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FNIRSI 1014D review by Kerry Wong (2022)

Source. One of the cheapest oscilloscopes available at the time.

Vacuum tube by

Ciro Santilli  40 Updated 2025-07-16

Transistor by

Ciro Santilli  40 Updated 2025-07-16

A solid-state electronic switch and amplifier.

Although transistors were revolutionary, it is fun to note that they were just "way cheaper and more reliable and smaller" versions of exactly the main functions that a vacuum tube could achieve

Relaxation oscillator by

Ciro Santilli  40 Updated 2025-07-16

Crystal oscillator by

Ciro Santilli  40 Updated 2025-07-16

First watch: Video "Oscillators: RC, LC, Crystal by GreatScott! (2015)"

From Raw Crystal to Crystal oscillator

. Source. by United States Army Signal Corps (1943)

Maxwell's equations by

Ciro Santilli  40 Updated 2025-07-16

Unified all previous electro-magnetism theories into one equation.

Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.

The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.

The equations are a system of partial differential equation.

The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:

$E_{x} (t, x, y, z)$ , $E_{y} (t, x, y, z)$ , $E_{z} (t, x, y, z)$ : directions of the electric field $E : R^{4} \to R^{3}$
$B_{x} (t, x, y, z)$ , $B_{y} (t, x, y, z)$ , $B_{z} (t, x, y, z)$ : directions of the magnetic field $B : R^{4} \to R^{3}$

and two known input functions:

$ρ : R^{3} t o R$ : density of charges in space
$J : R^{3} \to R^{3}$ : current vector in space. This represents the strength of moving charges in space.

Due to the conservation of charge however, those input functions have the following restriction:

\frac{\partial ρ}{\partial t} + \nabla \cdot J = 0

(1)

Equation 1.

Charge conservation

Also consider the following cases:

if a spherical charge is moving, then this of course means that $ρ$ is changing with time, and at the same time that a current exists
in an ideal infinite cylindrical wire however, we can have constant $ρ$ in the wire, but there can still be a current because those charges are moving
Such infinite cylindrical wire is of course an ideal case, but one which is a good approximation to the huge number of electrons that travel in a actual wire.

The goal of finding

E

and

B

is that those fields allow us to determine the force that gets applied to a charge via the Equation "Lorentz force", and then to find the force we just need to integrate over the entire body.

Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:

d i v E = \frac{ρ}{ε _{0}}

(2)

Equation 2.

Gauss' law

d i v B = 0

(3)

Equation 3.

Gauss's law for magnetism

\nabla \times E = - \frac{\partial B}{\partial t}

(4)

Equation 4.

Faraday's law

\nabla \times B = μ_{0} (J + ε_{0} \frac{\partial E}{\partial t})

(5)

Equation 5.

Ampere's circuital law

You should also review the intuitive interpretation of divergence and curl.

Magnetism by

Ciro Santilli  40 Updated 2025-07-16

Breakout board by

Ciro Santilli  40 Updated 2025-07-16

General-purpose input/output by

Ciro Santilli  40 Updated 2025-07-16

Jump wire by

Ciro Santilli  40 Updated 2025-07-16

Notably used to connect:

pin headers
breadboard holes

You can buy large sets of them in combitation of male/male, male/female, female/female. Male/male is perhaps the most important

Making Jumper Wires by PCBurn! (2018)

Source.

Pin header by

Ciro Santilli  40 Updated 2026-08-21

These often come pre-soldered on devboards, e.g. and allow for easy access to GPIO pins. E.g. they're present on the Raspberry Pi 2.

Why would someone ever sell a devboard without them pre-soldered!

USB by

Ciro Santilli  40 Updated 2025-07-16

Electric guitar player by

Ciro Santilli  40 Updated 2025-07-16

Allan Holdsworth

Available battery voltages by

Ciro Santilli  40 Updated 2025-07-16

Only certain battery voltages exist, because this voltage depends intrinsically on the battery's chemical composition.

learn.sparkfun.com/tutorials/battery-technologies/all (CC BY-SA) has a very good summary list, reordered from lowest to highest voltage:

Battery Shape	Chemistry	Nominal Voltage	Rechargeable?
AA, AAA, C, D (Rechargeable)	NiMH or NiCd	1.2V	Yes
AA, AAA, C, and D	Alkaline or Zinc-carbon	1.5V	No
Coin Cell	Lithium	3V	No
Silver Flat Pack	Lithium Polymer (LiPo)	3.7V	Yes
9V	Alkaline or Zinc-carbon	9V	No
Car Battery	Six-cell lead acid	12.6V	Yes

Bibliography:

Nine-volt battery by

Ciro Santilli  40 Updated 2025-07-16

Weston cell by

Ciro Santilli  40 Updated 2025-07-16

youtu.be/HQ1lrEQsj4c?t=51 shows Fluke 731B Voltage Standard which contains 1.018 values due to Weston cell voltage standard

Raised and lowered indices by

Ciro Santilli  40 Updated 2025-07-16

TODO what is the point of them? Why not just sum over every index that appears twice, regardless of where it is, as mentioned at: www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf.

Vectors with the index on top such as

x^{i}

are the "regular vectors", they are called covariant vectors.

Those in indices on bottom are called contravariant vectors.

It is possible to change between them by Raising and lowering indices.

The values are different only when the metric signature matrix is different from the identity matrix.

Implicit metric signature in Einstein notation by

Ciro Santilli  40 Updated 2025-07-16

Then a specific metric is involved, sometimes we want to automatically add it to products.

E.g., in a context considering the common Minkowski inner product matrix where the

η

4x4 matrix and

μ

is a vector in

R^{4}

x^{μ} x_{μ} = x^{μ} η_{μν} x^{ν} = - x_{0}^{2} + x_{1}^{2} + x_{2}^{2} + x_{3}^{2};

(1)

which leads to the change of sign of some terms.

Einstein notation for partial derivatives by

Ciro Santilli  40 Updated 2025-07-16

The Einstein summation convention works will with partial derivatives and it is widely used in particle physics.

In particular, the divergence and the Laplacian can be succinctly expressed in this notation:

In order to express partial derivatives, we must use what Ciro Santilli calls the "partial index partial derivative notation", which refers to variables with indices such as

x_{0}

x_{1}

x_{2}

\partial_{0}

\partial_{1}

and

\partial_{2}

instead of the usual letters

x

y

and

z

Covariance and contravariance of vectors by

Ciro Santilli  40 Updated 2025-07-16

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