New Technology Increases the Dynamic Ranges of Data Acquisition Systems

The linear operating range of high-quality measurement accelerometers and microphones has for many years been significantly better than that of the analog signal conditioning electronics and analog-to-digital converters (ADCs) of the data acquisition systems. This is despite the fact that data acquisition systems today are typically based on 24-bit ADCs, and theoretically able to handle signal dynamics of up to 144 dB. In practice, however, most of these systems do not have a useful dynamic range higher than 100 110 dB. Consequently, the system operators must be very careful in optimizing the analysis chain dynamics in order to avoid overload and underrange situations. This paper describes some of the analysis chain imperfections that are present in data acquisition systems and how high dynamic ranges can be achieved using today’s state-of-the-art designs. INTRODUCTION This paper outlines the system performance that can be expected of present and future analysis systems. First some practical considerations regarding the potential dynamic range of high-quality transducers are given followed by a brief overview of the factors that reduce the system performance to less than the theoretical limit. Then, a few theoretical considerations regarding the potential dynamic range of a digital system, and the potential improvements when using narrowband analysis, are provided. Finally, a new technology optimizing the dynamic range of the system is introduced and illustrated with measurements showing system performance of 160 dB or more when using narrowband analysis. DYNAMIC RANGE AND FREQUENCY RANGE The ratio between the highest and lowest signal a system can handle is defined as the dynamic range of the system. If the dynamic range is too low, then high signals will be clipped and distorted while low signals will be buried in system noise originating from the transducer element and the electronics conditioning the transducer. In technical terms, the dynamic range (DR) is the ratio between the RMS value of a full-scale sine wave VFS and the RMS value of the system base noise VN. It is typically given in dB: N FS V V DR log 20× = (1) When discussing dynamic range, the frequency range of the measurement must be taken into consideration. In a well-designed system the inherent system noise can be characterized as white noise. Consequently, if all elements of the measurement chain are linear in nature, the dynamic range of the measurement can be improved by reducing the measurement frequency range. This is actually one of the advantages of the commonly used FFT analysis. For the above statement to be valid, it is essential that no artifacts are introduced in either the time domain or the frequency domain, when performing narrowband analysis. DYNAMIC RANGE OF TRANSDUCERS For the last 30 to 40 years, sound and vibration transducers have outperformed the subsequent analysis systems as regards linearity and dynamic performance. A high-quality transducer, including preamplifier, can deliver a practically noise-, spuriousand distortion-free signal over a dynamic range of 120 to 130 dB using broadband, and 160 dB using narrowband, analysis. In a well-designed transducer, the limiting factors for achieving a high dynamic range are mainly the noise floor and the clipping level of the pre-amplifier’s electronics. The transducer element itself does not limit the performance. The noise floor VN of a high-quality preamplifier has for the last 30 to 40 years been in the region of 3 μV to 15 μV in the audible frequency range and the maximum linear output VFS of a DeltaTron/ICP transducer is 5 VRMS (7.071 Vpeak). Table 1 provides examples of dynamic ranges that can be expected for a high-quality transducer. Bandwidth [Hz] 25.6k 1.024 24 6 1 VFS [VRMS] 5 VN [VRMS] 3μ 600n 92n 46n 19n DR [dB] 124 138 155 161 169 Table 1. Dynamic ranges for a high-quality DeltaTron/ICP transducer Throughout this paper a bandwidth of 25.6 kHz is used for broadband comparisons. For narrowband comparisons 24 Hz, 6 Hz and 1 Hz are used, where e.g. 6 Hz corresponds to the effective noise bandwidth of a 25.6 kHz FFT analysis with 6400 lines using Hanning weighting [1]. So, a high-quality transducer can be used for narrowband measurements over a dynamic range of 160 dB (effective noise bandwidth 6Hz) given that no other factors affect the measurement chain. ANALYSIS CHAIN IMPERFECTIONS The clipping level and the noise floor are not the only factors limiting the useful dynamic range of the analysis system. The list below includes some other factors that limit the analysis system performance. Harmonic Distortion: Signals caused by non-linearities in the analog signal conditioning. Typically characterized as a family of harmonic components leveled relative to the measurement signal. Cross-talk: Signals caused by inter-channel coupling. Leveled relative to the signal level of the originating channel. Spurious: Signals caused by various phenomena such as power supply imperfections, clock