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Some of the most important components in digital audio systems are the converters. Previous sections have shown the need for high resolution to obtain a satisfactory signaltonoise ratio. In video applications, an 8bit conversion is more than sufficient. A 14bit conversion (or an equivalent) seems a minimum for good audio performance and, for professional use, 16bit conversion is required to leave a margin for further processing (e.g., filtering, mixing). In the PCMF1 and compact disc system, 16bit converters are used, while the PCM Video 8 system uses a 10bit converter. A/D convertersFundamentally, A/D converters operate in one of two general ways. They either convert the analog input signal to a frequency or a set of pulses whose time is measured to provide a representative digital output, or compare the input signal with a vari able reference, using an internal D/A converter to obtain the digital output.
Basic types of A/D converters Voltagetofrequency, ramp and integratingramp methods are the three leading conversion processes that use the timemeasurement method. Successive approximation and parallel/modified parallel circuits rely on comparison methods. Dualslope integrating A/D converters The dualslope integrating A/D converter contains an integrator, some control logic, a clock, a comparator and an output counter, as shown in FIG. 1. A graph of integrator output voltage against time is shown in FIG. 2. The input analog signal is initially switched to the integrator, and the output of the integrator ramps up for a time t1. The slope of the ramp, and hence the integrator output voltage at the end of this time, depends on the amplitude of the analog input signal and the time constant t of the integrator: So the integrator output voltage V0 at the end of time t1 is: The reference signal is then switched to the integrator input, and the integrator output voltage ramps down until it returns to the starting voltage. The slope of the ramp during time t2 similarly depends on the integrator time constant and the integrator input voltage, this time the reference signal amplitude: So the integrator output voltage at the initial time t2 is: However, as these voltages are the same: Therefore: which shows that time t2 is totally dependent on the input signal amplitude, and independent of the integrator time constant. By counting clock pulses during time t2 , a digital measure of the analog input signal's amplitude is made. Average conversion time, i.e., the time the converter takes to perform the conversion of an applied input signal, is two clock periods times the number of quantization levels. Thus, for a 12bit converter with a 1 MHz clock, the average conversion time is: 2 × 1 µs × 4096, or 8.192 ms. The precise conversion time, how ever, depends on the applied input signal amplitude. Due to this long conversion time, integrating converters are not useful for digitizing highspeed, rapidly varying signals, although they are useful to 14bit accuracy, offering high noise rejection and excellent stability with both time and temperature. They can be modified to increase conversion speeds and are used mostly in 8 to 12bit converters for digital voltmeters (DVMs), digital panel meters (DPMs) and digital multimeters (DMMs). However, basic dualslope integrating A/D converters are too slow for general computer applications.
Successiveapproximation A/D converters The main reasons that the successiveapproximation technique is used almost universally in A/D conversion systems are the reliability of the conversion technique, simplicity and inherent high speed data conversion. Conversion time is equal to the clock period times the number of bits being converted. Thus, for a 1 MHz clock, a 12bit converter would take 12 µs to convert an applied analog signal. A successive approximation converter consists of a comparator, a register, control logic and a D/A converter. The output of the D/A converter is compared with the input analog voltage (FIG. 3). Each bit line in the D/A converter corresponds to a bit position in the register. Initially, the converter is clear. When an input signal is applied the control logic instructs the register to change its MSB to 1. This is changed by the D/A converter to an analog voltage equivalent to onehalf the converter's fullscale range. If the input voltage is greater than this, the next most significant bit of the register becomes 1. If, however, the input is less, the next most significant bit remains 0. Then the circuit 'tries' the following bits through to the LSB, at which stage the conversion is complete. Thus, the number of approximations occurring in any conversion equals the number of bits in the dig ital output. FIG. 4 shows the operation of the successive approximation A/D converter graphically. The main advantage of the successiveapproximation converter is speed and this is limited by the settling time of the DAC. Accuracy is limited by the accuracy of the DAC, and a high susceptibility to noise is its major drawback. As only one comparator is used and ancillary hardware is limited to logic, register and D/A converter, the successiveapproximation technique provides an inexpensive A/D converter.
