One of the most useful features of the Boss TAE is the built-in power amp. It enables the TAE to deliver a very consistent sound regardless of volume level – a feat that traditional attenuators struggle with. It also enables a lot of other capabilities such as easily adding a master volume, reverb, and an effects loop to amps that don't have them.
But there are a couple of nuances to the built-in amp that aren't readily apparent.
First, the manual makes it very clear that the impedance settings on the TAE and your tube amp must match. Not doing so can damage your amp! But what about the speaker cab you connect to the TAE's power amp? Does that have to have the same impedance?
The answer is no. The Tube Amp Expander presents the proper load to your tube amp so long as its impedance switch is set correctly, regardless of the speaker cabinet impedance. The TAE’s sold-state power amp deals with its load (the speaker cabinet) completely independently and any cab rated between 4 and 16 ohm will work.
This is great because it means that you can set your tube amp and the TAE to 16-ohms, which will reduce the likelihood of input signal overload, and still use your 4- or 8-ohm cabinet with the TAE's built-in power amp.
For that matter, you don’t have to connect a speaker cab to the TAE at all if you don’t need it. This is handy when you're recording and you want to listen to everything through your studio monitor, or if you're simply want to play your amp through headphones.