Author Topic: How does one "learn electronics"?  (Read 3316 times)

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Offline slavoy

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Re: How does one "learn electronics"?
« Reply #25 on: July 15, 2024, 06:06:18 pm »
“Tell me and I will forget, show me and I may remember; involve me and I will understand.”
Read a good textbook on the basics of electronics, grab a breadboard, a handful of components, a multimeter an oscilloscope and just start making anything you desire. There's no better way to understand electronics than working with a physical circuit. Just learn to work on your own first. Simulations, YouTube videos, magazines and kits are good as supplements.

Offline Picuino

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Re: How does one "learn electronics"?
« Reply #26 on: July 15, 2024, 07:18:27 pm »
There are so many fields in electronics to learn and in a university degree they are going to feed you with them as if you were a goose they want to fatten. It's like doing a marathon, not like doing a walk for fun.
Anyway, you can go forward and everything you learn will be good for you to be more motivated and to know some topics in more depth.
These are some of the topics that you will find studying electronics:

1. Electrical circuits. From direct current to alternating current. From Thevenin's theorem to quadrupole theory. From resistors to transformers.
2. Electronic components. How each one works, from a simple capacitor to a thyristor. How to connect them in parallel or in series and their modes of operation.
3. Analog electronics. From transistor stages (bjt or field effect) to operational amplifiers.
4. Digital electronics. From basic logic gates, through combinational circuits (multiplexer, adder, decoder, etc.) to sequential systems (flip-flops, memories, etc.)
5. Automatic regulation. Systems and feedback theory. Analysis of the stability of feedback systems. Bode plot, Roots placement, Nyquist, PID regulators.
6. Digital systems. Internal study and programming of microprocessors and microcontrollers.
7. Instrumentation. Measurement bridges, voltage and current references, instrumentation and isolation amplifiers, ADC and DAC converters, transducers and physical magnitude sensors (NTC, RTD, thermocouples, strain gauges, etc.).
8. Manufacturing technologies. PCB manufacturing. PCB. THT and SMD Components, welding techniques, Trace techniques, Hybrid circuits. Silkscreen printing. Etc.
9. Industrial computing. Structured programming in high-level languages. Modeling of graphs and Petri nets. Semaphores, messages, synchronization of concurrent tasks. Producer-consumer problem. Real-time operating systems. Etc.
10. Power electronics. Both with linear and switched power circuits.
11. Industrial PLC. Robotics.
12. Communication and data transmission networks.

You can choose one of your liking and start experimenting with it.
« Last Edit: July 17, 2024, 04:24:24 pm by Picuino »
 

Offline rstofer

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Re: How does one "learn electronics"?
« Reply #27 on: July 15, 2024, 07:19:27 pm »
You can do a lot with Arduino-type controllers and pre-built modules, but that's not exactly "learning electronics".  If you want to learn programming, networking, and interfacing then these are a great way to start, but I would suggest starting with simple analog circuits: resistors, capacitors, transistors, op-amps, etc.  The Arduinos and Pi's come later.

If the OP wants to study capacitors, a signal source is required.  The Arduino can supply a square wave and this may be adequate for studying the forced response (RC time constant). It would still require a scope unless the constant is very long where a decent DMM may be adequate.  How about an Arduino Oscilloscope project - check Google...  There are also some Arduino Signal Generator projects - check Google...  There are at least 2 themes here.

I should put in a plug for Digilent's Analog Discovery 3 - a decent lab in a small box.  This is a very powerful tool for learning (and beyond)

https://digilent.com/shop/test-and-measurement-devices/essential-instruments/analog-discovery-3/

Don't make the mistake of assuming this is a toy.  It's quite capable!



« Last Edit: July 15, 2024, 09:50:36 pm by rstofer »
 

Offline tggzzz

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Re: How does one "learn electronics"?
« Reply #28 on: July 15, 2024, 07:23:48 pm »
There's no better way to understand electronics than working with a physical circuit.

That's half of it. You also need the fundamental theory.

One simple example: just playing around with an IQ signal generator won't lead you to understand where and why they are useful. For that you need to understand the maths.

"Theory without practice is mental masturbation. Practice without theory is blind fumbling" - me :)
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Offline SteveThackery

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Re: How does one "learn electronics"?
« Reply #29 on: July 15, 2024, 08:28:28 pm »

That's half of it. You also need the fundamental theory.


