A young volunteer at work has recently gotten a real interest in learning basic electronics and has been building little circuits left and right. It took me back to my early days as a sound nerd. I had a book on basic electronic theory, a bread board, and boxes of components that I had yanked out of dead electronics. I read that book over and over again. I never managed to do much more than build a rudimentary distortion pedal for my guitar, but the interest stuck with me and resurfaced many times over the years.
Later on in college I found myself troubleshooting computers down at the component level, usually just to figure out which card or board had gone bad to order a new one, but my previous experience served me well. Then as I was developing my skills as a budding audio engineer, knowing what went on inside a transistor helped me get a grasp on what gain stages were actually doing. Studying up on tube gear as a ham radio enthusiast was where I really started to grasp what was going on inside all my gear.
These days with the proliferation of the internet and sites like instructables.com it's incredibly easy to look up circuit designs and find help building your own. And while Radio Shack still has a few components on hand, with mega suppliers like mouser.com you can order just about everything under the sun. Things get even more exciting with the advent of small processing packages like the Arduino and even credit card sized computers like the Raspberry Pi. A crafty inventor could have a key chain RTA or build his own wireless amp rack monitoring system that talks to his phone.
But the real reason I'm writing this is to encourage you to learn what's going on inside the most basic components inside your gear. It's not easy, and a lot of times it will take reading and re-reading the same material before you really get it. To this day I find myself finally understanding things I started to look into over twenty years ago.
To get you off on the right track, start out with the transistor and it's precursor the vacuum tube. The concepts involved stretch from the tiniest preamp to the largest power amp. Knowing how gain stages behave can really help you get in touch with a system, especially if it's not an ideal one and parts of it are being pushed to the limit. You'll likely get to know power supplies along the way, another worthwhile subject. After that take a look at filters. You can build everything from an EQ to a crossover and a lot of stuff in between with just a resistor and a capacitor. Filters are fascinating circuits. Learning how they interact with a signal can really take you to the next level as an engineer.
Which brings me back to a concept that I've written about before. Audio is the only occupation where some one can call themselves an engineer without actually having a degree in the subject. For that reason there are a lot of people out there giving us a bad name. People that just push faders and turn knobs should call themselves mixers or sound techs. It's the people who are inquisitive about the gear they use and work on not just the art of mixing but the science of the technology that are the real engineers, diploma or not.