Circuits, Switches, and Samples

Kirchhoff's current law says current into a node sums to zero. Kirchhoff's voltage law says voltages around a loop sum to zero. A MOSFET uses those constraints as a switch: cutoff is open, saturation is closed, and a program is a pattern of such switches. A continuous signal becomes a sequence only if you sample faster than twice the highest frequency you intend to keep (Nyquist–Shannon). I spent my first years at the University of Illinois in this curriculum to see how transistors worked, spent time in a photonics lab, and sorted components for engineering students.

#>electrical_engineering_essentials

Principles

KCL and KVL

Node current sums to zero. Loop voltage sums to zero. A capacitor then makes current proportional to how fast voltage changes, which is why circuits become differential equations.

mit ocw: 6.002

The transistor as a switch

Cutoff, triode, saturation. Digital logic lives in cutoff and saturation. The in-between region is where analog circuits work, and where a careless gate burns power.

wiki: MOSFET

Nyquist–Shannon

Sample above twice the highest frequency you mean to keep, or the reconstructed wave aliases into a lower one. Compression starts after that choice: what you decided not to store.

wiki: sampling theorem

Fields, locally

Electric and magnetic fields are vector fields. Their divergence and curl are the local form of the circuit laws. Vector calculus is the math course this curriculum assumes.

wiki: Maxwell

#>parallel_theories

Parallel and Competing Theories

The circuit laws above carry European names. These results came from India and China, in parallel or earlier, and each extended what electromagnetism could do.

J. C. Bose and millimeter waves

In 1890s Calcutta, Jagadish Chandra Bose generated and detected millimeter-wave radiation with waveguides and semiconductor detectors, decades before microwave engineering became a field.

wiki: J. C. Bose

Shen Kuo and the compass

In the eleventh century, Shen Kuo described the magnetic needle compass and noticed it points slightly away from true north: the first written account of magnetic declination.

wiki: Shen Kuo

Current into a node sums to zero. Voltage around a loop sums to zero. Sampling keeps a wave only past twice its highest frequency.

Kirchhoff, 1845. Kotelnikov, 1933, between Nyquist and Shannon. MIT 6.002 for the course. Differential equations for i = C dv/dt.

An acequia junction obeys the same sum as Kirchhoff: water in equals water out. Ibn al-Haytham's Book of Optics is the experimental account of straight-line light. Read the ditch with a crop clock, and the ray with vector calculus.