Yes, but the OP is doing pre-university prep work. Electronics theory fundamentals is pretty tough to self-teach, especially from a cold start. As such I think he'd be better leaving most of that to the university course.  The suggestions discussed above are excellent, in my view, and ideal for the pre-university stage.
 

Offline tggzzz

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Re: How does one "learn electronics"?
« Reply #30 on: July 15, 2024, 08:52:29 pm »

That's half of it. You also need the fundamental theory.


Yes, but the OP is doing pre-university prep work. Electronics theory fundamentals is pretty tough to self-teach, especially from a cold start. As such I think he'd be better leaving most of that to the university course.  The suggestions discussed above are excellent, in my view, and ideal for the pre-university stage.

Fair comment, but it doesn't change the point. If nothing else the practical experience should encourage the OP to realise why theory is important, and to understand "in theory the practice is the same as the theory, but in practice it isn't".

It should also inoculate him against the too frequent statements that practice is more important than theory.
There are lies, damned lies, statistics - and ADC/DAC specs.
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Online fourfathom

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Re: How does one "learn electronics"?
« Reply #31 on: July 15, 2024, 08:59:58 pm »
I was "learning electronics" in elementary and jr. high school, and I guarantee that I learned a lot without knowing advanced math and physics.  OK, I suppose it was more "learning electricity", but I did gain a very basic knowledge of vacuum tube operation, Ohm's Law, etc.  It was many years later that I would consider myself an engineer, but there is no reason not to start out along the hobbyist / technician path.  So don't assume that you need a rigorous theoretical understanding before you can begin doing practical electronics projects.  The rigor can come later.  We all learn differently.
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Offline tggzzz

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Re: How does one "learn electronics"?
« Reply #32 on: July 15, 2024, 09:59:10 pm »
I was "learning electronics" in elementary and jr. high school, and I guarantee that I learned a lot without knowing advanced math and physics.  OK, I suppose it was more "learning electricity", but I did gain a very basic knowledge of vacuum tube operation, Ohm's Law, etc.  It was many years later that I would consider myself an engineer, but there is no reason not to start out along the hobbyist / technician path.  So don't assume that you need a rigorous theoretical understanding before you can begin doing practical electronics projects.  The rigor can come later.  We all learn differently.

I presume the OP is interested in "understanding electronics" at least as much as they are interested in "learning electronics". Understanding requires the theory. If you don't understand the theory then you are left with "cargo-cult engineering".

I started with the Philips EE20 kits. The instruction manuals were divided horizontally, the top half was the theory of operation, the bottom half the practical circuit and components. Now at maybe 10yo I realised I didn't understand all the theory, but it made me understand what I wanted and needed to know.

Realising I couldn't create novel circuits or reliably modify existing circuits without theory was a critical revelation.

« Last Edit: July 15, 2024, 10:39:26 pm by tggzzz »
There are lies, damned lies, statistics - and ADC/DAC specs.
Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".
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Offline shabaz

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Re: How does one "learn electronics"?
« Reply #33 on: July 15, 2024, 10:58:41 pm »
By chance, I still have one of my first-year lab write-ups. It might look boring to someone who has yet to start their course and perhaps expects immediate exposure to a variety of microchips and so on, but there are reasons behind it all. Probably the first year of college/university might only involve a few construction projects, and a lot of the practical lab work may well just be experiments to support the theory learning.

Some of the first-year practical element may seem trivial, but there's a method to it; for instance, in another practical lab, we had to assemble a simple mains transformer power supply (to teach us a tiny bit of construction techniques, how to use a simple voltage regulator, and how not to electrocute each other for a better future). Not every person had encountered tools, safe ways of working, and so on, so it was important.
 

Online fourfathom

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Re: How does one "learn electronics"?
« Reply #34 on: July 16, 2024, 01:02:18 am »
Understanding requires the theory. If you don't understand the theory then you are left with "cargo-cult engineering".

I started with the Philips EE20 kits. The instruction manuals were divided horizontally, the top half was the theory of operation, the bottom half the practical circuit and components. Now at maybe 10yo I realised I didn't understand all the theory, but it made me understand what I wanted and needed to know.

Realising I couldn't create novel circuits or reliably modify existing circuits without theory was a critical revelation.