circuits, bus communication and EMC coupling between circuits. ADC Resolution: The ADC resolution is given by the number of bits N as 2. ADC Non-linearity: Digital distortion components caused by uneven quantization step sizes in the ADC and the on-chip DSP. Aliasing: Signal artifacts originating from signal components of frequencies higher than the Nyquist frequency. Typically leveled relative to the measurement signal. DSP Imperfections: Modern analysis systems perform filtering, decimation and the actual analysis in the digital domain. Throughout the whole digital analysis chain a high dynamic range requires high-speed calculations of high accuracy. High-speed DSPs are both expensive and have high power consumption. SYSTEM CONSIDERATIONS No system is better than its weakest link. The analysis chain consists of coupled elements each with a limited dynamic range as illustrated in Figure 1. Figure 1. Example of dynamic ranges of an analysis chain The ADC has been the weakest link in the analysis chain ever since the invention of digital signal processing. New ADC designs have, however, improved performance dramatically. Table 2 gives a rough overview of the historical evolution in ADC specifications for sound and vibration analysis. Traditional ADC designs still lack performance when compared to the transducer (Table 1). Year ADC Resolution [bits] Dynamic Range (DC – Fs/2) [dB] 1970 10 – 12 60 dB 1980 14 – 16 70 dB 1990 16 80 dB 2000 24 100 dB 2005 24 110 dB Table 2. A historic overview of specifications of ADCs. Fs: Sampling frequency Overcoming the Analysis Chain Imperfections The fact that the transducer has historically always outperformed the analysis chain with respect to dynamic range has been compensated for by the inclusion of an input attenuator in the analysis chain. This has, in practice, compensated for the limited dynamic range of the ADC and also the limitations in the following DSP chain. The drawback is, however, a quite high risk of bad measurements as overload and underrange situations can occur (Figure 2). An overloaded measurement is erroneous and has to be re-measured. There is no way of estimating the correct result. Figure 2. The effect of using an input attenuator illustrated for sound measurements Overloads are probably the biggest cause of bad measurement results. It is becoming a still bigger issue in multichannel and/or multi-analysis measurements as it is getting more and more difficult to overview the whole measurement scenario and avoid defective measurements. Potential Dynamic Range of a 24-bit System An approach similar to the one applied to the transducer can be applied to the system with respect to broadband and narrowband analysis. The theoretical dynamic range in dB, can be calculated as [2]:         × × × = NBW S N F F DR 2 2 log 20 (2) where N is the system quantization in bits, FS the sampling frequency and FNBW the effective narrowband analysis bandwidth in Hz. Careful system design can ensure that the quantization noise is, theoretically, random and thus with a uniform spectral density (white). Under this assumption, the theoretical dynamic range in dB, can be calculated as [2]:         × × × × = 5 . 1 2 2 log 20 NBW S N F F DR (3) giving an increased dynamic range of approximately 1.8 dB compared to equation (2). Using equation (2) table 3 shows the dynamic range in different bandwidths as a function of system quantization. Dynamic Range FNBW [Hz] N [bits] Resolution 32.768 1.024 24 6 1 16 65.536 96 111 128 134 141 20 1.048.576 120 135 152 158 166 24 16.777.216 144 160 176 182 190 Table 3. Dynamic ranges for different system quantization and bandwidth using equation (2). Fs = 65.536 Hz Using equation (2) or equation (3), the theoretical increase in dynamic range DR ∆ can be expressed as a ratio between the sampling frequency Fs and the width of the narrowband analysis FNBW [2]: NBW F Fs DR × × = ∆ 2 log 20 (4) FNBW [Hz] 1.024 24 6 1 ∆DR [dB] 15 31 37 45 Table 4. Potential increase in dynamic range, ∆DR. Fs = 65.536 Hz Narrowband analysis can improve the analysis depth quite dramatically and an ideal 24-bit system can fully match the performance of modern transducers. NEW TECHNOLOGY INTRODUCTION The above discussion shows that if ADC performance can be significantly improved in combination with a careful design of the whole analysis chain, then the problematic input ranging can be eliminated. Brüel & Kjær has, over the years, looked into this and has recently introduced a new technology designed to increase the useful dynamic range of the whole analysis chain sufficiently to eliminate the use of input attenuators. Dyn-X Technology This new technology is called Dyn-X. In brief, the technology utilizes a specialized analog input design to provide a very high dynamic range of the analog circuit pre-conditioning the transducer signal before forwarding it to the ADC. The Dyn-X input channels have no input attenuators, but a single input range from 0 to 10 Vp. The digitizing is performed synchronously in two specially selected, high-quality, 24-bit delta-sigma ADCs