Other types of A/D converters Voltagetofrequency converters FIG. 5 shows a typical voltagetofrequency converter. Here, the input analog signal is integrated and fed to a comparator. When the comparator changes its state, the integrator is reset and the process repeats itself. The counter counts the number of integration cycles for a given time to provide a digital output. The principal advantage of this type of conversion is its excel lent noise rejection due to the fact that the digital output represents the average value of the input signal. Voltagetofrequency conversion, however, is too slow for use in dataacquisition sys tem applications because it operates bitserially (with a maximum of approximately 1000 conversions/s). Its applications are mostly in digital voltmeters (DVMs) using converters with resolutions of 10 bits or less. Ramp converters Ramp conversion works by continuously comparing a linear reference ramp signal with the input signal using a comparator (FIG. 6). The comparator initiates a counter when changing state and the counter counts clock pulses during the time the comparator is logically HIGH; the count is therefore proportional to the magnitude of the input signal. The counter output is the digital representation of the analog input.
This method is slightly faster than the previous one, but it requires a highly linear ramp source in order to be effective. It does offer good 8 to 12bit differential linearity for applications requiring high accuracy. Parallel A/D converters Parallelseries and straight parallel converters are used primarily where extremely high speed is required, taking advantage of the fact that the propagation time through a chain of amplifiers is equal to the square root of the number of stages times the individual setting time, as opposed to adding up the times of each stage. By adding a comparator for every binaryweighted net work, as shown in FIG. 7, it is possible to take advantage of this higher speed. Parallel A/D converters are often called flash converters because of their high operating speeds. The parallel A/D converter of FIG. 7 uses one comparator for each input quantization level (i.e., a 6bit converter would have six comparators). Conversion is straightforward; all that is required besides the comparators is logic for decoding the comparator outputs.
Because only comparators and logic gates stand between the analog inputs and digital outputs, extremely high speeds of up to 50 000 000 samplings/s can be obtained at low resolutions of 6 bits or less. The fact that the number of comparators and logic elements increases with resolution obviously makes this converter increasingly impractical for resolutions greater than 6 bits. Modified parallel designs can provide a good tradeoff between hardware complexity and the resolution/speed combination at a slight addition in hardware and a sacrifice in speed. They can provide up to 100 000 conversions/s for up to 14bit resolutions. Sequential conversion (FIG. 8), for example, is often used for such applications. However, because of the increase in the number of comparators and the need to use an amplifier for every weighting network, cost is considerably more than that of a successive approximation. The first 4bit converter in the circuit in FIG. 8 provides the four most significant bits in parallel. These outputs are converted back to an analog voltage which is subtracted from the input. The difference is applied to the next converter and the process is continued until the required 10 bits are obtained. This approach gives a reasonable tradeoff among speed, cost and accuracy.
Deltasigma modulator A deltasigma modulator is the key device in a 1bit A/D converter. FIG. 9 shows a firstorder deltasigma modulator. Operation is performed at each clock cycle, which corresponds to the oversampling frequency. At the beginning of each clock cycle, the differential amplifier outputs the difference between the input voltage V and the output voltage of the singlebit D/A converter. The integrator adds the voltage a to its own output from the preceding clock cycle. This voltage b is provided to the zero comparator. The output of the comparator will be logically HIGH or LOW, depending on voltage b being higher or lower than 0 V. The output then becomes a piece of singlebit A/D data, which is also used to determine the output of the 1bit DAC for the next clock cycle. The 1bit DAC outputs a positive fullscale voltage if its input is HIGH and a negative fullscale voltage if its input is LOW. Table 5.1 shows an example of actual operation in which the input is 0.6 V, with the fullscale voltage being ±1 V and all initial values 0. The 1bit A/D converter outputs only HIGH or LOW, which has no meaning in itself; this only becomes meaningful when a string of 1bit data is averaged.
Because of the high sampling frequency (64 times oversampling) a very gentle lowpass filter can be used, resulting in low phase distortion. Compared to successive approximation A/D converters, singlebit A/D converters provide better performance while circuit complexity and cost remain equal. Noise shaping A deltasigma modulator is sometimes also called a noise shaper because it passes signals and noise according to different transfer functions (FIG. 10). The signal transfer function for the modulator simplifies to: This is the sdomain representation of a firstorder lowpass filter. Deriving the noise transfer function for the same modulator produces: This is the sdomain representation of a simple highpass filter. Plotting the transfer functions gives the result shown in FIG. 11. The signal is attenuated at higher frequencies, while the noise is shaped so that very little of its content is in the low frequency region. By using higher order deltasigma modulators, the inband noise can even be reduced further; however, outof band noise will increase. In practice, a third or fourthorder deltasigma modulator is used to avoid stability problems while still using most of the noise shaping capabilities.
