Secrets of Home Theater and High Fidelity - John E. Johnson, Jr.

DACs seem to be popping up everywhere now, especially USB DACs. They are integral to SSPs and receivers, but are also available as stand-alone DACS, some inexpensive, and some very expensive.

DACs are not very well understood by the average audiophile, including yours truly. All we really want is for it to do a good job decoding the digital signal and send high quality analog audio to the amplifiers.

One perfomance characteristic that has not been given enough attention is “Linearity” This refers to how linearly the output follows the input.

The following figure shows a theoretical DAC that has perfect linearity. It’s expressed in dB, since the digital input is dB. So, at 0 dBFS, which is defined as 1 volt, the input and the output are the same: 0 dB or 1 volt. The actual output will be more than one volt, since preamplifiers need several volts to work with. This comes from the op-amp that is fed by the DAC’s own output.

JJ's Now-and-Then Blog - DAC Linearity and Perceived Audio Detail

So, let’s take a look at a DAC. I don’t identify the DAC brands because this is not about them. It’s about DACs in general.

DAC 1 is linear down to about -95 dB, where it begins to flatten out. The noise floor is -110 dB. What this means is that all the musical detail that is between -100 dB and -95 dB gets raised to -95 dB. We can’t say if detail lower than -110 dB is raised because that detail is buried in the noise floor.

Somewhere in the range of -80 dB to -90 dB, is the limit of our ability to hear recorded musical detail. Of course this depends on several factors, such as how good your hearing is to begin with, or if you are using headphones, but it is a good rule of thumb.

So, if DAC 1 has a noise floor is -110 dB, and it is linear to -95 dB, musical detail that was recorded at -1oo dB gets raised to -95 dB, and you just might be able to hear it if you have good hearing and are using headphones. This would give the sense that the music has a lot of detail, when actually it is detail that you shouldn’t be hearing at all, because it was recorded at -100 dB, well below audibility.

The Y axis on the right is the output, expressed in dBr. The Y axis on the left is voltage output, corresponding to the dBr values on the right. The X axis is the input, expressed in dB. So, at 0 dBFS input (X axis), the output is 32 dBr (right Y axis) and 4.4 volts (left Y axis). Click on the Linearity graphs to see an expanded version that makes it easier to read the X axis.

JJ's Now-and-Then Blog - DAC Linearity and Perceived Audio Detail

Of course, this depends on the DAC having good Time Domain response. Here is a Time Domain spectrum (1 kHz, 24 bit) for DAC 1 at -110 dB. Notice that the waveform is clearly defined. So, with this DAC, you would hear that -110 dB detail rather distinctly, particularly during quite musical passages.

JJ's Now-and-Then Blog - DAC Linearity and Perceived Audio Detail

Here is the linearity curve for DAC 2. The linearity begins to flatten out at about -85 dB. The noise floor was -120 dB. So, all musical detail between -85 dB and -120 dB would be raised to an audible level (-85 dB). If the noise floor were -85 dB, then the flattening would have been due simply to the noise floor, and no detail lower than -85 dB would be audible.

JJ's Now-and-Then Blog - DAC Linearity and Perceived Audio Detail

The Time Domain spectrum for DAC 2 is shown below. The waveform is not as distinct as compared to DAC 1, so the fine musical detail would not be quite as clear.

JJ's Now-and-Then Blog - DAC Linearity and Perceived Audio Detail

If the flattening out of the curve at -85 dB were actually just the noise floor, the -110 dB sine wave would not be seen. It would have just shown a noise spectrum.

Here is a 1 kHz sine wave at 0dBFS from DAC 2. Note that the noise floor is at -120 dB. Both the linearity curve and the 1 kHz sine wave spectrum shown below use dithered test signals. The Time Domain is measured using an undithered test signal.

JJ's Now-and-Then Blog - DAC Linearity and Perceived Audio Detail

DAC 2 is actually much more expensive than DAC 1 (in the thousands of dollars), and yet the time domain is not as good. I liked the sound of the enhanced detail, which was very noticeable, but if you didn’t know that it was due to the DAC, you could attribute it mistakenly to the SSP or receiver.

I will be adding more data to this particular blog as I obtain a few more DACs, particularly the inexpensive USB DACs that proliferate the market (e.g., $399).

John E. Johnson, Jr.


The author wishes to acknowledge the comments and suggestions from Nelson Pass and David Rich.