ELEC1103_Fundamentals Of Elec And Electronic Engineering_2014 Semester 1_Ch4-nodal.pdfVIP

ELEC1103 136 ELEC1103 – Semester 1 Chapter 4. Nodal Analysis Dr. Craig Jin 26 March 2012 ELEC1103 137 PLANAR CIRCUITS Ch4. I. Circuit Definitions – Planar Circuit ? Planar Circuit: A planar circuit is a circuit that can be drawn on a plane with no crossing branches. Is the circuit below planar ? Yes. Move R7 outside. ELEC1103 138 PLANAR CIRCUITS Ch4. I. Circuit Definitions – Planar Circuit ? Planar Circuit: A planar circuit is a circuit that can be drawn on a plane with no crossing branches. Is the circuit below planar ? ELEC1103 139 PLANAR CIRCUITS Ch4. I. Circuit Definitions – Planar Circuit ? Planar Circuit: A planar circuit is a circuit that can be drawn on a plane with no crossing branches. Is the circuit below planar ? R10 R8 No way to uncross R7 therefore not planar. X X ELEC1103 140 NODES, LOOPS, AND BRANCHES Ch4. I. Circuit Definitions. Recall: Nodes, Loops, and Branches ? An essential node is a node where three or more circuit elements join. ? An essential branch is a branch path connecting two essential nodes. ? A network with bE branches, nE nodes, and L independent loops will satisfy the fundamental theorem of network topology: ? bE = L + nE - 1 How many essential branches, essential nodes, loops ? 2 Essential Nodes 3 Loops 4 Essential Branches 4 = 3 + 2 - 1 Node 3 is not an essential node. ELEC1103 141 TECHNIQUES OF CIRCUIT ANALYSIS Ch4. II. Circuit Analysis Techniques – Nodal Analysis and Mesh Analysis ? There are two primary systematic techniques for circuit analysis: (1) Node-Voltage Analysis and (2) Mesh-Current Analysis. ? Nodal analysis can solve both planar and non-planar circuits. Mesh analysis (in its standard form) can only solve planar circuits. How many equations are required to fully determine or specify a circuit ? Topology tells us that: bE = nE + L - 1. We need one equation for each independent loop. In other words, we require L = bE - nE +1 independent eq