05 February, 2007

Supernode

A "supernode" is assumed sometimes in circuit theory to solve a circuit, whereby a voltage source on a wire is viewed as a point source voltage in relation to other point voltages located at various nodes in the circuit, relative to a ground node assigned a zero charge.

A supernode can also refer to Nodal analysis which is a circuit analysis technique used in Electrical Engieering. In general engineering circuit analysis, supernode is that in which voltage source is in between the two nodes.
Example :
The green shading shows the supernode. The sum of the currents leaving the supernode must sum to zero - for the same reason that the sum of the currents leaving a node sum to zero - conservation of charge!
Write the KCL equations for the entire super node:
Ix + Iy + Iz = 0.
But Ix = (Vy -Vx)/Rx , Iy = Vy / Ry , Iz = Vz / Rz= (Vy - V2)/ Rz
And the KCL equation for the supernode becomes:
(Vy -Vx)/Rx + Vy / Ry + (Vy - V2)/ Rz = 0.

And, for this circuit that is the one independent KCL equation that can be written (unless you choose to keep Vz as your unknown, but there is still only one equation.) That means writing this in the standard form, we would have:
(1/Rx + 1 / Ry + 1/ Rz)Vy - Vx/Rx = V2/ Rz
The coefficient of Vy is the sum of the conductances connected to the supernode, the source appears on the right hand side, and the negative reciprocal of the shared resistor shows up just where we might expect it.
For more information on this topic visit the below sites :

1 comment:

David Way said...

Nicely done! Thanks for the help!

You might want to post this to Wikipedia, as there isn't much of a page on supernodes there!