There are different levels of "theory", and there is plenty of respectable, reliable, and novel design you can do without a deep understanding of solid state physics, linear network analysis, etc.  I hope you don't apply the "cargo cult" pejorative too broadly, because then I would be compelled to strongly disagree with you.
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Offline tggzzz

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Re: How does one "learn electronics"?
« Reply #35 on: July 16, 2024, 08:44:06 am »
Understanding requires the theory. If you don't understand the theory then you are left with "cargo-cult engineering".

I started with the Philips EE20 kits. The instruction manuals were divided horizontally, the top half was the theory of operation, the bottom half the practical circuit and components. Now at maybe 10yo I realised I didn't understand all the theory, but it made me understand what I wanted and needed to know.

Realising I couldn't create novel circuits or reliably modify existing circuits without theory was a critical revelation.

There are different levels of "theory", and there is plenty of respectable, reliable, and novel design you can do without a deep understanding of solid state physics, linear network analysis, etc.  I hope you don't apply the "cargo cult" pejorative too broadly, because then I would be compelled to strongly disagree with you.

To be provocative, when it comes to software I partially agree with your first sentence - but your last sentence is too optimistic. All you have to do is look at the many gross software failures at all levels, from language designs to final systems :(

Simple example about network analysis. A vital key is the concept of superposition, and that requires understanding the components' equations must be of the form y=mx+0. After you understand that you realise why so much component characterisation and analysis is based on finding linear approximations, and hence large-signal vs small-signal analysis and operation. Without the theory, large-vs-small is a hidden mysterious topic.

Without that you end up with people that think that the resistance of a component is defined to be V==IR. Such people cannot comprehend that negative resistance exists and is useful - both conceptually and for basic circuit operation. I've been in long discussions with people on this forum about that; they can just begin to see the glimmer of a cell's V-I characteristics, but a diode's resistance is "dynamic small signal" resistance is too much for them, and they cannot even begin to do anything with the V-I characteristic of a tunnel diode (e.g. looking at the V-I graph, for V=V1, what is the current and resisitance :) )..
« Last Edit: July 16, 2024, 09:01:10 am by tggzzz »
There are lies, damned lies, statistics - and ADC/DAC specs.
Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".
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Offline tggzzz

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Re: How does one "learn electronics"?
« Reply #36 on: July 16, 2024, 08:48:57 am »
By chance, I still have one of my first-year lab write-ups. It might look boring to someone who has yet to start their course and perhaps expects immediate exposure to a variety of microchips and so on, but there are reasons behind it all. Probably the first year of college/university might only involve a few construction projects, and a lot of the practical lab work may well just be experiments to support the theory learning.

Some of the first-year practical element may seem trivial, but there's a method to it; for instance, in another practical lab, we had to assemble a simple mains transformer power supply (to teach us a tiny bit of construction techniques, how to use a simple voltage regulator, and how not to electrocute each other for a better future). Not every person had encountered tools, safe ways of working, and so on, so it was important.

Agreed.

In my first two weeks we were taught Thevenin, Norton, and resistor networks. I confidently skimmed the material, having done many things like that before.  I then fell flat on my face during a self-assessment test, because I hadn't appreciated the subtleties of what a "linear system" means in this context. Yes y=mx+c is a linear equation, but for the vitally important concept of superposition to apply, c==0.

That quick lesson was invaluable: I realised I couldn't just drift and had to apply myself to detailed understanding. The alternative was that I would have learned that lesson far too late for me to be able to recover.
There are lies, damned lies, statistics - and ADC/DAC specs.
Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".
Having fun doing more, with less
 

Online fourfathom

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Re: How does one "learn electronics"?
« Reply #37 on: July 16, 2024, 03:55:08 pm »
but your last sentence is too optimistic. All you have to do is look at the many gross software failures at all levels, from language designs to final systems :(

I'm going to let this drop now, because we agree much more than we disagree.  But looking at gross failures in any field can reveal that theoretical knowledge is insufficient and sometimes secondary to other factors.  I've known highly-educated engineers who were hopelessly inept when it came to actual original design work.  I think the creativity / skill / knowledge spectrum is fascinating, but this probably isn't the place for that discussion.
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Offline Old Printer

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Re: How does one "learn electronics"?
« Reply #38 on: July 16, 2024, 04:06:20 pm »
The Art of Electronics and it's accompanying lab book are a great resource, and well organized to keep you from wandering off in a bunch of different directions. That was my problem with the self-taught approach, I am easily distracted when I see another interesting topic. Lots of wasted time back and forth. Buying those books new is very expensive, but if you look at used book sources they can be had cheaply if you look for older editions, and the basics haven't changed much. I bought a set of the 2nd edition (silver cover) in pristine condition for about $40 US shipped from a used online book seller. If you can find an old Analog Discovery (black case) they are very close to the current offering and a very useful learning tool. I picked up one on ebay a few years ago for $50.
 

