2.3 Circuit Analysis: Basic Method

Basic method of circuit analysis:

1. Define each branch current and voltage in the circuit (follow associated variables convention)
2. Assemble the element laws for the elements
3. Apply Kirchhoff’s current and voltage laws
4. Jointly solve the equations assembled in Steps 2 and 3 for the branch variables defined in Step 1

Summary:

1. Define voltages and currents for each element
2. Write KVL
3. Write KCL
4. Write constituent relations
5. Solve 

2.2 Kirchhoff's Laws

• Kirchhoff’s current law (KCL) - The current flowing out of any node in a circuit must equal the current flowing in. That is, the algebraic sum of all branch currents flowing into any node must be zero.
• Kirchhoff’s voltage law (KVL) - The algebraic sum of the branch voltages around any closed path in a network must be zero.
• Voltages across two parallel connected elements must be the same.

2.1 Terminology

• The junction points at which the terminals of two or more elements are connected are referred to as the nodes of a circuit
• The connections between the nodes are referred to as the edges or branches of a circuit
• Circuit loops are defined to be closed paths through a circuit along its branches

• Branch current is the current along a branch of the circuit
• Branch voltage is the potential difference measured across a branch

2.0 Resistive Networks

• Solving or analyzing a circuit generally involves finding the voltage across, and current through, each of the circuit elements
• When circuit obeys the lumped matter discipline, Maxwell's Equations can be simplified into two algebraic relationships stated as Kirchhoff's voltage & current law (KVL & KCL)

1.8 Signal Representation

• Signals in the physical world are most commonly analog
• Value discretization forms the basis of the digital abstraction, which yields a number of advantages such as better noise immunity compared to an analog signal representation.

1.7 Modeling Physical Elements

• Resistor self-heating, with the associated change in value, prompts manufacturers to provide power ratings for resistors, to indicate maximum power dissipation (pmax) without significant value change or burnout.

• Battery terminal voltage expression: vt = V + iR

1.6 Ideal Two-Terminal Elements

• An ideal voltage source is a device that maintains a constant voltage at its terminals regardless of the amount of current drawn from those terminals.
• Two type of voltage source: independent & dependent
• An ideal conductor is a element in which any amount of current can flow without loss of voltage or power.
• An ideal linear resistor obeys Ohm's law
• Conductance (G) is the reciprocal resistance:

G = 1 / R

• The element law for a independent voltage source supplying a voltage V:

v = V

• The element law for ideal wire (short circuit):

v = 0

• The element law for open circuit:

i = 0

• The element law for a current source supply a current I:

i = I