Hello guys recently I bought the A4 B5 2000 1.6 AHL engine.

The car has a rough idle problem, once it gets warmed up it randomly stars shaking and running rough only when idling at the stop-lights and at random intervals. The RPMS don't get too low it has never shut off, it's more of a pulsating rough idle that lasts until I give it some gas and goes back to normal for a few seconds or minutes.

I don't know if it feels sluggish as I just bought it, but throttle input is perfectly fine when giving some beans when it'd shaking and I don't feel any hesitation.

As basic maintenance I changed the spark plugs wires as they were arcing slightly and I changed the spark plugs because they were buggered. No check engine light is on.
Sometimes when engine braking or coasting I can hear slight pops coming from the exhaust.

TD:lr

Car shakes when idling when warm randomly, normal throttle input, new spark plugs and wires, no check engine light.

 

Did you look at coil connections? You can swap coils between 2 cylinders to verify the coil is ok. The symptoms are what happen when you lose a cylinder. #2 in my case. Pretty sure the wiring and/or connector to coil has gone bad. Take a close look at connectors and wire. If connector keeper is missing that could cause it. I peeled a bit of harness back and all 3 wires are that peculiar shade of scorched brown. The same color as melted wiring inside ignition switch on column. MAF might have something to do with it and easy enough to clean. Another thing to see about is injector if/when you nail it down to a specific cylinder. The coil wiring harness travels over top of engine and is subject to constant heat, vibration and occasional THUMPS. Tiptronic on mine won't do the Tip gear changes. Starting from a stop is extremely sluggish and hesitant until about 2800rpm where turbo kicks in. Still wraps up into 5k range but can tell it is much slower than when I bought it with the melted wires inside ignition switch assy. Babble OFF.
Does your year have a 3 or 4 prong connector at coil over spark. 98 has 3 and very hard to find. Good luck with it.