This is an old post, preserved for reference.
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One of the common issues with the ZX81 is the good old RAM pack wobble. Depending on the state of your edge connectors on your ZX81 and RAM pack, it sometimes does not take much to interrupt one or more connections and crash the ZX81.
ZX81 Internal 16K RAM.
ZX81 composite video modification), the input wire is desoldered and pulled back into the modulator, and the resistor connected to the phono socket is desoldered at the top and bent out of the way, and a TFW8B video amp board fitted in the remaining space.
Update - Testing the upgrade:
Once done, time to power up and wait for the K. If all is well, it should take a few seconds longer for the K to appear. You can test it by typing
PRINT PEEK 16388+256*PEEK 16389