Electronics > Beginners
Capacitive Reactance, Inductive Reactance, Power Factor, Switching Hz
TheDood:
Capacitive reactance = 1/(2π·Hz·F)
Inductive reactance = 2π·Hz·H
If you've a series C L cct, and both the capactive reactance and the inductive reactance were equal, does your ideal cct have a PF of 1?
If you've a capacitive dropper cct, and you're bypassing the inductor at a certain Hz, can you effectively manipulate your inductive reactance to match the capacitive reactance by changing your Hz at which you bypass? The series X1 cap is at a constant 60Hz from the AC side, but the coil Hz can be manipulated by the frequency of your bypass period?
2.2μF X1 cap @ 60Hz = 1205.72Ω
0.1H L @ X = 1205.72Ω
X = 1,918.96Hz
If you bypassed @ ~1919Hz, would you correct your PF?
Thanks
TheDood:
Nevermind.
MagicSmoker:
--- Quote from: TheDood on December 11, 2019, 05:55:51 am ---...
If you've a series C L cct, and both the capactive reactance and the inductive reactance were equal, does your ideal cct have a PF of 1? ...
--- End quote ---
No, PF would be zero if the components are ideal (no resistive losses) because the lagging PF of the inductor is exactly cancelled by the leading PF of the capacitor at resonance (ie - when XC and XL are equal).
TheDood:
--- Quote from: MagicSmoker on December 11, 2019, 10:58:19 am ---
--- Quote from: TheDood on December 11, 2019, 05:55:51 am ---...
If you've a series C L cct, and both the capactive reactance and the inductive reactance were equal, does your ideal cct have a PF of 1? ...
--- End quote ---
No, PF would be zero if the components are ideal (no resistive losses) because the lagging PF of the inductor is exactly cancelled by the leading PF of the capacitor at resonance (ie - when XC and XL are equal).
--- End quote ---
Thanks MagicSmoker,
Is that what we want? No lead, no lag? If a capacitive dropper creates leading, an appropriately sized coil would cancel and correct PF to what is desired? Im confused on what is wanted because I thought .95 was the threshold for compliance?
Can a UC385, or an MC33262 be used to correct PF of a capacitive dropper?
https://www.onsemi.com/pub/Collateral/AND8179-D.PDF
https://www.ti.com/lit/ds/symlink/uc3854.pdf
T3sl4co1l:
Well, yes and no, depends where you measure. Assuming there's some resistance in that circuit (because if not, the circuit is meaningless!), the PF as seen by the source will go to 1.
If there's no resistance, then at resonance, reactive power goes to infinity while real power is still zero, so you have a \$\frac{0}{\infty}\$ form. Since it's symmetrical around resonance, the limits match and the result is zero (as noted above).
You cannot synthesize a reactance from behind a FWB though, and you'll also have a hard time doing so in front of the FWB by using lossy devices (transistors can only switch or dissipate power, they cannot produce it). Note the definition of reactance is that it alternately consumes and returns power to the circuit!
This does mean you can synthesize a reactance by using, say, a nice compact capacitor, a switching converter, and a controller to set the voltage and current accordingly (within some limited frequency and energy range, since the capacitance stores energy inversely to the desired inductance; this is quite doable at a fixed mains frequency). But that's a rather worse solution than what would satisfy your underlying problem. :)
(Such solutions are actually useful, though -- when absolutely required. Such a device can be used to effectively multiply a capacitor, allowing one to implement a filter that would otherwise require, say, a lot of bulky electrolytics. The Google Little Box contest winner (2014) used such an approach. Similarly, industrial equipment can be power-factor-corrected by bolting on an inverter and controlling its current draw inversely of the attached load, thus using its supply (DC link) capacitor as PFC storage.)
Tim
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