I've asked other questions about having a career in electronics without an EE degree. I'm wondering specifically about being an analog IC designer. What would it take to land a position doing that before having that degree? What would convince an employer to hire me despite lacking that piece of paper? What kind of employer would I best off sending my resume and other info to?
The fastest route would be to get an EE degree, then a Masters specializing in analog IC design. I can't imagine how you'd work your way up in less time, or that many companies would give you the opportunity. Most analog IC designers have advanced degrees, and so there is a high barrier of entry. A BS in EE actually provides very little in the way of analog IC design, and unlike things like programming, you can't really build an impressive resume hacking away in you're mom's basement. The amount of money you have to drop for getting your own designs fabricated would be better spent on a degree. Analog IC design is something where the "piece of paper" really comes in handy. If you can't devote all your time to schooling, try getting a job at a tech company and go to school part time. They may help pay for some of your education.
I have an MSEE and spent around 15 years doing analog IC design for several companies including large multinationals and a few startups (especially around 1999-2000). I don't do that kind of work anymore because it has largely been outsourced to cheap but highly qualified labor in India (mostly) and China (more recently). A few years ago, my department head finally told me he had more Phds than products he needed to be designed and since I didn't have a Phd, he could no longer let me do analog design anymore (Phds like to do this kind of work because they can publish papers and eventually most hope to move on to teaching. But don't worry, there are plenty more coming in the pipe all the time to take their place). This even though I had a proven track record of high quality design work and many products in production. Not sure why you would want to go down that path at all and certainly can't imagine anyone hiring someone for that kind of work with no degree. The field is very mature, highly theoretical (which is why the emphasis on an advanced degree - you're not going to learn that on the job), heavily outsourced and with few entry level openings. The large US multinational I last worked for hires mostly at their Asia design centers. Any US based hiring (which has been almost nil for the past 3 years and included huge layoffs of top experienced people in 2009) is highly targeted to specific tasks with solid qualification requirements. I think you might want to look at a different line of work. Maybe one hope is if you happen to speak Mandarin and are willing to work in sales and are familiar with Asia, that could be a possible back door way in. Not kidding. Good luck.
Is it possible? Absolutely!
Are you going to get a job doing full-blown IC design straight off the bat? No.
The best (and really only reliable) way to get a job doing high-level engineering without a related degree is to work your way up the chain.
Basically, get a job doing scut-work at a IC design company. Ask lots of intelligent questions, do lots of reading, and try to make intelligent suggestions. Assuming the company you work for is at all open to new talent, eventually you should be able to start working on more advanced topics.
Take your time, work your way up, and learn as much as you can as you go.
Now, the viability of this sort of approach is highly dependent on how rigid the corporate structure at the place you work is. A rigidly structured organization is less willing to consider people without degrees, but a lot of it just depends on the people you are working with.
Personally speaking, it's how I got my current jobs (Consulting/Board layout/CAD).
The only thing I can think of outside of what is mentioned above would be to dive into a program like Electric, teach yourself how to use it (hopefully with guidance from an experienced engineer), make some kind of awesome and before unseen circuit, and finally get it in the hands of someone who matters and has the ability to hire you.
Jeri Ellsworth took a similar path with digital (granted, which has lower entry costs and less need to be near the process node and device physics) but did not have any education. She stated in a recent interview that it was all because of mentors. So in the event you think it's something you'd really want to do, that'd be a first step. Even with a MS, a good mentor will get you farther than anything else IMHO.