This walks through how to diagnose and fix the most common cause of a shaking engine in a 2007 VW Passat with a 2.0T FSI engine. Some professionals would recommend all coils be replaced when one goes bad, to reduce the expense and inconvenience of a callback when another coil fails. It’s important to think through the causes of why a coil would fail, and specifically look at the plugs and probably replace all at the same time.
Without a scan tool this is not an easy procedure in this engine, because the short harness does not allow coils to be removed one at a time in a cylinder balance test. However you don’t need an expensive scan tool to do this procedure. Even a code reader would give clear guidance if swapping coils results in movement of the problem to a bystander cylinder.
Off camera I did do resistance testing on the bad coil and I found no difference compared to the other coils on the engine. It's possible that a scope might show a difference in current ramps and waveform analysis, but scope work is usually reserved for coils that pass a cylinder swap test to be sure the signal from the PCM is intact.
The useful thing about the swapping procedure shown in the video is that you easily prove that the computer driver, wiring, and cylinder mechanics are OK if you can get the problem to move to a bystander cylinder.
This amateur presentation is offered in good faith, for free, but with no guarantees as to accuracy or safety. DIY Automechanics will always involve risk. Any misadventure you encounter if you decide to accept those risks is on you.