From 314d3389df58973424dc48e79539f97c9114659e Mon Sep 17 00:00:00 2001 From: eggy Date: Mon, 23 Jan 2023 20:58:12 -0500 Subject: [PATCH] ece140: add nodal analysis --- docs/1b/ece140.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/docs/1b/ece140.md b/docs/1b/ece140.md index b44e071..5a1c2c1 100644 --- a/docs/1b/ece140.md +++ b/docs/1b/ece140.md @@ -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. $$\sum v_\text{loop}=0$$ + +### 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: + +$$i=\frac{v_\text{higher}-v_\text{lower}}{R}$$