I think coupled output means that the signal goes through it and therefor the sound should be affected. I'm sure Boswell will have a better explanation ;)
Again with my limited knowledge, a transformer can be coupled with the signal at the input or the output or it could only give power to a circuit without any audio getting in it.

We had a thread recently on the next level up, the AT5040 and AT5047, where I talked about a possible reason why AT decided to bring out the AT5047, essentially a transformer-output version of the AT5040. In the case of the 5047, I speculated that they found that the 5040's reliance on the pre-amp performing the summing of the microphone capsule outputs worked well in many cases, but not in all, particularly with non-transformer input pre-amps.

Choosing to couple the microphone output through a transformer allows the designer to present an accurate differential signal to the receiving pre-amp, since the number of transformer turns either side of the centre-tap is a controllable integer, where the voltage output balance between the capsules is not. The transformer will always give the same perfect balance at its output, whether its input is balanced or not.

The imperfect capsule balance may become more apparent with microphone age, as capsules are known to change their output over time. It will be interesting to see how the 5040 ages.

In terms of character, there's less of a difference between similar microphones with and without transformer outputs and pre-amps with and without transformer inputs. It's probably not until you get to a pair of models like the AT 5040 and 5047 that it would be possible to carry out a meaningful comparison test, knowing that the only significant difference between them is an output transformer in the microphone.

Part of the character variation in a pre-amp that a transformer input imparts is due to the transformer almost always being used to give a voltage step-up, so the following circuitry can be quite different in terms of impedance and noise level.

Hey Boswell, do having a transformer also affect how the mic will react to different preamp impedance ? Will impedance changes be more noticeable with or without a transformer ?

You should regard the transformer as just a part of the microphone, and simply make a note of how that microphone sounds with a particular pre-amp and input impedance.

A few years back I got an old SM57 from a boot sale for next to nothing and wondered why it had such a low output and poor LF response. When I got round to investigating it, I found someone had taken the transformer out of it so the output was directly from the moving coil. I tried it with various pre-amps, but they all gave a similar unsatisfactory result. It goes to show that the transformer is a crucial part of a microphone's sound that we have come to know and love.

It's worth noting that a transformer with a turns ratio of N gives a voltage step-up of N but at the expense of an impedance increase of N squared. This would mean that the higher the transformer ratio, the more likely it is to be sensitive to impedance variation at the input of the pre-amp.

thank you for such an excellent explanation.

Transformers also give the highest CMRR possible, making mics less sensitive to external noise, like HF infiltrating from nearby AM transmitters.

Maybe AT released these mics cause the 4040 and 5040 are reasonably popular in classic music recording setups and these guys sometimes use very long cables?