If digital-to-analogue conversion is a limiting factor to convey the quality of fully digital system into high quality studio monitors, Genelec products have a dynamic range capability that is larger than the dynamic range available from any DA converter today. But in any system, any digital audio signal will finally be turned into an analogue signal to be reproduced.

For an analogue signal, there is a practical minimum and a maximum value. The low limit is the noise level in the audio system; the high limit is the distortion or clipping level of the system. In some analogue systems there is no significant distortion before the clipping occurs. In others, there is a slow increase in distortion that limits the useful signal magnitude.

The digital signal is represented by numbers. Usually the signal is represented with fixed point numbers. This means that we cannot represent fractions of values. Therefore, there is a very distinct minimum value to a signal, as well as a distinct maximum value. It is not possible to have any values outside of these ranges.

Dynamic range

The dynamic range is the range of useful values of the signal representation. For an analogue signal, it is determined by the noise level and the distortion or clipping. For a digital signal it is determined by the largest and the smallest value of the signal we can represent.

Let’s take a practical example. A typical two-way active speaker by Genelec has an input referred noise level of 3 uVrms in the most sensitive 3-5 kHz region. The maximum input signal is 1 Vrms. This is determined by the clipping limit in the Genelec speaker, not by distortion limitations, as the Genelec products have been designed to provide maximum performance with digital sources. The dynamic range of this speaker becomes a comfortable 130 dB. This is enough to render the noise generated inside the loudspeakers amplifiers inaudible in all normal listening situations. The speaker can accept a signal that has a peak value of 1.4 V.

A digital studio may process audio with 24 bit resolution. As both positive and negative voltages need to be represented, only 23 bits can be used to represent the signal value. The smallest value is represented with one bit. If we use one bit we can represent two values (0 and 1). If we use two bits, we can represent four values (0, 1, 2 and 3). If we use 23 bits, we can represent 8388608 values. Therefore, we can process the signal with 138 dB digital dynamic range.

Digital-to-Analogue conversion

The problems really begin when we want to move from digits to voltages. This is done using the digital-to-analogue converter (DA converter). As the DA converter represents an interface between the digital and analogue worlds, it is plagued with both the problems of digital signal processing as well as difficulties of analogue signal processing.

The DA converter has an analogue noise level. This sets one limit to the lowest signal that can be usefully generated with a particular DA converter.

As we make the signal smaller, we use less and less bits. This is called digital attenuation (see Figure 1). When we represent a very small signal with only few bits, we can only represent few possible signal values. This is called quantization. As we quantize to a small number of bits we are making a rather gross approximation. This approximation produces distortion. And this distortion is very disturbing, if it happens to fall to such voltages where we can still hear the signal. High quality digital audio systems take special measures to reduce the audible effects of quantization.

We can never emphasize enough the central importance of the monitoring DA converters -- after all they are the main instruments you will use to decide on the quality of your audio material. As a rule, the DA converter should be of the highest quality because the problems in it will be reflected to everything.

Figure 1. The effect of digital attenuation.

Matching the dynamic ranges

To make most of our equipment, we would like to match the digital and the analogue dynamic ranges in the best possible way. We should match the maximum voltage that the DA converter can generate with the maximum voltage the active speaker can accept.

To do this we should first check what is the maximum voltage produced by the DA converter when it is driven with a full scale signal -- at this point the digital input is said to be 0 dBfs. Use a 1000 Hz digital sinus signal to make this check. Such a signal is readily available on most test signal CD records. Turn off your monitor speakers, play the test CD and measure the peak value of the voltage present at the input to the monitor speakers using a precision voltage meter or a high quality multimeter. Let’s say that this voltage on some digital mixing console happens to be +18 dBm, or 6.2 V.

We immediately see a problem. The speaker can only accept a 1.4 volt signal. The DA converter is supplying 6.2 volts. We lose 4.8 volts of the useful signal range. This will result in two things. Firstly, the noise level in the digital system appears to be higher than expected because we are mismatching the digital system dynamic range with the analogue system dynamic range at the DA converter. Secondly, the audio signal will clip at signal levels exceeding the 1.4 volt limit.

To correct the clipping the audio engineer may take down the digital output level pot (Figure 2). This is not wise. The required attenuation in our example would be 13 dB. The noise voltage at the DA converter does not change, so it appears that the noise level is left some 13 dB higher than it should be. We have lost a total of 26 dB of the useful dynamic range because the output voltage range of the DA converter does not fall on the input voltage range of the monitor loudspeaker. We are operating with only about 74 dB of effective dynamic range, and the expensive digital console operates with the quality of a 13-bit system. We have lost 11 of the 24 bit resolution. This is clearly unacceptable!

Figure 2. Wrong gain matching in digital domain.

The right match

The output voltage range of the digital mixing console should be matched with the active monitor speaker dynamic range by using analogue attenuation or gain padding between the mixing console and the active monitor (see Figure 3).

If the output voltage is too high, then we will use a voltage divider network to reduce the input voltage to the active monitor speaker. This also reduces the bottom noise voltage of the DA converter simultaneously, maintaining the maximum dynamic range.

In practice several attenuations may be needed to optimize the DA converter dynamic range for all listening situations. There may be different settings for low and high output levels. Such an analogue gain adjustments should actually reside inside a mixing console as a part of the monitoring output DA converter.

Figure 3. Correct gain matching with analogue attenuator.

If the gain needs to be increased, we have an exceptional situation. First check that you have not missed any gain adjustment, set the output gain to maximum, and re-measure. If you are still reading smaller values than needed to obtain maximum output from the monitor speakers, then we need a very high quality gain stage. The noise level in this gain stage should be lower than the noise level of the DA converter and the monitor speaker. As this is extremely unlikely, please recheck again that you have not missed some adjustment in the DA converter.