Highdensity linear A/D converter The A/D converter currently used in Sony RDAT recorders and some MiniDisc recorders is the highdensity linear converter. This converter uses two fourthorder deltasigma modulators for simultaneous sampling of two audio channels. Its output is a serial data signal with 16bit resolution coded in two's complement at a sampling frequency of 32, 44.1 or 48 kHz. The deltasigma modulators operate at 64 times oversampling; for a system sampling frequency of 48 kHz, the analog audio signals are actually sampled at: f s = 48 kHz × 643.072 MHz This high sampling frequency eliminates the need for a sample hold circuit and a complex analog lowpass filter. A firstorder RC network can be used as antialiasing filter because the audio signals do not normally contain frequencies above 1/2 f s (approx. 1.5 MHz). As a consequence, circuit complexity is greatly reduced. The 1bit stream, output from the deltasigma modulators is hardly usable for further application. A builtin digital filter recalculates the singlebit input data at 64 f s to 16bit words at f s. The socalled requantization is performed by the decimation filters. FIG. 12 shows a block diagram of the highdensity linear converter. This converter is clearly separated into an analog and a digital section. The analog part contains the voltage reference source and the deltasigma modulators, while the digital part includes the digital filters, a controller and the output interface. Each section has its own power supply to prevent digital noise from entering the analog signals. During initialization, the converter performs an automatic calibration to compensate for possible offset errors in the converter itself. The analog inputs are grounded while the resulting out put is measured and its value stored in SRAM as an offset. After calibration, the actual data are corrected by this offset value before being output.
With a harmonic distortion (THD) of less than 0.002% and a signaltonoise ratio of more than 94 dB (EAIJ), the highdensity linear converter is ideally suited for highquality digital audio signal processing. This type of converter is used in all Sony's RDAT recorders, such as DTC77ES and DTC59ES, as well as in the MDS101 MiniDisc recorder. D/A conversion in digital audio equipmentWeighted current D/A converter The most common D/A converter in digital audio is the weighted current type. It consists of a series of electronic switches, each of which is connected to a current source. In an nbit D/A converter there are n weighted current sources with a current value of 2(n 1) times the original current value 1. The current sources corresponding to the weight of the bit in the digital data signal are added to obtain a current that represents the value of the digital data. In fact, the digital data input directly controls the electronic switches that turn the current sources on or off. A currentto voltage amplifier converts the obtained current into a voltage before being output. FIG. 13 shows a typical block diagram of the weighted current type or current summing type D/A converter.
Although this is basically a very simple converter, it has some serious drawbacks. The constantcurrent sources must be very accurately matched to prevent nonlinear distortion. Suppose that the current 1 equals 0.1 mA, the constantcurrent source for the MSB should then deliver 2(n 1) × 1 = 3276.8 mA or more than 3 A! Moreover, to maintain 16bit resolution the accuracy of the MSB constantcurrent source must be better than the current delivered by the LSB constantcurrent source. Another type of D/A converter, more or less based on the same principles, is the ladder network type D/A converter as shown in FIG. 14. The socalled 'ladder network' is composed of resistors with values R and 2R to form a voltage divider. The electronic switches, controlled by the digital input data, change the output voltage of the voltage divider. The output voltage therefore represents the digital input signal. Accuracy is also a problem because all the resistors must be perfectly matched to ensure linearity. Temperature variations and ageing inevitably have a bad influence on the D/A converter linearity. The ON resistance of the electronic switches must be sufficiently low com pared to the resistor value R to prevent it from having too much influence on the output signal. Actual D/A converters are in fact a combination of a ladder network type converter with constantcurrent sources added for the upper and lower bits.