Offline tggzzz

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Re: How does one "learn electronics"?
« Reply #39 on: July 16, 2024, 06:13:00 pm »
but your last sentence is too optimistic. All you have to do is look at the many gross software failures at all levels, from language designs to final systems :(

I'm going to let this drop now, because we agree much more than we disagree.  But looking at gross failures in any field can reveal that theoretical knowledge is insufficient and sometimes secondary to other factors.  I've known highly-educated engineers who were hopelessly inept when it came to actual original design work.  I think the creativity / skill / knowledge spectrum is fascinating, but this probably isn't the place for that discussion.


Thanks for recapitulating and for emphasising the point I made earlier in this thread...

There's no better way to understand electronics than working with a physical circuit.
That's half of it. You also need the fundamental theory.
...
"Theory without practice is mental masturbation. Practice without theory is blind fumbling" - me :)
There are lies, damned lies, statistics - and ADC/DAC specs.
Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".
Having fun doing more, with less
 

Offline Zenith

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Re: How does one "learn electronics"?
« Reply #40 on: July 16, 2024, 08:55:37 pm »
You can approach electronics as putting things together with a minimum of maths, (Ohm's Law is useful), or as a branch of Applied Mathematics, with no need to dirty your hands with so crude a thing as a soldering iron.

The best way has to be somewhere in the very wide space in between.

I can't add much to the excellent advice you've been given so far, apart that side cutters, snipe nosed pliers and a wire stripper make life easier. The wire strippers save your front teeth. Cheap side cutters will do, the expensive ones are expensive for good reason. An oscilloscope is a very nice thing to have.

A solderless bread board is handy within limits. I'm waiting for the hate to flow here. They do let you assemble simple circuits, change them, rip them down and reuse it all. Use them for anything complicated (more than ten components), especially when they've had a lot of use, and they throw up problems.

Soldering: easy if you are using new parts, a new PCB and new solder (60/40 tin/lead) and have one of those little copper turning things to clean the bit. You tin the iron with solder, dip the tip in the cleaner, apply the tip to the two parts to be joined, then feed the solder  to the intersection between the bit and the work. It works like magic - with practice.

Old parts with tarnished leads need cleaning up - I use 1000 grade wet and dry paper. Old prototype board needs cleaning - I use an abrasive block for cleaning home made PCBs. Old solder may need cleaning to remove the surface oxide - I pull it through a handful of toilet roll a few times.

Good luck on your voyage of discovery!
 

Offline tggzzz

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Re: How does one "learn electronics"?
« Reply #41 on: July 17, 2024, 12:15:27 pm »
You can approach electronics as putting things together with a minimum of maths, (Ohm's Law is useful), or as a branch of Applied Mathematics, with no need to dirty your hands with so crude a thing as a soldering iron.

The best way has to be somewhere in the very wide space in between.

I can't add much to the excellent advice you've been given so far, apart that side cutters, snipe nosed pliers and a wire stripper make life easier. The wire strippers save your front teeth. Cheap side cutters will do, the expensive ones are expensive for good reason. An oscilloscope is a very nice thing to have.

I use side cutters to strip wire. Wire strippers will make your life faster/easier if you have many identical wires to strip. Fortunately I've never used my teeth!

Any working scope is better than none.

Quote
A solderless bread board is handy within limits. I'm waiting for the hate to flow here. They do let you assemble simple circuits, change them, rip them down and reuse it all. Use them for anything complicated (more than ten components), especially when they've had a lot of use, and they throw up problems.

Here's a current thread about problems with a DC circuit https://www.eevblog.com/forum/projects/diode-connected-transistor-has-negative-resistance/msg5574719/#msg5574719
Now that's rats nest construction, but solderless breadboard would have made things worse.

