Y-Delta conversion for Capacitors

Remember how capacitors combined differently in series and parallel than do resistors?

What you can do is convert all your capacitances to their equivalent impedance, then use those formulae. Impedances mix and match like resistances.

 

[tex]Zc = 1/(j\omega C[/tex])

[tex]\omega[/tex] is the operating frequency. The result is in Ohms, and will be an imaginary value.

Don't panic! You don't need to know the frequency for the math to work out; it's a constant for the given Y to Delta situation. If you do the algebra, a pretty simple result obtains. If the resistor version is:

Ra = (R1*R2 + R2*R3 + R3*R1)/R2
Rb = (R1*R2 + R2*R3 + R3*R1)/R3
Rc = (R1*R2 + R2*R3 + R3*R1)/R1

Then the capacitor version looks like:

Ca = C1*C3/(C1 + C2 + C3)
Cb = C1*C2/(C1 + C2 + C3)
Cc = C2*C3/(C1 + C2 + C3)

 

Right.

You're welcome.

 

Sure. Just substitute the appropriate capacitor impedances into the formulas for resistance, stir and serve. Note that a capacitor impedance is of the form [itex] 1/(j \omega C) [/itex].



So for example, given that for resistors
[tex] R_1 = \frac{R_a R_b}{R_a + R_b + R_c} [/tex]
then
[tex] \frac{1}{C_1} = \frac{C_c}{C_b C_c + C_a C_c + C_a C_b} [/tex]

and so on.

EDIT: Fixed up the expression. Should have been 1/C1 on the LHS.