Electronics - revision history

Dank: /* First order: lumped elements */

2025-03-05T09:13:50Z

First order: lumped elements

← Older revision		Revision as of 09:13, 5 March 2025
Line 76:		Line 76:

	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==		==PCB design==

Dank: /* Current */

2025-03-05T08:53:49Z

Current

← Older revision		Revision as of 08:53, 5 March 2025
Line 70:		Line 70:
	*** 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==

Dank: /* First order: lumped elements */

2025-02-26T12:34:18Z

First order: lumped elements

← Older revision		Revision as of 12:34, 26 February 2025
Line 75:		Line 75:

	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.

			==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.

Dank: /* Classic Emag */

2025-01-17T08:32:01Z

Classic Emag

← Older revision		Revision as of 08:32, 17 January 2025
Line 49:		Line 49:
	===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:

Dank: /* Maxwell's equations */

2025-01-17T08:31:43Z

Maxwell's equations

← Older revision		Revision as of 08:31, 17 January 2025
Line 61:		Line 61:
	* ∇ ⨯ <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).

	* 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>.

	==Current==		==Current==

Dank: /* Maxwell's equations */

2025-01-17T08:31:30Z

Maxwell's equations

← Older revision		Revision as of 08:31, 17 January 2025
Line 61:		Line 61:
	* ∇ ⨯ <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).

	* 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].		* 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>.		** This formulation makes plain the mixing of <b>E</b> and <b>B</b>.

Dank: /* Classic Emag */

2025-01-17T08:30:57Z

Classic Emag

← Older revision		Revision as of 08:30, 17 January 2025
Line 54:		Line 54:
	** <b>v</b> ⨯ <b>B</b> is orthogonal to the particle's velocity vector and <b>B</b> at the particle's position.		** <b>v</b> ⨯ <b>B</b> is orthogonal to the particle's velocity vector and <b>B</b> at the particle's position.
	* The "force" on a particle is due to changes in the field.		* The "force" on a particle is due to changes in the field.
	* μ<sub>0</sub>: permeability of the vacuum = 1 / ε<sub>0</sub>c<sup>2</sup>		* μ<sub>0</sub>: permeability of the vacuum = 1 / ε<sub>0</sub><i>c</i><sup>2</sup> = 1.25663706127(20)×10<sup>-6</sup> N/A<sup>2</sup>.
	* ε<sub>0</sub>: permittivity of the vacuum = 1 / μ<sub>0</sub>c<sup>2</sup> = 8.8541878188(14)×10<sup>-12</sup> F/m.		* ε<sub>0</sub>: permittivity of the vacuum = 1 / μ<sub>0</sub><i>c</i><sup>2</sup> = 8.8541878188(14)×10<sup>-12</sup> F/m.
	====Maxwell's equations====		====Maxwell's equations====
	* ∇ ⋅ <b>E</b> = ρ / ε<sub>0</sub>.		* ∇ ⋅ <b>E</b> = ρ / ε<sub>0</sub>.

Dank: /* Classic Emag */

2025-01-17T08:29:54Z

Classic Emag

← Older revision		Revision as of 08:29, 17 January 2025
Line 54:		Line 54:
	** <b>v</b> ⨯ <b>B</b> is orthogonal to the particle's velocity vector and <b>B</b> at the particle's position.		** <b>v</b> ⨯ <b>B</b> is orthogonal to the particle's velocity vector and <b>B</b> at the particle's position.
	* The "force" on a particle is due to changes in the field.		* The "force" on a particle is due to changes in the field.
	* ~~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].~~		* μ<sub>0</sub>: permeability of the vacuum = 1 / ε<sub>0</sub>c<sup>2</sup>
	** This formulation makes plain the connection between <b>E</b> ~~and~~ <b>B</b>.		* ε<sub>0</sub>: permittivity of the vacuum = 1 / μ<sub>0</sub>c<sup>2</sup> = 8.8541878188(14)×10<sup>-12</sup> F/m.
	====Maxwell's equations====		====Maxwell's equations====
	* ∇ ⋅ <b>E</b> = ρ / ε<sub>0</sub>.		* ∇ ⋅ <b>E</b> = ρ / ε<sub>0</sub>.
Line 61:		Line 61:
	* ∇ ⨯ <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).
			* 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>.

	==Current==		==Current==

Dank: /* Classic Emag */

2025-01-17T08:23:33Z

Classic Emag

← Older revision		Revision as of 08:23, 17 January 2025
Line 56:		Line 56:
	* 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].		* 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 connection between <b>E</b> and <b>B</b>.		** This formulation makes plain the connection between <b>E</b> and <b>B</b>.
			====Maxwell's equations====
			* ∇ ⋅ <b>E</b> = ρ / ε<sub>0</sub>.
			* ∇ ⋅ <b>B</b> = 0.
			* ∇ ⨯ <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).

	==Current==		==Current==

Dank: /* Particle physics */

2025-01-17T08:12:20Z

Particle physics

← Older revision		Revision as of 08:12, 17 January 2025
Line 26:		Line 26:
	** [https://en.wikipedia.org/wiki/Bremsstrahlung Bremsstrahlung], [https://en.wikipedia.org/wiki/Synchrotron_radiation synchrotron radiation] (magnetobremsstrahlung), [https://en.wikipedia.org/wiki/Cyclotron_radiation cyclotron radiation], these are all subsets of photon emission due to charged particle accleration		** [https://en.wikipedia.org/wiki/Bremsstrahlung Bremsstrahlung], [https://en.wikipedia.org/wiki/Synchrotron_radiation synchrotron radiation] (magnetobremsstrahlung), [https://en.wikipedia.org/wiki/Cyclotron_radiation cyclotron radiation], these are all subsets of photon emission due to charged particle accleration
	* Photons are massless, and thus tend to move very quickly.		* Photons are massless, and thus tend to move very quickly.
	** Nothing moves faster than <i>c</i>, the speed of a ~~photon~~ in a vacuum.		** Nothing moves faster than <i>c</i>, the speed of a massless particle in a vacuum.
	** <i>c</i> = 299792458 m/s, or about one foot in a nanosecond.		** <i>c</i> = 299792458 m/s, or about one foot in a nanosecond.
	** Sometimes photons are not the fastest thing in a given medium, hence [https://en.wikipedia.org/wiki/Cherenkov_radiation Cherenkov radiation] at constant velocity (no acceleration)		** Sometimes photons are not the fastest thing in a given medium, hence [https://en.wikipedia.org/wiki/Cherenkov_radiation Cherenkov radiation] at constant velocity (no acceleration)