Why? Similar circuit at  https://entertaininghacks.wordpress.com/2024/03/16/practical-traps-with-a-one-transistor-audio-amplifier-solderless-breadboards-and-oscilloscopes/

Quote
Soldering: easy if you are using new parts, a new PCB and new solder (60/40 tin/lead) and have one of those little copper turning things to clean the bit. You tin the iron with solder, dip the tip in the cleaner, apply the tip to the two parts to be joined, then feed the solder  to the intersection between the bit and the work. It works like magic - with practice.

Old parts with tarnished leads need cleaning up - I use 1000 grade wet and dry paper. Old prototype board needs cleaning - I use an abrasive block for cleaning home made PCBs. Old solder may need cleaning to remove the surface oxide - I pull it through a handful of toilet roll a few times.

Good luck on your voyage of discovery!

Good tips.

I use brass turnings, but certainly wouldn't use steel turnings. (Brass and copper are softer than steel).

And have fun, safely.
There are lies, damned lies, statistics - and ADC/DAC specs.
Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".
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Offline rich t

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Re: How does one "learn electronics"?
« Reply #42 on: July 17, 2024, 12:38:05 pm »
I have a bunch of these hackerboxes available: https://hackerboxes.com/products/hackerbox-0102-flea-scope

PM me a mailing address and I'm happy to mail you one free of charge.

The online guide is here: https://www.instructables.com/HackerBox-0102-Flea-Scope/

It takes you thru some basic electronics skills, and then you can build a "simon" game or "morse code trainer" or almost anything else microcontroller'ish that you want -- there are videos and everything.

In addition, you end up with an oscilloscope and logic analyzer (and function generator) which can help you with all other circuits you might build.

-- Rich

PS and if you want to learn about building this kind of stuff for yourself, I have build instructions here: https://hackaday.io/project/192598-flea-scope-usb-oscilloscope-18-18-msps-webusb
 

Offline rstofer

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Re: How does one "learn electronics"?
« Reply #43 on: July 17, 2024, 04:25:29 pm »
One problem with this thread and all similar queries is not having a concise definition for 'learn' from the OP's point of view.  Learn enough for copy-and-paste projects?  Learn enough to design simple circuits by combining information from datasheets or learn enough to design the circuits described by datasheets (real engineering)?  Maybe learn enough to teach the subject at a post grad level?  Perhaps 'learn' implies that Maxwell's Equations flow from your fingertips.

When I think about 'learn', I usually consider 5 years of undergrad as learning.  Clearly, that isn't necessary for hobby level electronics which tends toward copy-and-paste. 

The definition to use in these threads should certainly come from the OP and perhaps the first reply should ask the question:"What do you mean by 'learn'?"  Perhaps the OP is thinking Ohm's Law and we're thinking about Laplace Transforms and Control Systems.

« Last Edit: July 17, 2024, 04:40:36 pm by rstofer »
 
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Offline tggzzz

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Re: How does one "learn electronics"?
« Reply #44 on: July 17, 2024, 04:34:05 pm »
One problem with this thread and all similar queries is not having a concise definition for 'learn' from the OP's point of view.  Learn enough for copy-and-paste projects?  Learn enough to design simple circuits by combining information from datasheets or learn enough to design the circuits described by datasheets (real engineering)?  Maybe learn enough to teach the subject at a post grad level?  Perhaps 'learn' implies that Maxwell's Equations flow from your fingertips.

When I think about learn, I usually consider 5 years of undergrad as learning.  Clearly, that isn't necessary for hobby level electronics which tends toward copy-and-paste. 

The definition to use in these threads should certainly come from the OP and perhaps the first reply should ask the question:"What do you mean by 'learn'?"  Perhaps the OP is thinking Ohm's Law and we're thinking about Laplace Transforms and Control Systems.

There's validity in those points.

It is, of course, difficult for a youngster to distinguish between the different types of "learning", and a beginner to articulate what they don't know. The latter can be helped if the beginner does their best to learn with whatever materials are available, and then to be able to state what puzzles them.
There are lies, damned lies, statistics - and ADC/DAC specs.
Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".
Having fun doing more, with less
 

Offline armandine2

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Re: How does one "learn electronics"?
« Reply #45 on: July 17, 2024, 07:05:53 pm »
Learning from tutors - some may "resonate" or simply demystify, whereas others confuse.

... is it a personal, or cultural affect?


