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--- formulas [2023-10-29 21:50] – created asdf
+++ formulas [2023-12-17 21:57] (current) – [Electronics] asdf
@@ Line 16: / Line 16: @@
 $$Z_L = j\omega L$$
-Given two resistors $R_1$ and $R_2$ with $R_2=nR_!$, the parallel combination has total resistance $\frac{nR1}{n+1}=\frac{R2}{n+1}$.
+Given two resistors $R_1$ and $R_2$ with $R_2=nR_1$, the parallel combination has total resistance $\frac{nR1}{n+1}=\frac{R2}{n+1}$.
+<figure center|passive_mixer>
+{{ ::passive-avg.png?400 |}}
+<caption>Passive mixer</caption>
+</figure>
+$V_*$ in {{ref>passive_mixer}} is related to $V_A$ and $V_B$ by: $$V_* = \frac{V_A\cdot R_B + V_B\cdot R_A}{R_A+R_B}$$ Note that each input voltage is weighted by the resistor //opposite// $V_*$. This generalizes to $n$ voltages and $n$ resistors as: $$V_*=\left(\sum_{k=1}^n \frac{V_k}{R_k}\right) \cdot\left(\frac{1}{\sum_{k=1}^n \frac{1}{R_k}}\right),$$ that is, the short-circuit current times the total parallel resistance.
 ==== Ebers-Moll BJT model ====