Electronics

I find the study of electronics to be somewhat frustrating. Maybe things might have been different if I'd been CmpE or EE, but I've found no real axiomatic treatment of the material. You've got QED (largely irrelevant save to confuse), and classical emag (magnets end up being rather less important than thought), and circuit laws (lots of these), and rules of thumb, and there's no great taxonomy of components, and the people on the forums are mostly braindead. So I'm taking notes here.

Charge

Particle physics

• Electric charge is quantized: there exists a smallest positive amount of charge.
  • We'll denote this with q.
  • All other charges are integer multiples of this quantum of charge.
  • This implies a largest negative amount of charge, -q, the additive inverse of q.
• The electron-like leptons (i.e. not the neutrinos), the W^± bosons, and all quarks carry intrinsic electric charge.
  • By convention, the electron-like leptons, the W^- boson, and the down, strange, and bottom quarks carry negative charge.
    • The d, s, and b quarks carry -q; the W^- boson, electron, muon, and tau all carry -3q.
    • The up, charm, and top quarks carry positive charge, 2q. The W⁺ boson carries 3q.
  • The proton's up-up-down valence quarks yield a net charge of 3q.
  • The neutron's up-down-down valence quarks yield a net charge of 0.
  • The Konami code up-up-down-down left-right-left-right b-a-b-a start gave you 30 lives.
• Since electrons are -3q, and quarks are usually confined, and always add up to some integer multiple of 3q, we consider 3q our working quantum of charge.
  • We call it e, the elementary charge. Electrons have -1. Protons have 1.
  • This (e) is also how the electron is represented.
    • This will not be the last unnecessarily confusing thing encountered in our study of electronics.
• Photons do not carry a charge, but they do carry energy, and are the mediators of the electromagnetic interaction.
  • Photons interact strongly with charged particles, imparting energy, but
  • from a distance, a neutral atom looks a lot like an uncharged particle.
• Photons are emitted when charged particles are accelerated.
  • Charged particles are coupled to the electromagnetic field; accelerations excite it.
  • Bremsstrahlung, synchrotron radiation (magnetobremsstrahlung), cyclotron radiation, these are all subsets of photon emission due to charged particle accleration
• Photons are massless, and thus tend to move very quickly.
  • Nothing moves faster than c, the speed of a photon in a vacuum.
  • Sometimes photons are not the fastest thing in a given medium, hence Cherenkov radiation at constant velocity (no acceleration)

Atomic physics

• In a normal environment, electrons and protons carry a charge, equal in magnitude and opposite in sign, neutrons do not carry a charge, and everything else that might carry a charge (muons, taus, electron-like antileptons, some mesons, heavy quarks, W bosons) is vanishingly rare (and decaying very soon).
• Atoms in their pristine state are neutral, but are regularly found with fewer or more electrons than normal; they are (partially) ionized, and known as ions.
• Atoms generally want (enjoy lower energy states via) full valence shells more than they want to be electrically neutral.
• Molecules often provide the best of both worlds: full (to first order) chewy shell centers plus neutral (to first order) combined form.
  • Noble gases (aerogens) enjoy this happy state naturally.
• At the atomic scale, one need deal with quantization of angular momentum, and solve for lowest energies with the Schrödinger equation, and the electromagnetic interaction is described by QED, and the Heisenberg principle applies. Suffice to know that electrons do not slam into the nucleus.
  • Most of the time. Electron capture sees an electron combine with a proton, yielding a neutron and an electron neutrino, but this is actually a weak interaction, not an electromagnetic one! The electron exchanges a W boson with an up quark in the proton, changing it to a (heavier) down quark (and ν_e), but reducing total energy of the bound system.
• Despite the fact that at larger scales (the regime of classical emag):
  • Charges of equal sign repel, while charges of opposite sign attract, and
  • the effect of charge between two charged bodies falls off with the square of the distance, and
  • the effect of charge can be superimposed, and
  • charged particles will flow between isolated regions of opposite charge.

First order: lumped elements

An component is any discrete unit in a circuit that is doing more than linking multiple components. Elements which link components are wires, and are usually reasonably conductive (otherwise they wouldn't be very good links).

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.