Dave Curran has a nice build log on his ZX80 clone, which he call Minstrel:
Here is a new ZX80 clone that I have called the Minstrel. It is a fairly accurate clone electrically to the ZX80, using the same chips and the original schematic with only a few concessions to the modern world. All the parts are the same, the part numbers and pins are the same, other than the ROM and RAM, I’ve only added a few extra decoupling capacitors and a one resistor / one transistor composite video amplifier.
More info at Tynemouth Software blog.
