Highres recordings

CD quality is 16 bit / 44.1 kHz sample rate.

Today you can buy 24 bit / 192 kHz recordings.

Can your gear resolve this?

Sample rate

Let’s do some calculations (always tricky in my case)
Playing 192 kHz is 1/192.000 sample per second= 0.000005208333333333330 s

If the clock driving the DAC has an intrinsic jitter of 10 nano seconds then time step produced at DA conversion fluctuates between:
0.00000001 = 10 ns
0.000005218333333333330 +10 ns
0.000005208333333333330
0.000005198333333333330 -10 ns


Obvious the fluctuations in clock speed are pretty close to the time step.

Ok, let’s use a better clock, one with an intrinsic jitter of 1 pico second.


0.000000000001 = 1 ps
0.000005208334333333330 +1 ps
0.000005208333333333330
0.000005208332333333330 -1ps

 

In this case the variations in the time step look more decent.

The higher the sample rate the more import low jitter values become.

Of course jitter performance is far more complex but it looks like even a clock with an extreme low intrinsic jitter of 1 ps is not able to generate the correct time step.
Therefore, our gear can’t play 192 kHz with the right timing.

Bit depth

If we have a 16 bits recording, there are 2^16=65536 steps.
If we have a 24 bits recording, there are 2^24=16777216 steps.

If the maximum output of our DAC is 2 V, the output will fluctuate between +2 and -2 so a range of 4 V
At the analog site of the DAC we have a step size of
4/2^16=0.0000610351562500000000000 V
4/2^24=0.0000002384185791015620000 V

 

Any DAC able to resolve 0.000000238418579101562 V exactly?

No, this is such an extremely low value that it is at the present not possible to resolve this correctly.
Even if this was the case, it will be drown in the noise floor of your gear.

1 Bit is 6 dB (6N+1.8 dB to be exact but let’s forget this 1.8)

 

Bit

dBFS

16

-96

17

-102

18

-108

19

-114

20

-120

21

-126

22

-132

23

-138

24

-144

 

If the noise floor of your DAC is at -96 dBFS, you can resolve CD quality.
If you have a DAC with whisper quiet circuits at -132 dBFS you can resolve 22 bits.
The Resonessence Labs Invicta is the only DAC known to me able to do this.
No DAC at the present is able to resolve 24 bits as none have a noise floor of -144 dBFS.

 

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