Branch analysis involves analyzing individual branches of a circuit to determine the currents, voltages, and power dissipation within each branch.
Loop analysis involves applying Kirchhoff's Voltage Law (KVL) to loops or closed paths in a circuit to determine the currents and voltages in each loop.
Node analysis involves applying Kirchhoff's Current Law (KCL) to nodes or junction points in a circuit to determine the currents flowing into or out of each node.
In loop analysis, KVL is applied to closed loops in a circuit to write equations based on the sum of the voltage drops around the loop, considering the polarity of each voltage source.
In node analysis, KCL is applied to each node in a circuit to write equations based on the sum of currents entering or leaving the node, accounting for the direction of each current.
Loop analysis simplifies circuit analysis by reducing the number of equations needed to solve the circuit, especially for complex circuits with many branches.
A supernode is formed in node analysis when a voltage source is connected between two nodes, resulting in a constraint on the voltage difference between the nodes.
Supernodes are handled by writing a KCL equation for the supernode, taking into account the current through the voltage source and the currents entering or leaving the supernode.
Mesh analysis involves applying Kirchhoff's Voltage Law (KVL) to mesh or loop currents in a circuit to determine the currents and voltages in each loop.
Current sources are treated as additional unknowns in mesh analysis, and mesh currents are chosen to either flow in the same direction as the current source or opposite to it, depending on the source's polarity.