What are the formal paths to expanding my understanding of circuit design?

Going back to school for a degree in Electrical Engineering is the obvious path I see. But perhaps there are others that I'm not seeing? Are there trade schools that would be helpful in this regard? Other possibilities?

Assume for the sake of this post that I'm specifically interested in formal approaches, and set aside the wealth of information available on the internet.
 
Practically speaking, just study the Art of Electronics book. The second edition is best for a beginner,
and the third edition is best for the more advanced student.

Circuit design per se is not really the primary focus of EE, rather it is understanding the fundamental principles.
This is because technology changes rapidly, and so the circuits that will be used will also often change.
Many first and second year students end up looking elsewhere, because they did not realize the levels of math required in EE.
 
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Apart from the Art of Electronics I learned a lot from both books of Sergio Franco (Analog Circuit Design; Design with Operational Amplifiers). Lot of formulae in there, but plenty of worked examples, which really helped me in getting the concepts on a more quantitative way.
 
I agree with Rayma above: most, if not all, of the curriculum is about analysis, not synthesis. And you may find that a lot of the topics are not worthy of interest. I spent most of my 4 years locked up in the library and reading everything I could lay my hands on.

But since you mentioned "formal", I must admit a MS is kind of an entry level to pass the human resource gatekeepers. So, if you're thinking of a career, i.e., job hunting, get ready to grind your teeth.
 
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I enrolled on a City and Guilds electronics course in 1980.
It covered basic electronics.
However that just got me a job testing and repairing electronic equipment.
If you want to go into design then you really need a degree or higher.
I stuck at it for a couple of years then got moved into software department as I knew the Z80 processor well.
I did a year of programming then left to become a electronics design consultant.
I did that for 13 years and learned a lot from taking on numerous design projects.

I now work for myself designing hardware and software.
 
I agree with Rayma above: most, if not all, of the curriculum is about analysis, not synthesis. And you may find that a lot of the topics are not worthy of interest. I spent most of my 4 years locked up in the library and reading everything I could lay my hands on. But since you mentioned "formal", I must admit a MS is kind of an entry level to pass the human resource gatekeepers. So, if you're thinking of a career, i.e., job hunting, get ready to grind your teeth.

The voice of experience. An engineering education is best viewed as an opportunity for self-education
while earning a formal degree. This will be the only time during your career that you will have the time
and discretion to do so. Take maximum advantage of this.
 
I spent a couple of years after getting my EE repairing music gear (not many jobs in my home town), which turned out to be a pretty good post-graduate education in how to, and how not to, design stuff. I still fix my own gear -- the latest was a used parametric equalizer rode hard & put up wet before I got it -- and seeing how other people approach problems can be fun. Then there was the subwoofer which made farting sounds, maybe because the power supply capacitors were bulging. That'll happen when you put 35 volt caps on a 36 volt supply right beside a class-AB heatsink. Oops.

Open eequipment before even plugging them in violates the warranty? Why would I do that? (hide screwdriver)
 
Maybe the future of education is in the Advanced Studies (Certificate (CAS), and Diploma (DAS)).
The way I see it: pick a topic you really like or need, and drill down as deep as you can. You can pick as many topics as you want, collect the credits, and exchange them for a degree.
The deal breaker is, at least currently, a master is required for admission. However, depending on where you are, this requirement is not necessarily enforced. I used to teach a Data Science module, and I'm pretty sure half of my students don't have it.
A few years ago in Switzerland, they introduced the COS (Certificates of Open Studies): no prerequisites, study online, and still get credits. Maybe this is the answer; we'll see in a couple of centuries given the metabolism of academia.
 
Here is a link to an entire series of electronics courses from the U.S. Navy for it’s electronics technicians. They are freely available for public use.

http://www.compatt.com/Tutorials/NEETS/NEETS.html

That said, I recommend that you take an instructor lead course from a local trade school if possible. Such schools typically offer training programs from certificate level, up to 2-year Associate Degree. They typically offer part-time programs and night classes, as well as full-time day classes.
 
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In addition to TAOE, older editions of textbooks are really inexpensive, and just as good as current (no pun...) editions for learning (among other things) the basics of DC and AC circuits. See if you can find the titles and authors of textbooks used in various EE college curricula.

