[tigereyeTO]

> In today’s article, I’m hoping to provide an introduction to radio that’s free of ham jargon and advanced math

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> The identity for cos(α + β) can be trivially extended to cos(α - β), because subtraction is the same as adding a negative number:

…(scroll)…

> From the formula we derived earlier on, the result of this multiplication necessarily indistinguishable from the superposition of two symmetrical sinusoidal transmissions offset from a by ± b, so AM signals take up bandwidth just the same as any other modulation scheme.

[mholt]

I got my amateur radio license last year, and this is precisely why I haven't been able to do much with it: seemingly all the guides, even the license study materials, use vocabulary I'm not familiar with. I have two CS degrees and a solid foundation in math, but I can't understand how radios work because of vocabulary more than the math.

My uncle who's been building his own radios for over 60 years, tried to explain to me how antennas work, and even to him it comes down to "black magic".

I'm told the way they work is not really intuitive, so you just have to math it out.

Maybe I should have gotten an EE degree.

[mkipper]

I work in software now, but I have an electrical engineering degree and started my career on a project developing a radio. Our project probably had ten or more electrical engineers on it, and only one or two of them really understood the RF side of it. It's a very specialized skill -- even EEs with >20 years of experience would describe things as black magic.

So I don't think you're alone feeling this way. Even with a good foundation in the theory and math, I think most people hit a wall with radios at some point. All the people I worked with who intuitively "got" RF stuff had been doing nothing else professionally for over a decade.

[cfraenkel]

A long time ago, worked on a comm satellite program. It used a whack of tuned cans to combine high powered transmit signals with harmonics in each others' frequency bands to feed into the antenna. I once asked how they worked. The answer was 'magic'. I mean, they were physical RF filters, but no one could explain or reproduce how they worked. There was this one guy who could tighten the screws that adjusted the inside baffles so they 'worked'. No one else could.

[lormayna]

Antennas are really black magic: optimizing an antenna requires stocastich method like genetic algorithms, simulated annealing, etc. Moreover if you want to model the radiation patterns and the electrical characteristics you need to use finite element calculation methods. So, you need a lot of computation power as antenna are not a problem that can be solved in a closed form.

Source: I almost burnt my PC on simulating a dipole array while studying for the antennas course at the university

[zppln]

Related: https://en.wikipedia.org/wiki/Evolved_antenna

[ux266478]

I assure you, that doesn't go away in electrical engineering or even theoretical physics. Electromagnetism exhibits a large degree of behavioral emergence. It's one of the most well studied aspects of physics, but remains a rather convoluted and seemingly arbitrary puzzle box of nonsense especially at a macroscopic level.

[hedgehog]

Even just the theory is kind of mind expanding. I've done a little signal processing and ideas like "negative frequency" sound absurd up front and then seem reasonable once you've worked with them.

[richiebful1]

I've had my ham license for ten years, but I've only ever used a basic car-based mobile setup and my handhelds. My morse code speed is abysmal. QRP and all that are really cool, but I just use ham radio to supplement my fire/ems handheld in a natural disaster.

[_whiteCaps_]

I'd love to see more people on the air. My advice is to get a radio with a good tuner, build a simple dipole with the online calculators, and try to make contacts that way.

[esseph]

It gets crazier when you start talking about things like a Tarana BN. The amount of processing in them is pretty insane.

But yeah, black magic is right!

[kragen]

This is basic math, not advanced math. If you don't know it, don't worry, you can learn it pretty quickly. Maybe watch some 3Blue1Brown videos and do some textbook exercises and/or game programming. Git gud. There is no royal road to radio modulation.

I learned that subtraction was the same as adding a negative number sometime around second grade, and I learned (then forgot) the trigonometric angle-sum identities in tenth grade. And that was even with the handicap of having to attend school in the US.

And, just above the text you're complaining about, he even provides a straightforward geometric proof of the angle-sum identity! So you don't even have to know it to read the article! You just have to know what a cosine is! I learned what a cosine was in eighth grade because I wanted to program a game where objects would fly across the screen at a constant velocity but a varying angle. You can learn it too!

He's not, like, invoking the convolution theorem or anything in those quotes. Although he does get into it a bit.

I think that, if you know the convolution theorem and Euler's formula, things like the production of sum and difference frequencies from the multiplication of sinusoids start to seem obvious rather than sort of random. When I was in high school they seemed sort of random. My uncle had tried to explain Euler's formula to me, along with the Taylor expansions for sine, cosine, and the exponential, but I hadn't really understood, because I didn't have the background knowledge to appreciate them then.

[anthomtb]

> Euler's formula

So much EE-related math becomes trivial (or at least not-hard) once you've internalized this formula.

What I am trying to decide is 1) Did I zone out in class when Euler's formula was introduced or 2) Did my secondary school mathematics classes just kind of gloss over it?

I lean towards 2 but unfortunately none of my college classes reintroduced the formula and I ended up making a lot of problems harder than they should have been (I have an EE undergrad).

[kragen]

I'm not sure any of my secondary-school classes taught it, but I dropped out of secondary school to go to the university, so maybe they would have in the following year. In secondary school I was in the "smart kids" math track, though, and they also had an "average kids" track and a "dumb kids" track, and I really doubt those tracks covered it.

[peterfirefly]

Are you objecting to the trivial extension to cos(α - β)? The cos(α + β) identity itself is nicely explained in the text.

The third thing you quote is the result of fairly simply symbol manipulation that requires no new knowledge apart from the original cosine identity and the obvious corollary about subtracting an angle being the same as adding a negated one.

There is zero advanced math there. No complex numbers, no calculus, no limits, no Fourier, no "functions are vectors, too".

[Isamu]

To be fair, I think most people regard “not advanced math” to exclude trig, and maybe algebra too. Fear and loathing of math is a thing.

[peterfirefly]

skill issue

[foobarian]

To be fair, they did qualify it as "advanced" math :-)

[pengaru]

What do you consider advanced math? This isn't solving differential equations...

[andoando]

How I wish I could quit my job and go back to school.