diff --git a/docs/1b/ece140.md b/docs/1b/ece140.md index 4faac55..a2442f6 100644 --- a/docs/1b/ece140.md +++ b/docs/1b/ece140.md @@ -173,17 +173,28 @@ The arrow of the current source must point in the positive direction of the volt Any part of a circuit including an independent source can be replaced with exactly one voltage source and a resistor in series. Two circuits are **Thevenin equivalent** if their $\lambda$ are equal in $V=\lambda I$. -1. Cut off the load. -2. Group the rest of the circuit together, removing all independent sources (short / open). -3. The Thevenin resistance of the new resistor is the same as the load $R_{Th}=R_L$. +If there are no dependent sources, all independent sources should be removed to determine the resistance across points $AB$: -If dependent sources exist, the load should be replaced with an independent source of arbitrary value (e.g., 1 V) and the other variable determined to find $R_{Th}=V_{Th}/I$, where $V_{Th}$ is the voltage drop across the load. +$$R_{Th}=R_{AB}$$ + +Otherwise, $V_{AB}$ and $I_{AB}$ should be found by repeating these steps: + +1. Cut off the load (open if finding voltage, short if finding current) + - If dependent sources depend on elements inside the load branch, zero them +2. Use analysis to determine the desired quantity Across the load: $$ I_L=\frac{V_{Th}}{R_{Th}+R_L} \\ V_L=R_LI_L = \frac{R_L}{R_{Th}+R_L}V_{Th} +$$ !!! warning A negative resistance $R_{L}$ indicates that the load supplies power. + +### Maximum power transfer + +To maximise the power transferred from the circuit to the load, $R_L$ should be equal to $R_{Th}$. + +$$P_L=v_Li_L$$