Lecture 3

Lecture 3 Review:

KVL simply said that I can sum the voltages in any loop in a circuit and the result then would be zero. Similarly, I can sum the currents that enter or exit any node and the sum will also be zero.

Element relationships

Method 1: Basic KCL, KVL method Write KVL for all the loops, write KCL for all the nodes and write element VI relationships.

Method 2: Apply element combination rules: The basic idea behind this method was to learn some simple rules of how resistors add and conductances add and look at a circuit and simplify them.

Example:

Method 3: Node Voltage analysis A particular way of applying KVL and KCL. Applies to linear circuits, nonlinear circuits, etc.

1. Select reference nodes (ground) from which voltages are measured. 2. Label voltages of remaining nodes with respect to ground. These are the primary unknowns. Voltage sources are dependent variables. 3. Apply KCL at each node with an independent variable, and express each current in term of the adjacent voltages. 4. Solve for node voltages. 5. Back solve for branch voltages and currents (the secondary unknowns). Example 1:

ia=1mA, ib=2mA, R1=1k, R2=500, R3=2.2 k, R4=4.7k

3. Apply KCL at nodes a and b:

Rewriting:

Or

Using linear algebra:

Example 2 (Voltage sources):

R1=2, R2=2, R3=4, R4=3, I=2A, V=3v

Method 4: Mesh Current analysis 1. Define each mesh current. Unknown mesh current are clockwise, known currents are defined in the direction of the current source. 2. With n meshes and m current sources, n-m independent equations will result. 3. Apply KVL to each mesh containing an unknown mesh current. 4. Solve the linear system. Example 1: V1=10, V2=9, V3=1, R1=5, R2=10, R3=5, R4=5

1. Assume clockwise currents i1 and i2. 2. Apply voltages to each mesh individually, and then do KVL.

Example 2 (Current sources): I=0.5, V=6, R1=3, R2=8, R3=6, R4=4

1. Assume clockwise currents.

Dependent Sources Example:

Independent variables are v and v3.