## Fundamental Laws ### Kirchhoff’s Current Law (KCL) The current arriving at any junction point in a circuit is equal to the current leaving that junction. Current is the same everywhere inside a series circuit ### Ohm's Law $ V = IR $ Voltage declines after resistors but current does not. Voltage is relative Ground is *absolute zero* ## Circuit Components ### Diodes Ideal: Zero resistance once "turn-on" voltage is reached, infinite resistance otherwise. Reality: ![[Pasted image 20240313215542.png|475]] ### Capacitors $ i = C \frac{dv}{dt} $ $ q = CV $ C is capacitance q is charge held ### Bipolar Junction Transistors #### NPN ![[Pasted image 20240313221914.png]] ![[Pasted image 20240403014508.png]] ![[Pasted image 20240403014528.png]] ### Op-Amp #### Negative Feedback ![[Pasted image 20240403053447.png|325]] $i_{+}=i_{-}$ $V_{\text{out}}$ assumes whatever is needed to set $V_{+}=V_{-}$ $V_{\text{out}}$ is unaffected by amount of output current ### Golden Rules $ v_{out} = A \cdot (v_{+} - v_{-}) $ A is very large $i_{in} \approx 0$ with feedback, $v_{+} = v_{-}$ ### Inductor $ V_{L} = L \frac{di}{dt} $ Current is continuous, voltage can jump around Analogous to mass: velocity is continuous, but forces can be instantaneous and determined by external factors Think of it like $F = ma$ $ P_{mech} = F\cdot V $ $ P_{elec} = V\cdot i $ $ i = C \frac{dV}{dt} $ $ V = k \cdot \frac{dF}{dt} \implies F = kx $ capacitor is a spring ![[Pasted image 20240430104050.png|450]] Big capacitor -> constant voltage that makes slopes simple lines with known slopes current in inductor is always a zig zag Assume that you can make this steady state (rises and falls the same amount) What conditions must have been true to make it stable? ### Motor $ i = K_{t}\tau $ $ \omega= K_{v} V $ $ i^{2}R + \omega\theta $ ### Mosfet Electrically controlled switches Drain to source is connected if and only if $V_\text{GS} \geq V_\text{th}$ Ground is never connected to anything (current at ground is zero) lotta mostfets, some motors, potentially all that other stuff ### Buck Converter ### Boost Converter ## Circuits ### Half Wave Rectifier Only lets one polarity through ![[Pasted image 20240313221230.png|375]] ![[Pasted image 20240313221243.png|600]] ### Full Wave Rectifier "Rectifies" everything to one polarity ![[Pasted image 20240313221134.png|450]] ![[Pasted image 20240313221149.png]] ### Smoothing Capacitor Turns AC current into DC current when combined with a full wave rectifier ![[Pasted image 20240313221410.png]] ### Emitter BJT Circuit ![[Pasted image 20240313222258.png]] ![[Pasted image 20240313222340.png]]