I0+I1+I2=0,! Notice the directions of the currents !
{I0=V0−VXR0 I1=V1−VXR1 I2=V2−VXR2
V0−VXR0+V1−VXR1+V2−VXR2=0
V0R1R2−VXR1R2+V1R0R2−VXR0R2+V2R0R1−VXR0R1R0R1R2=0|×R0R1R2
V0R1R2+V1R0R2+V2R0R1R1R2+R0R2+R0R1=VX
Note: the VX is the unmarked voltage point on the schematic !
It is easy to see the calculation scheme easily adjusts for N voltages all connecting to the single VX
VXN=N−1∑i=0ViN−1∏k=0RkRiN−1∑i=0N−1∏k=0RkRi
thus BWD chek ::
for N=2 :
VX=V1R0+V0R1R0+R1
incase of the V0=0 it reduces to a trivial 2 resistor divider formula :
VX=V1R0R0+R1
Simulation example/chk. for N=4 :
[Eop]
{I0=V0−VXR0 I1=V1−VXR1 I2=V2−VXR2
V0−VXR0+V1−VXR1+V2−VXR2=0
V0R1R2−VXR1R2+V1R0R2−VXR0R2+V2R0R1−VXR0R1R0R1R2=0|×R0R1R2
V0R1R2+V1R0R2+V2R0R1R1R2+R0R2+R0R1=VX
Note: the VX is the unmarked voltage point on the schematic !
It is easy to see the calculation scheme easily adjusts for N voltages all connecting to the single VX
VXN=N−1∑i=0ViN−1∏k=0RkRiN−1∑i=0N−1∏k=0RkRi
thus BWD chek ::
for N=2 :
VX=V1R0+V0R1R0+R1
incase of the V0=0 it reduces to a trivial 2 resistor divider formula :
VX=V1R0R0+R1
Simulation example/chk. for N=4 :
[Eop]
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