« Last Edit: July 17, 2024, 07:08:29 pm by armandine2 »
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Offline Zenith

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Re: How does one "learn electronics"?
« Reply #46 on: July 17, 2024, 09:49:50 pm »
One problem with this thread and all similar queries is not having a concise definition for 'learn' from the OP's point of view.  Learn enough for copy-and-paste projects?  Learn enough to design simple circuits by combining information from datasheets or learn enough to design the circuits described by datasheets (real engineering)?  Maybe learn enough to teach the subject at a post grad level?  Perhaps 'learn' implies that Maxwell's Equations flow from your fingertips.


Reading the OP' s first post, I think it's obvious where he's coming from. He's in the second half of his teens, he can see the possibilities of electronics, and would like to get things working and would like to understand how and why they work. He has a desire to pursue this through higher education. Most of us were there and can sympathise. He has limited means. So tinkering together things like a simple audio amplifier, or investigating astables, bistables and monostables would be immensely instructive. At one time there were educational electronic toys/outfits that would cover these things. Many of us profited from them.

He has an ambition to make an electronic dice, presumably from discrete parts.  The obvious approach to me was to use a µcontroller,  but that's not basic electronics, and gets us into software.

As for soldering, I gave my best advice, although I'm not entirely sure what a "hot stick" is. It could be anything from a 250W iron to a 12W number, and probably not a soldering station or instant heat soldering gun. I normally use an 18W Antex pencil iron, and manage to struggle by. I have numerous others, useful at times.
 

Offline westfw

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Re: How does one "learn electronics"?
« Reply #47 on: July 17, 2024, 11:33:20 pm »
There are two usual methods:
  • Go through official channels (ie 4-year university degree) to learn theory, and read up on the practical aspects.
  • Do "stuff" (kits, magazines, web, reading, technical school, ham license) to learn practical aspects, and pick up as much theory as you can.
My experience suggests that the degree teaches too much theory (SO MUCH CALCULUS!) and not enough practical stuff, but it is ... helpful ... if you want to be employed in the field :-)
(It was Senior year at my f'ing prestigious Ivy League University that we noticed that some of the EE candidates didn't know how to solder...  But we had analyzed the 555 timer at the transistor level, so I'm sure it was all fine.)

It's vaguely possible that "digital Electronics" isn't really electronics (until suddenly it is!)

Software has similar issues.  They used to teach secretaries "how to code" (in COBOL, of course.  It's mostly typing, you know, and men don't know how to type), and yet I've met CS PhDs who "can't code their way out of a paper bag."
 

Offline Infraviolet

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Re: How does one "learn electronics"?
« Reply #48 on: July 18, 2024, 04:48:50 pm »
"And the Pi has a full blown network stack"
I think this is a clear indication of why, for this scenario the OP would want an Arduino not a Pi (Pi Pico exempted, that is a true MCU and could be just as good as an arduino). If you want to learn electronics an arduino is better for low level interaction with electronic components and circuits, the Pi is for higher level matters like networking with existing hardware.

This is definitely my opinion, but I'd suggest that thesedays, low-level embedded software at the bit-banging and ADC sort of level counts as "electronics" whereas networking enters the realm of "computer science / software enginering / sysadmin stuff". There is definitely a continuum between them, but the Pi is a device you use for operations mid way on that continuum, an arduino compatible MCU is something you use for electronics directly.
 

Offline tggzzz

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Re: How does one "learn electronics"?
« Reply #49 on: July 18, 2024, 05:13:21 pm »
My experience suggests that the degree teaches too much theory (SO MUCH CALCULUS!) and not enough practical stuff, but it is ... helpful ... if you want to be employed in the field :-)

Everybody over here learned calculus before they went to university. In my case our my state school syllabus included integration and differentiation of polynomials (except 1/x) for "O-Level" exams at 15.

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(It was Senior year at my f'ing prestigious Ivy League University that we noticed that some of the EE candidates didn't know how to solder...  But we had analyzed the 555 timer at the transistor level, so I'm sure it was all fine.)

Doctors over here are likely to be incompetent at taking blood samples; they leave that to nurses and phlebotomists. Does that make doctors useless?

Who would you rather have set the standard pathways for cancer treatments - a researcher, a doctor, or a nurse?

Who would you rather have diagnose your disorder - a doctor or a nurse?

Who would you rather have take your blood or apply a plaster cast - a doctor or a nurse?

Does it matter that someone sufficiently skilled to determine a course of treatment can't draw blood safely? No, of course it doesn't.
There are lies, damned lies, statistics - and ADC/DAC specs.
Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".
Having fun doing more, with less
 


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