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ece140: add nodal analysis

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eggy 2023-01-23 20:58:12 -05:00
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@ -114,3 +114,15 @@ $$\sum i_\text{entering node}=0$$
Kirchoff's **voltage law** states that the sum of all voltage in a **closed loop** must be zero. Kirchoff's **voltage law** states that the sum of all voltage in a **closed loop** must be zero.
$$\sum v_\text{loop}=0$$ $$\sum v_\text{loop}=0$$
### Nodal analysis
Nodal analysis uses the voltages at the **nodes** instead of elements to calculate things in a three-step process:
1. Determine a reference node with $v=0$ and stick a ground out of that node.
2. Use KCL and Ohm's law on non-reference nodes to get their currents in terms of the reference node.
3. Solve the system of equations with the formula below.
On either side of a resistor, the current flowing that entire segment can be determined via the following formula:
$$i=\frac{v_\text{higher}-v_\text{lower}}{R}$$