nodicity - NODICITY One of the important ways that physical...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
NODICITY One of the important ways that physical system behavior differs between domains is the way elements may be connected. Electric circuit elements may be connected in series or in parallel — networks of arbitrary structure may be assembled This not true of all domains Electric circuit elements have a special property called nodicity Mod. Sim. Dyn. Sys. Nodicity page 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
N ODICITY Nodicity means that a network element (or sub- network) has behavior analogous to a “node” in an electric circuit. Consider a “delta” network of resistors Assuming linear inductors, the relation between currents and voltages may be written as i 1 i 2 i 3 = G 1 +G 2 –G 2 –G 1 –G 2 G 2 +G 3 –G 3 –G 1 –G 3 G 1 +G 3 e 1 e 2 e 3 where G i is conductance i i = G i e i 1 G i = R i Note that this conductance matrix is singular — the sum down each column is zero. i.e., the sum of currents flowing into the network is zero i 1 + i 2 + i 3 = 0 Mod. Sim. Dyn. Sys. Nodicity page 2
Background image of page 2
As a result, the three constitutive equations describing the currents may be re-arranged as follows i 1 i 2 = G 1 +G 2 –G 2 –G 2 G 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 9

nodicity - NODICITY One of the important ways that physical...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online