Chapter 4-1 Terminology and rules Node Voltage Review Matrix representation of a systems of equations

Planar circuit: a circuit that can be drawn on a plane with no crossing branches

Identify essential nodes and meshes

Need n equations to solve for n unknowns Let be represent number of essential branches Let ne represent number of essential nodes Node-Voltage method: allows us to solve a circuit using (ne – 1) equations Mesh-Current method: allows us to solve a circuit using be – (ne -1) equations

Node-Voltage method 1. Draw circuit with no branches crossing

Node-Voltage method 2. Count the number of essential nodes (ne ), you will need (ne -1) equations to describe the circuit,

Node-Voltage method 3. This circuit has three essential nodes 4. Choose one as a reference node, typically the node with the most branches 5. Assign remaining essential nodes with node voltages, in this case, nodes 1 and 2. A Node Voltage is defined as the voltage rise from the reference node to a non-reference node

6. Label the nodes and label currents as leaving the nodes, one node at a time apply KCL, using ohms law to write in terms of voltages summed to zero at the node 7. Repeat step 6 for the other nodes

    Things to remember: work on one node at a time. Define currents as leaving the node, based on node voltage definition If a current exist in the circuit that enters the node, it is assigned a minus sign

Matrix representation for a system of equations    

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What you should know Basic circuit definitions required for node-voltage method. Application of node-voltage Have a method to solve a system of equations