Chapter 3 Circuit Analysis Techniques: Node Voltage Mesh Current Norton & Thevanin Equivalents Max Power Transfer

As the circuits grow… …so must our methods Node Voltage – Use volts to determine KCL at each node Mesh Current – Use KVL on each current loop in circuit Both are suitable for software analysis Plug and chug, systems of equations

Planar vs Non-Planar Circuits Node Voltage does both Mesh Current can’t do non-planar

Some Definitions

Identify Components

Number of Unknowns The previous circuit has 4 essential nodes (ne = 4) 6 essential branches (be = 6) w/ 6 unknown i’s KCL: gives (ne-1) node equations 3 KVL: gives (be-(ne-1)) mesh eqns 3 Total 6

Node Voltage Method a) establish a reference node (typically, the one with most branches) b) label other essential node voltages c) write the node-voltage equations (KCL) to solve for v1,v2 d) from there, all currents can be derived using OL

Mesh Current Method Write KVL for each mesh current, then solve

Basis for MC Method Look at branch (not mesh) currents i1,i2,i3 v1 = i1 R1 + i3 R3 -v2 = i2 R2 – i3 R3 Substituting i3 = i1 – i2…

Basis for MC Method Substituting i3 = i1 – i2 v1=i1 (R1 + R3) – i2 R3 -v2= -i1 R3 + i2 (R2+R3)

Same Circuit, in Meshes V1 = ia R1 + (ia – ib) R3 = ia (R1 + R3) – ib R3 -V2 = ib R2 + (ib – ia) R3 = -ia R3 + ib (R2 + R3)

Summarizing So, i1 = ia i2 = ib i3 = ia – ib Once you know ia, ib, you know all branch currents, and then node voltages

What’s the benefit? By writing mesh equations, you automatically skip the substitution step for branch eqns, i.e. removing i3: i3 = i1 – i2 You are closer to a system of eqns to solve (in Matlab)