VS Resistor Tree
Resistor Tree:
Vs = 4V, Is = 1A
V1 = 4V
V2 = 3V
V3 = 2V
V4 = 1V
==> R1 = 1Ohm
==> R2 = 2Ohm (2 in parallel, equivalent resistance = 1Ohm)
==> R3 = 3Ohm (3 in parallel, equivalent resistance = 1Ohm)
==> R4 = 4Ohm (4 in parallel, equivalent resistance = 1Ohm)
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Reactance Tree:
==> Frequency = 1kHz, Vs = 4V*sqrt(2) = 5.65V [PEAK], Is = 1A*sqrt(2) = 1.41A [PEAK]
==> V1 = 4V*sqrt(2) = 5.65V [PEAK] = 4V [RMS]
==> V2 = 3V*sqrt(2) = 4.24V [PEAK] = 3V [RMS]
==> V3 = 2V*sqrt(2) = 2.83V [PEAK] = 2V [RMS]
==> V4 = 1V*sqrt(2) = 1.41V [PEAK] = 1V [RMS]
==> X1 = 1Ohm (@ frequency = 1kHz)
==> X2 = 2Ohm (@ frequency = 1kHz)
==> X3 = 3Ohm (@ frequency = 1kHz)
==> X4 = 4Ohm (@ frequency = 1kHz)
X = 1/(s*C) = 1/(j*w*C) = 1/(j*2*pi*f*C)
Using the above, once can calculate the capacitance required at a specific frequency, ex:
C1 = 1/(2*pi*1kHz*1Ohm) = 159uF
C2 = 1/(2*pi*1kHz*2Ohm) = 79.6uF
C3 = 1/(2*pi*1kHz*3Ohm) = 53.1uF
C4 = 1/(2*pi*1kHz*4Ohm) = 39.7uF
