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There appears to be a great deal of interest in understanding basic electronic circuits, and the hobby level design of such. A most important resource necessary for the casual dabbler in electrical and electronic systems is, of course, a good entry-level text. A very good resource can be found at http://www.allaboutcircuits.com/, either for perusal on line, or downloadable in *.pdf format. These series of documents begin with basic electromagnetic theory and work through some basic circuitry.
These volumes also provide a great introduction to SPICE (Simulation Program with Integrated Circuit Emphasis), which is actually one of the granddaddies of OpenSource software, being released as a Public Domain project long before anyone knew what OpenSource meant. Originally developed in the early 1970's at the Electronics Research Laboratory of the University of California, Berkley, SPICE simulation programs combine component models (resistors, transistors, capacitors, IC's, etc) and their interconnections into a "netlist". The component models and netlist are generally ASCII text files. The simulation machine then uses the netlist to build a mathematical model to be solved. (the original SPICE did not include a GUI and schematic capture , having been developed before sophisticated graphics capabilities were available, and produced the output in pages and pages of tabulated data). For the most part, component models and netlists can be developed on one package and analyzed on another, although there are some exceptions to this.
Vendors of commercial software packages and the various free packages available have added schematic capture front-ends to SPICE from which the netlist is automatically generated. In addition, graphing utilities have been added to see waveforms and graphs of circuit parameters. My favorite for years has been a free version of National Instruments Multisim (available free, for instance, from Analog Devices- other component manufacturers have similar packages available to support their product lines). One of my favorite features of Multisim is that the GUI provides graphical models of measuring equipment, such as DMM's or oscilloscopes, that simulate the actual connection and appearance of the instruments (including, for instance the time base and trigger settings for the oscilloscope, which can be quite helpful for the newbie).
Pspice is another popular package (available in a free limited version here). One can find a list of additional free schematic capture and simulation programs here. These packages are usually very well documented and easy even for the newbie to grasp.
The limitations of a free package from a component manufacturer are that component models are generally limited to models of the manufacturer's products (plus a few standard components available in all packages), and size limitations on the circuits one can design (generally not a limitation for the amateur in that the number of elements and sub-circuits allowed are generally quite generous). One can expand one's library either by downloading models from device manufacturers (such as the TI device model library), or, if you are sufficiently advanced in your capabilities, you can edit one of the generic models to more closely match the parameters of the device you want to model.
Most of these packages are available primarily for Windows environments, but those of us living in the OpenSource world (i.e., Linux) have options as well. A lot of the packages will run in a virtual machine such as VirtualBox. A native basic package for Linux that is easy to use and provides the essentials of schematic capture and simulation of simple circuits is called Oregano. Unfortunately, my attempts to link to the developer web site have ended in broken links, suggesting that the development team may no longer be active, but it is still available *,deb package from Ubuntu, and possibly for other distros as well. Www.sourceforge.net still offers the package in *.tar-gz format, although it appears the last update was back in 2004. Here is a sample screen shot of the schematic capture from Oregano:

And a shot of the simulation results:

The the next option we look at is a bit less integrated, but more flexible. The gEDA suite, which includes a schematic capture package (gschem), with a more extensive parts library. However, once the schematic is created, one then must use another program, such as EasySpice or Gspice to do the actual simulation.
Scilab, a "numerical computation package providing a powerful computing environment for engineering and scientific applications", includes a simulation package known as Xcos, an editor designed to build models of hybrid dynamical systems. It is based on the older Scicos developed at INRIA (Institut national de recherche en informatique et en automatique, or, in English, The National Institute for Research in Computer Science and Control, created in 1967 and originally housed at SHAPE, central command of NATO military forces). Scicos may still be encountered in older versions of Scilab, and is still available as a stand alone package. Models are assembled, loaded, saved, compiled, and simulated, using the Xcos GUI. Xcos serves as an interface to the various block diagram compilers and the hybrid simulator scicosim. A sample screen shot from the web site:

Once you have designed and simulated your circuit and determined that it actually does what you intend it to do, it is time to build it. We will assume you have already breadboarded the circuit and proved that it works as the simulation says it does. Now you want to convert it to a printed circuit board. One can always use what are called prototype boards, printed in a variety of patterns and styles (available from your local electronics hobby shop or on line at DigiKey):

or you can build a customized printed circuit board specific to your project. The gEDA project includes a package called pcb which will help you optimize the layout of your circuit, or there is another package called eagle from Cadsoft (available in freeware version). The output from these files is something called a Gerber file, which can be sent off to someone like Sunstone Circuits, or if you are really adventuresome, you can print your own circuit board, using a print of the graphic image created in your layout software as a mask for etching the board. Vendors such as Digikey offer a variety of such kits to suit most any budget, or here is a set of instructions to follow to "roll your own".
The Internet is inundated with many other resources, such as the Analog Circuit Library from Analog Devices that provides a collection of "tested circuit designs that address common design challenges and have been engineered for quick and easy system integration", and many sources of free circuit designs such as http://www.electronics-lab.com/, where "you can find useful circuits with full description, diagrams...electronics articles, links and downloads."
We have only scratched the surface here, and I am sure we have missed most of your favorite electronics sites. Join in with your own recommendations and suggestions!
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