ece140: add mesh analysis

docs/1b/ece140.md

@@ -126,3 +126,26 @@ Nodal analysis uses the voltages at the **nodes** instead of elements to calcula
 On either side of a resistor, the current flowing that entire segment can be determined via the following formula:
 
 $$i=\frac{v_\text{higher}-v_\text{lower}}{R}$$
+
+### Mesh analysis
+
+!!! definition
+    - A **mesh** is a loop with no inner loops.
+    - A **supermesh** is a combination of multiple meshes that share a common current source.
+
+Mesh / loop analysis is used to determine unknown currents, using KVL instead of KCL to create a system of equations.
+
+1. Assign mesh currents to each loop.
+2. Use KVL and Ohm's law to get voltages in terms of mesh currents.
+3. Solve the system of equations.
+
+It may be easier to delete the branch of the current source in supermeshes, treating the region as one mesh with multiple mesh currents.
+
+## Linearity
+
+Circuits are linear if and only if their voltages, resistances, and currents can be expressed in terms of linear transformations of one another. They contain only linear loads, linear dependent sources, and independent souces.
+
+$$\text{output}\propto\text{input}+C$$
+
+!!! example
+    Halving voltage must halve current (or at least halve it relative to a base current / voltage).