Box-to-Box Phase Accuracy of Benchmark DAC1 and DAC2 Converters

Phase Accuracy in an Asynchronous Environment

Two or more Benchmark DAC1 or DAC2 converters can be used together in phase-coherent multichannel audio systems even though their internal clocks are not synchronized. This seems to defy logic, but an examination of the system details reveals why this is possible.

Benchmark D/A Converters can be Used Together in Phase-Coherent Systems

Our bench tests show that if identical signals are fed to two separate DAC1 boxes, the outputs will be precisely in phase with each other, at sample rates up to about 110 kHz. Below this sample rate, the L to R differential phase response of a single DAC1 is almost identical to the differential phase between the outputs of two separate DAC1 boxes.

Similar tests show that two or more DAC2 converters can be used to create phase-coherent multi channel systems at any sample rate. Please note that the time delay through a DAC1 is not the same as a DAC2. This means that the two generations of Benchmark D/A converters should not be mixed when phase-coherence is required.

Benchmark converters achieve nearly perfect box-to-box phase matching without using a separate clock input. This note discusses some of the technical details that contribute to this box-to-box phase matching.

ASRC System in the DAC1

The DAC1 uses an AD1896 asynchronous sample rate converter (ASRC) to isolate the incoming digital audio clock from a free-running low-jitter conversion clock. Every DAC1 has its own free-running master clock. These free-running clocks do not need to be synchronized in order to have a predictable delay through the system. The DAC1 uses the AD1896 to upconvert the audio to a sample rate of about 111 kHz. When upconverting, the AD1896 has a fixed delay that is a function of the input sample rate only. The phase relationship between the input and outputs clock will not change the delay through the SRC. The SRC filter coefficients are always selected to maintain a constant delay from the average phase of the input clock signal. The averaging function prevents jitter artifacts, and is one of 3 significant advantages provided by an upsampling SRC topology.

In a multi-channel system, the digital signals feeding multiple DAC1 converters are all derived from the same clock, and are in phase. However, the internal conversion clocks (inside the DAC1 boxes) are all running independently and yet phase accuracy is maintained (see the plots in the manual). The phase accuracy between two DAC1 boxes is only a function of the frequency matching of the two independent fixed-frequency conversion oscillators. These are crystal oscillators and are actually much more closely matched than they need to be. The clock frequencies are matched to +/- about 50 PPM (+/- 0.005%), and if we do the math, the worst-case miss-match will produce a phase error of only +/- 0.004 degrees at 20 kHz! The analog circuits (and the measurement equipment) have orders of magnitude more phase error than the SRC & D/A conversion systems in the DAC1!

DAC1 Converters can be used in Multichannel Systems at Sample Rates up to 100 kHz

Multiple DAC1 boxes are phase accurate up to an input frequency of 110 kHz. We do not claim phase accuracy between DAC1 boxes running at 176.4 or 192 kHz.

The Math

The delay on the 110 kHz side of the SRC is 1.01 ms +/- 50 ppm. The +/- 50 ppm variation is due to the +/- 50 ppm variation in the oscillator used for the 110 kHz D/A conversion clock.

50 ppm is 0.00005

0.00005*1.01 ms = 50.5 ns

50.5 ns is equivalent to moving the position of a microphone by 0.00005 feet, and is equivalent to the electrical delay through a 25 foot cable.

At 20 kHz, +/- 50.5 ns is:

50.5E-9*20000*360=0.36 degrees (at 20 kHz)

This +/- 0.36 degree variation is insignificant, even when the channels are summed.

The amplitude error after summing is: 20*Log((cos(0.36*2)+cos(0))/2)=-0.00035 dB at 20 kHz

What about comb filtering? The first null in the comb filter will occur no lower than: 1/(2*50.5 ns/2)= 19.8 MHz

The bandwidth of 96 kHz digital audio is limited to 48 kHz, so a null at 19.8 MHz is of no consequence.

DAC2 Converters can be used at any Sample Rate in a Multichannel System

The DAC2 system is also asynchronous, but due to improved technology, it maintains box-to-box phase accuracy at all input sample rates.