Looking over a variety of circuits (with their descriptions, if at all possible) has always helped me, and it helped that I had an interest in this in high school (and an electronics class in high school). Heathkit assembly manuals may not be easy to find, but each has a schematic and a "circuit description" section that's well worth reading over. There's seven volumes of "Encyclopedia of Electronic Circuits" - each book has maybe a couple hundred schematics, each schematic has a description, often too-short but still instructive. Earlier volumes (and textbooks) are inexpensive enough on bookfinder.com.
electronics courses from the U.S. Navy ...
Had a quick look at Module 2 on AC and p.1-4 has a "SIGN WAVE" made of what looks more like semicircles than a sine wave. Hopefully it becomes more accurate later on when it's important.
 
Starting with Ernst Nordholt's Ph. D. thesis Design of high-performance negative-feedback amplifiers in the early 1980's, people from the Delft university have written some interesting books about the systematic design of circuits, particularly preamplifiers (not specifically audio preamplifiers, just anything that is connected to some sort of low-level signal source). The interesting thing about them is that they are not just catalogues of known circuit topologies. They are all for advanced students, though.
 
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Had a quick look at Module 2 on AC and p.1-4 has a "SIGN WAVE" made of what looks more like semicircles than a sine wave. Hopefully it becomes more accurate later on when it's important.
Evidently, the depictions are sufficient to help teach the fundamentals radar systems, sonar systems, ship board communication and navigation systems, etc. So, I will risk supposing they are also sufficient to teach audio.
 
... people from the Delft university have written some interesting books about the systematic design of circuits, particularly preamplifiers (not specifically audio preamplifiers, just anything that is connected to some sort of low-level signal source). The interesting thing about them is that they are not just catalogues of known circuit topologies. They are all for advanced students, though.
Thank you Marcel!! Can you recommend a place where students can find a large collection of these interesting books about the systematic design of circuits? I tried repository.tudelft.nl but came up with zero search hits on any of the sub-pages, looking for "electronics" and/or "circuits".

I found Nordholt's thesis as a used book on Amazon and just purchased it.

Gratefully, --MJ
 
Assume for the sake of this post that I'm specifically interested in formal approaches, and set aside the wealth of information available on the internet.

I think it's a mistake to intentionally ignore EVERYTHING on the internet. For example, the "Open Courseware" videos of classroom lectures given at MIT, are truly excellent. If you want to design amplifiers for a living, for example, you had better master one hundred point zero percent of the material taught in (this series of videos) by Professor James Roberge, entitled "Electronic Feedback Systems". Even if you enroll in a fulltime four-year EE curriculum at another university, Jim Roberge still has much to teach you. And it's free.
 
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Thank you Marcel!! Can you recommend a place where students can find a large collection of these interesting books about the systematic design of circuits? I tried repository.tudelft.nl but came up with zero search hits on any of the sub-pages, looking for "electronics" and/or "circuits".

I found Nordholt's thesis as a used book on Amazon and just purchased it.

Gratefully, --MJ

No, I can't, but I can be more explicit about what books I mean.

After Nordholt's thesis, several people have tried a similar approach to other circuits, or to further systematize Nordholt's approach. To name a few:

Ph. D. thesis of Hans Stoffels on (partly) automatic amplifier design: J. Stoffels, Automation in high-performance negative feedback amplifier design,
https://repository.tudelft.nl/islandora/object/uuid:95f67f55-2942-4d5d-b9a2-03fab6099299
It's not just about optimizing values in a given topology, but also about generating topologies. As far as I know, his program does so interactively rather than fully automated. Mind you, Hans is a colleague of mine and he never uses his own program. He says that in practice there are too many vague constraints.

C. A. M. Boon, Design of high-performance negative-feedback oscillators, https://repository.tudelft.nl/islandora/object/uuid:081e592e-d3da-44b7-9c41-5ade42bb258d
Method to split the non-linear part of an oscillator with non-linear amplitude stabilization from the amplifying part, so both can be optimized independently.

Arie van Staveren, Structured Electronic Design of High-Performance Low-Voltage Low-Power References, https://repository.tudelft.nl/islandora/object/uuid:745807c5-76cd-40f2-b2f0-451cba22a36a

Chris J.M. Verhoeven, Arie van Staveren, G.L.E. Monna, M.H.L. Kouwenhoven, E. Yildiz, Structured Electronic Design: Negative-feedback amplifiers, only available as an expensive book as far as I know

Anton Montagne, Structured Electronic Design: A conceptual approach to amplifier design

I never read those last two books, only browsed through them, but knowing the authors, they must be pretty good.