Step 1: The Big Idea
Well, we're going to make a solar panel from scratch that can charge up a simple phone.
See, cheap phones like mine are real simple to charge--they just need 5V and they'll take care of the rest. They'll draw as much power as they can (my little nokia will draw up to an amp while charging), but they're smart enough to limit their current draw to whatever the source can provide.
So, that means we need to make a 5V solar panel. Solar panels are made by wiring up a set of solar cells--big silicon P-N junctions. A solar cell puts out a very low voltage--0.65V open-circuit, or around .55V under an ideal load. To get the 5V that we need to charge a phone, we have to wire up a bunch of solar cells in series.
But how many solar cells? Well, a solar cell without anything connected to it will produce .65V in bright sunlight, but as I draw power from the cell, the voltage will drop. This relationship is called an I-V curve. The max current the cell can output is based on the area of the cell, the intensity of the sunlight and the temperature of the cell, but the max voltage is always the same, regardless of the size of the cell.
Every solar cell has a peak power point, a current-voltage combination that gives me the most possible power for that cell. For my panel, I want to run my cells at their peak power point. I happen to know that the peak power point of my cells is .5V at 130mA. So, if I want to put out 5V, I need to stack up at ten solar cells in series, giving me an output of 5V. If I'm drawing less than 130mA, my output voltage will "float" up, and if I draw more, my voltage will get pulled down. Now, it so happens that phones are pretty smart and robust, so I can actually give them a bit more than 5V, and they'll be fine. I'm actually going to add an extra cell, giving me a total of 5.5V coming off my cell. This makes my panel a little more robust--the higher voltage means that, in lower light, it'll still put out enough voltage to charge up my phone, and it'll be less sensitive to shading or pointing it away from the sun.
So, I'm going to make a solar panel with eleven solar cells in series, I'm going to wire the output into a phone, and it's going to charge. Cool, right? It's pretty quick and easy to do, too. Here's a video of the whole process: