But really, if you want to get your hands dirty with some practical electronics, and also want to be able to communicate without relying much on nearby infrastructure, amateur radio is a great hobby.
The US ham test question pools are fully public. Your test will be a mixture of questions from the pool. HamStudy basically lets you churn the question pool, and then will offer explainer text / references to back up each question and correct answer.
I went on a vacation and used their phone app any time I was standing in a line. You can set it to just keep spinning through the questions, with a bias towards ones you're getting wrong.
The Extra exam is 50 multiple choice questions broken down by category as follows:
6 Commission Rules
5 Operating Procedures
3 Radio Wave Propagation
5 Amateur Practices
4 Electrical Principles
6 Circuit Components
6 Practical Circuits
3 Signals and Emissions
8 Antennas and Transmission Lines
4 Safety
Within each category there are subcategories. "Antennas and Transmission Lines" for example has 8 subcategories. The 8 questions in "Antennas and Transmission Lines" are one from each of those subcategories. The question pools for these subcategories each have 10-14 questions.
If you compare to the closest corresponding categories/subcategories from the General and Technician exam you'll probably find that there are a few cases.
1. The Extra is just more of the same. It's not harder per se. "Commission Rules" for example.
2. The Extra goes goes deeper and also adds new material that is more advanced.
3. The Extra is in new territory.
If you get to the point where the Technician and General are going to no problem, then you will probably have no trouble getting to the point where case #1 is also no problem, and case #2 is also well in hand. It is #3 where you might have trouble.
But remember that you can get 13 wrong and still pass!
Pick say 10 subcategories that are in case #3 that look like they would be the hardest to get good at and just write them off.
For example in "Antennas and Transmission Lines" you might decide that the "Smith chart" subcategory, which has a pool of 14 questions, would take a lot of time to get good at. So skip it. That's 14 less potential questions you have to be prepared to answer, leaving more time to study for things in class #2 and the class #3 things that look most doable.
It doesn't cost extra to take the Extra test at the same session that you take the Technician and General tests, and there is no penalty for failing, so might as well go for it.
It was mind blowing when I first heard the audio through IEMs ! It felt magical that this contraption was working without any battery source.
Such a simple radio can be a gateway drug to a very complex and deep hobby. In my case it went like that:
1. Built a simple radio
2. Could hardly hear anything, need to add an amplifier to it 3. Now it’s better but captures a lot of noise
4. Design a filter to select just that one station
5. Now I want to listen to more stations.
6. Ugh, you can’t design a good filter with variable frequency. Enter the superheterodyne world.
7. Now finally got something that resembles a tunable AM radio, but it kinda whistles / hums a lot. Ah, so the mirror image is a real thing?!
8. Need a higher IF to be able to better reject the image before the mixer. Ok, let’s make a double conversion superhet then.
9. Buy a set of ceramic filters and play with them to get the best selectivity.
10. Try to add more amplification only to learn if you go too far you get an oscillator instead of an amplifier.
11. The sound level is not stable. Add AGC.
12. Pick up some stations from 5000+ km away. Nice. But there is some weird distortion. Oh, I’ve been a culprit of frequency selective fading…
Fast forward and now I’m building a PLL synchronized AM product demodulator with a squaring loop for carrier recovery.
Fun. Lot of fun! Wholeheartedly recommend!
As someone who's always dabbled in electronics, skimmed and read some books, my primary complaint abot most electronics texts is that they just talk about individual topics: oscillators, amplifiers, etc.
What they never talk about, is putting them all together.
But as witnessed by this list, that's what a radio is. A collection of these "meta" components into a whole to get a better radio experience.
A radio built like this, with individual subsystems connected together, is much more understandable. Many (not all) radio schematics are presented as a whole, rather than the parts, or why you might (or might not) want to change one part or another (not components, but one, say, filter circuit to a different one).
It just seems to me that once you get past some basic theory, starting with a radio, and then systematically taking it apart is a better way of approaching electronics education.
Also I had seen some recon antennas in a certain campus (can't say much about that) when I was a kid. Those were like long wires hanging from towers. I believe they used to receive/decode SW/AM signals from far away. I realised this much much later in my life. But fascinating nonetheless. And adding to all these is SDR! That's a whole different thing.
Or a razor blade or a piece of roofing lead and a needle.
I tend to prefer these visual and intuitive explanations to the mathematically based ones usually given in lectures. The "open capacitor" example was something I hadn't thought of before.
Radios, how do they work? - https://news.ycombinator.com/item?id=39813679 - March 2024 (109 comments)
https://sg30p0.familysearch.org/service/records/storage/dasc...
You could also use signals from 2 antennas 90 degrees apart to get I and Q. This gives you the added ability in that signals from one side has a negative frequency. It's some really useful stuff.
The theory seems overly complex (because it is). but for practical radio you can tune up nearly anything and chat -- and be way more productive with it.
Imagine obsessing over the mechanics of baseball or fishing without ever tossing a ball or casting a reel.
…(scroll)…
> 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.
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.
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.
Source: I almost burnt my PC on simulating a dipole array while studying for the antennas course at the university
But yeah, black magic is right!
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.
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).
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".
I ran into the same thing earlier, but it worked fine after a couple refreshes.
Imagine a circuit. Like a flashlight. The electrons flow from the battery to the lightbulb and back. It’s like a race track. They proceed in an orderly fashion.
There are some other electrical components. If you hook them up in just the right way, you get something called an LRC circuit. The electrons don’t flow in an orderly way now. They go back-and-forth. In spurts and fits. You’re making them wiggle. There are some very nice equations that allow you to specify exactly how much and how fast the wiggling is.
One cool thing about a circuit with wiggling electrons is that if you put some wires close by those electrons will also start wiggling.
This is called radio.