and both data streams are forwarded to the DSP environment where dedicated algorithms in real-time merge the signals while obtaining an extreme high-accuracy match in gain, offset and phase. An important requirement of the design process was that no technical drawbacks must be introduced in either the time or the frequency domain with respect to distortion and other artifacts, when compared to existing designs (Figure 3). Figure 3. A simplified block diagram of the Dyn-X technology Figure 4 and 5 compare the dynamic range of a standard high-quality 24-bit input channel with the new Dyn-X input channel. In Figure 4 a 25.6 kHz bandwidth is used. In Figure 5 a 6 Hz bandwidth corresponding to what will be achieved with a 25.6 kHz FFT with 6400 lines and Hanning weighting is used. It can be seen that the Dyn-X input channel covers practically the same range as the 8 input attenuator settings of the standard 24-bit input channel and that the dynamic range of the Dyn-X input channel matches that of a high-quality transducer. The dynamic ranges are calculated using guaranteed noise levels. Dynamic Range Wideband 25.6 kHz 124 dB 125 dB 91 dB 90 dB 90 dB 89 dB 88 dB 82 dB 74 dB 66 dB 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 7 mVp (Std.) 22 mVp (Std.) 71 mVp (Std.) 224 mVp (Std.) 707 mVp (Std.) 2.24 Vp (Std.) 7.07 Vp (Std.) 12 Vp (Std.) 10 Vp (Dyn-X) High-quality Transducer Attenuator Settings M ax . I np ut to N oi se F lo or [V R M S ] Figure 4. Comparison of dynamic ranges for standard 24-bit input channel (Std.), the Dyn-X input channel (Dyn-X) and a high-quality transducer. Analysis bandwidth: 25.6 kHz Dynamic Range Narrowband 6 Hz 103 dB 112 dB 119 dB 126 dB 127 dB 127 dB 128 dB 128 dB 162 dB 161 dB 1.00E-08 1.00E-07 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 7 mVp (Std.) 22 mVp (Std.) 71 mVp (Std.) 224 mVp (Std.) 707 mVp (Std.) 2.24 Vp (Std.) 7.07 Vp (Std.) 12 Vp (Std.) 10 Vp (Dyn-X) High-quality Transducer Attenuator Settings M ax . I np ut to N oi se F lo or [V R M S ] Figure 5. Comparison of dynamic ranges for standard 24-bit input channel (Std.), the Dyn-X input channel (Dyn-X) and a high-quality transducer. Analysis bandwidth: 6 Hz Dyn-X Technology System Performance It has previously been mentioned that the whole analysis chain must provide a 25.6 kHz broadband dynamic range better than 124 dB, and correspondingly better than 160 dB in a 6 Hz narrow frequency band, in order to match the specifications of high-quality transducers. The following examples compare the performance of the Dyn-X input channel to a standard 24-bit input channel. Note that the standard channel when set to a lower input range can, in theory, provide measurements of similar quality, but with a high risk of generating overloads. The maximum input is 7 VRMS (10 Vpeak) for the Dyn-X input channel and 5 VRMS (7 Vpeak) for the standard 24-bit input channel. In Figure 6 (left) the two channels are compared for a 1 kHz sine wave attenuated 60 dB corresponding to a signal level of 7 mVRMS. FFT analysis in 25.6 kHz, 6400 lines and Hanning weighting was used resulting in an effective noise bandwidth of 6 Hz. For the Dyn-X input channel noise and spurious components are below –160 dB, thus matching the dynamic range of high-quality transducers. The noise floor of the standard 24-bit input channel is approx. 30 dB higher and ADC non-linearity is seen by the presence of spurious components. In Figure 6 (right), a similar comparison is done, but now with the sine wave attenuated 150 dB corresponding to a signal level of 0.22 μVRMS. The noise floor and the spurious components are below –160 dB for the Dyn-X input channel and the sine wave is easily detected. For the standard 24-bit input channel, the sine wave is buried in noise. Noise and ADC non-linearity are clearly visible in the standard channel. Figure 6. Comparison of Dyn-X input channel and standard 24-bit input channel. Left: –60 dB (7 mVRMS) 1 kHz sine wave. Right: –150 dB (0.22 μVRMS) 1 kHz sine wave In Figure 7 the two channels are compared in the time domain for a 1 kHz sine wave attenuated 90 dB corresponding to a signal level of 0.22 mVRMS. Again noise and ADC non-linearity are clearly visible in the standard 24-bit input channel. Figure 7. Comparison of Dyn-X input channel and standard 24-bit input channel for a –90 dB (0.22mVRMS) 1 kHz sine wave In Figure 8, a microphone measurement example is shown. The measurement is performed in a standard office environment with background speech and a person whistling. FFT analysis is used in 25.6 kHz with 1600 lines giving a frequency resolution of 16 Hz. The microphone signal is measured by both channels in parallel. Figure 8. Comparison of Dyn-X input channel and standard 24-bit input channel. Microphone measurement in office This simple measurement clearly illustrates the improved dynamics of the Dyn-X input channel when compared to the standard 24-bit input channel. The difference is close to 30 dB above 4 kHz. The standard 24-bit input channel is measuring system noise instead of environmental office noise.