Singlebit D/A converter The disadvantages of the weighted current D/A converter can be overcome by using advanced laser trimming techniques to accurately match resistors and current sources. However, this has a negative influence on manufacturing costs. The singlebit converter makes highprecision D/A conversion possible without the need for expensive matched components. FIG. 15 shows a block diagram of the singlebit D/A converter. The first step in the conversion process is the requantization of the multibit digital audio signal at f s 1 to 1bit signal with a much higher sampling frequency f_s 2. Operation of the requantizer is explained in FIG. 16. The requantizer will determine whether the input data Di is higher or lower than the reference data (Dr ), the reference data being the requantized result of the previous input data. Whenever the reference data is lower than the input data, the 1bit output of the requantizer will be 1 and the reference data will be incremented. This process is repeated for every block cycle of the sampling frequency f s 1. At a certain time the reference data will be higher than the input data. The resulting 1bit data now becomes 0 and the reference data decremented. The output sequence 010 continues until new input data are applied to the converter. The 1bit output is converted to a pulse width modulation (PWM) or pulse density modulation (PDM) signal which, after lowpass filtering, represents the analog output voltage (FIG. 17). Because of feedback of the reference data, the singlebit D/A converter acts as a noise shaper, similar to the singlebit A/D converter (FIG. 11). It shifts the requantization noise to the higher frequency regions, thereby lowering the quantization noise in the audible frequency range. Hence, the 1bit D/A converter easily achieves a resolution of more than 16 bits in the audio frequency range. Nonlinear distortion and DC offset are nonexisting problems. The only major disadvantage is high frequency noise radiation caused by the high sampling frequency f s 2, which is usually several megahertz. A carefully designed singlebit D/A converter is therefore an inexpensive alternative for highprecision D/A conversion.
FIG. 20 Timing diagram of an oversampling system. Words at a sampling frequency of 44.1 kHz have interpolated samples added, such that the effective sampling rate is 88.2 kHz.
Oversampling The output of a digitaltoanalog converter cannot be used directly; filtering is necessary. The converter output produces the frequency spectrum shown in FIG. 18, where the baseband audio signal (0f m) is reproduced symmetrical around the sampling frequency (f s ) and its harmonics. The lowpass reconstruction filter must reject everything except the baseband signal. A sampling frequency (f s ) of 44100 Hz and a maximum audio frequency (f m) of 20 000 Hz mean that a lowpass filter with a flat response to 20 kHz and a high attenuation at f s  f m (44 100  20 000 = 24 100 Hz) is needed. An analog filter can be made to have such a sharp rolloff, but the phase response will introduce an audible phase distortion and group delay. One approach to getting round this problem is oversampling. Oversampling is the use of a sampling rate greatly in excess of that stipulated by the Nyquist theorem. Practical implementations use a ×2 oversampling (f s = 88.2 kHz) or a ×4 oversampling frequency (f s = 176.5 kHz). The output spectrum of the D/A converter in a ×2 oversampling system is shown in FIG. 19, where the large separation between baseband and sidebands allows a lowpass filter with a gentle rolloff to be used. This improves the phase response of the filter. Digital words are input at the standard sampling rate of 44.1 kHz (i.e., no extra samples need be taken at the A/D conversion stage), and extra samples are generated at a rate of 88.2 kHz (FIG. 20). The missing samples are computed by digital simulation of the analog reconstruction process. A digital transversal filter (also known as a finite impulse response filter) is well suited for this purpose. Analog versus digital filters The discretetime signal produced by sampling an analog input signal (FIG. 21) is defined as an infinite series of numbers, each corresponding to a sampling point at time t = Tn for 8 < n < +8. Such a series is always referred to by its value at t = Tn which is x(n). The series x(n) is defined as: x(n) = …, x(2), x(1), x(0), x(1), x(2), … with element x(n) occurring at time t = Tn. Analog filters The firstorder lowpass analog filter shown in FIG. 22 is often described as a function of s, the independent variable in the complex frequency domain. The transfer function of such a filter is given by: ...where... ? = angular frequency = 2pf and ?0 is the angular frequency at the filter's cutoff frequency f c = 1/RC. Knowing this, the cutoff frequency of the filter can be calculated as follows: so: Digital filters A digital filter is a processing system which generates the out put sequence, y(n), from an input sequence, x(n), where: present and past past input output samples samples The coefficients a0 , a1 , …, aM and b0 , b1 , …, bN are constants which describe the filter response. When N > 0, indicating that past output samples are used in the calculation of the present output sample, the filter is said to be recursive or cyclic. An example is shown in FIG. 23. When only present and past input samples are used in the calculation of the present output sample, the filter is said to be nonrecursive or noncyclic: because no past output samples are involved in the calculation, the second term then becomes zero (as N = 0). An example is shown in FIG. 24. Generally, digital audio systems use nonrecursive filters and an example, used in the CDP102 compact disc player, is shown in FIG. 25 as a block diagram. IC309 is a CX23034, a 96thorder filter which contains 96 multipliers. The constant coefficients are contained in an ROM lookup table. Also note that the CX23034 operates on 16bit wide data words, which means that all adders and multipliers are 16bit devices.
