Electronics: Difference between revisions
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===Classic Emag=== | ===Classic Emag=== | ||
* Usable whenever distances are large enough and/or field strengths low enough that quantum effects can be ignored. | * Usable whenever distances are large enough and/or field strengths low enough that quantum effects can be ignored. | ||
* For a manifestly Lorentz-covariant theory, one must use [https://en.wikipedia.org/wiki/Four-current four currents] and the [https://en.wikipedia.org/wiki/Electromagnetic_tensor electromagnetic tensor] or [https://en.wikipedia.org/wiki/Electromagnetic_four-potential four-potential]. | |||
** This formulation makes plain the mixing of <b>E</b> and <b>B</b>. | |||
* An electric vector field <b>E</b> and a magnetic vector field <b>B</b> exist at all points. | * An electric vector field <b>E</b> and a magnetic vector field <b>B</b> exist at all points. | ||
* A particle having charge c (an integer multiple of <i>e</i>) is acted upon by the Lorentz force: | * A particle having charge c (an integer multiple of <i>e</i>) is acted upon by the Lorentz force: | ||
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* ∇ ⨯ <b>E</b> = -∂<b>B</b> / ∂t. | * ∇ ⨯ <b>E</b> = -∂<b>B</b> / ∂t. | ||
* ∇ ⨯ <b>B</b> = μ<sub>0</sub>(<b>J</b> + ε<sub>0</sub>∂<b>E</b> / ∂t). | * ∇ ⨯ <b>B</b> = μ<sub>0</sub>(<b>J</b> + ε<sub>0</sub>∂<b>E</b> / ∂t). | ||
==Current== | ==Current== | ||
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*** This is roughly (but not exactly) 6.241509074×10<sup>18</sup> <i>e</i> per second. | *** This is roughly (but not exactly) 6.241509074×10<sup>18</sup> <i>e</i> per second. | ||
*** This is exactly 10<sup>19</sup> <i>e</i> per 1.602176634 seconds. | *** This is exactly 10<sup>19</sup> <i>e</i> per 1.602176634 seconds. | ||
* I = dq/dt = nAEv<sub>d</sub> | |||
==First order: lumped elements== | ==First order: lumped elements== | ||
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The "lumped element model" concentrates components to single points, and assumes ideal (simple) behavior. This induces a graph of finitely many planes, and allows us to work with ODEs rather than PDEs. It's more useful IMHO to relax the concentration, and treat components as ordered cycles corresponding to their geometry. In this model, when wires intersect, they become a single wire. A wire is a node, and each pin is a node. | The "lumped element model" concentrates components to single points, and assumes ideal (simple) behavior. This induces a graph of finitely many planes, and allows us to work with ODEs rather than PDEs. It's more useful IMHO to relax the concentration, and treat components as ordered cycles corresponding to their geometry. In this model, when wires intersect, they become a single wire. A wire is a node, and each pin is a node. | ||
* Kirchhoff's Laws: corollaries of Maxwell's Laws in the low-frequency limit (wavelengths ≫ circuit size) | |||
** First Law / Junction Rule: the algebraic sum of currents at a node is zero (what flows in must flow out) | |||
** Second Law / Loop Rule: the directed sum of voltages around a closed loop is zero | |||
==PCB design== | |||
* Longer traces add inductance | |||
* Thinner traces add more resistance than wider ones. | |||
** For lowspeed, simple traces of length L, area A, and material resistance ρ: R = ρ(L/A) | |||
* Wider traces add more impedance than thinner ones. | |||