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

2. 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

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

4. Some Definitions

5. Identify Components

7. 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

8. 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

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

10. 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…

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

12. 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)

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

14. 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)