ANALOG TO DIGITAL TRANSFER FUNCTIONS
Author: Eric Alan Eckstein
This paper is designed to serve as a tutorial on the relative characteristics of transferring audio information across analog to digital domains. It has come to our attention at QEI that there are many misconceptions on interfacing analog and digital equipment among users and manufacturers. Today's broadcast environment contains a mixture of analog and digital domain equipment, such as a digital cart machine to an analog console to analog audio processing to a digital stereo generator. . . . , well you get the point! QEI designs and manufactures a wide variety of analog and digital equipment specifically for the broadcaster; from the CAT-LINK digital STL, Model 691 FM Modulation Monitor, Model 710 Digital Stereo Generator, and QUICK-LINK II Digital Remote Pickup and backup STL system; to the full line of High and Low Power Solid State and Tube FM broadcast transmitters and exciters. Since we manufacture both digital as well as analog equipment, we have become well versed in systems interface across the digital to analog domain. We hope this information will be a useful as guide in the present and (or is it to) the future.A short definition of dynamic range is probably in order at this point. Dynamic Range (DR) as used in this paper is best described as the ratio of the largest signal to the smallest signal in volts peak to peak, measured at a given single frequency. The largest signal would be determined by applying a signal to the unit and increasing the input to the unit until the unit's specified total harmonic distortion (THD+N) is surpassed. The smallest signal would be determined by applying a signal of the same frequency and reducing the input until the output of the unit can no longer be distinguished from the noise floor. This methodology works for either analog or digital systems and by measuring either the input swing required or the output swing given specifies input or output dynamic range (IDR or ODR) respectively.
Digital processors of any type have an inherent IDR limitation in bits by either their analog to digital converter (ADC) or the digital input bit resolution. A digital processors ODR is limited by its internal bus bit width and the output bit resolution. These DR limitations demand effective limiting and/or level control when the first transition is made from the analog to the digital domain. Equally important are the transfer elements in an analog to analog signal exchange, however, since these are "soft" dynamic limits, this process will produce distortion of a known and acceptable type. These various domain transfers and their characteristics are shown in figure 1.
In an analog to digital conversion there are "hard" dynamic limits that relate to the limitations of a digital processor. When these limits are exceeded, unpredictable and, possibly, undesirable effects are produced. It is therefore advisable, whenever an analog to digital transfer will take place, to employ some form of audio processing. This should entail both limiting to prevent exceeding the dynamic range capability of the processor and level control to maximize the signal to noise ratio. In the digital to analog conversion process the dynamic range of the system is set by the resolution (number of bits) of the digital to analog (D/A) converter. In this transfer mode, the dynamic range of the digital system will not exceed that of the analog system as long as the absolute peak levels are set equally.
In a digital to digital exchange, such as when an AES/EBU interface is used, it is impossible to exceed the upper dynamic range limit of the device (i.e. clipping) since, by common agreement, the digital word is encoded in an integer (+1. 0000 to -0.9999) format (see fig.2). The absolute dynamic range is limited by the respective resolutions of the source and object of the transfer. For example, if the source signal is coded in 16 bits (96.32dB dynamic range (DR)) and the device can only code into 12 bits (72.24dB DR), then the dynamic range of the signal in the device is limited by at least 6.02*(16-12){dB} or 24.08 dB. An interesting effect is if this information is then transferred back to a 16 bit coder. The signal would then have a dynamic range of 96.32 dB BUT a signal to noise ratio (SNR) of only 72.24dB! While it is impossible to over drive the upper limit of the dynamic range, it is possible to under-drive the system and not utilize the fully dynamic range of the system. Since AES/EBU is a not an FM Broadcast compatible standard, the final conversion to a composite signal will require that the audio signal be band limited to 15 kHz.
Because the digital domain has absolute limits and the analog domain has variable limits (see Fig.3), the audio transfer function is very critical. Therefore extreme care should be taken to employ limiting and level control when feeding audio from an analog source to a digital system. If the dynamic range of the digital processor is exceeded the audio will become becomes extremely distorted as it exceeds these limits and produces "digital clipping". As the signal is clipped, it will produce unwanted products, within the desired audio band-pass. Out-of-band emissions will effectively be removed by the Finite Impulse Response (FIR) filters, however the audio contained within the audio band-pass has acquired a significant amount of even order harmonics. This effect produces a particularly harsh sound on female vocals and any complex wave form introduced to the system. This phenomenon is true of all digital processors when the entire dynamic range of the device has been exceeded.
Digital Signal Processors (DSP's) offer the broadcaster a vehicle to deliver repeatable audio performance with increased separation, audio definition and long term stability. However with this performance advantage comes the requirement to adhere to strict guidelines on interface of dissimilar systems.