Thanks for the detailed answer, I don't use my pc internatl sound card, but a dedicated external soundcard called ID4, from Audient. I guess it havea better dac than my internal soundcard.
Also, in case we're talking about the HD6 which has a dac, I guess there's no reason adding another dac between them to the source? Is there any other logical source to connect to them besides things like phones or daps as AK? Another question - how do I know which dac is being used, the one inside the AK JR or the one inside the HD6? or both are being used? I have no idea how does it work.
This depends on what input on the speaker you connect to.
The HD5+ only has analog input, no DAC. I suppose you connect either through the 3,5mm jack or the 2 chinch plugs.
The HD6 has the same analog inputs, and additional an optical Toslink digital input.
If you have this cable and a source with optical output, you can use the built in DAC, otherwise you are using the DAC of your source and sending an analog signal to the speaker. The AK JR does not have optical out.
DAC output quality:
The quality of the analog output does not only depend on the DAC chip, but at least as much on its implementation.
The chip has a certain sound signature, but there is a lot around the chip which will influence the quality of the signal, especially the jitter and noise levels.
CHORD Mojo is using a proprietary FPGA chip, which has about 1000 times the calculation power of a regular DAC chip and en better reconstruct the original analog signal.
It also has a very good implementation which makes it sound exceptionally clean, dynamic, detailed and layered (3D soundstage)
I have it too, and when I got it I tested it with my speaker system ($6000 integrated amp, $4000 DAC, $2000 CD drive, and custom speakers)
The Mojo was so good I sold my DAC and replaced it with a CHORD 2Qute.
Just to tell you that there are really significant differences between DACs.
But your system seems to be a good match, and I think if you change the DAP, your speakers might become the bottleneck.
But its always great if you can borrow and test something, as
@SilverEars suggested.