up with. Remember to convert the final impedance you get back to a capacitance by reversing the formula.
Looks like it's just a bit of algebra. Logically, you know that ω should ultimately play no role in the capacitance values you obtain, so it should cancel out along the way. Might as well just eliminate it from the start (or choose a convenient working frequency such as ω = 1). That may make things less cluttered looking.Greg Arnald said:there for if capacitors.. 1/ωCa=(1/ωC2*1/ωC3)/(1/ωC1+1/ωC2+1/ωC3). (??)
How do I convert this back to capacitance so I just have Ca=...?