Modern data acquisition systems digitizers and dynamic range

Modern data acquisition systems: digitizers and dynamic range Reinoud Sleeman ORFEUS Data Center Royal Netherlands Meteorological Insitute (KNMI) sleeman @ knmi. nl IRIS Workshop Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil 13 – 19 August 2010 Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

analog signal How do we get a digital (bit stream) representation from an analog signal ? digital representation …. . 0011011110101000011010111010011 01111001001011101010010101011… Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Layout • introduction • digitizing theory (dynamic range, oversampling) • ADC - delta sigma modulator (analog-to-digital converter) • decimation (SEED) • measuring and representing instrumental noise • instrumental noise of today’s dataloggers • instrumental noise of the STS-2 Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Introduction and motivation seismic background noise (m/s 2) power spectral density STS-2 N-S • • • E-W STS-1 Z seismic station: Heimansgroeve (HGN), Netherlands sensors: STS-1, STS-2 time windows: 2002 (302 - 309) and 2003 (029 – 043) Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Introduction and motivation from STS-2 manual el mod e s i o n w Lo l eve l e s i 2 no STS- Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

• Johnson-Mathiesen seismometer > 1 Hz • STS-1 < 0. 01 Hz STS-1 STS-2 noise (Wielandt, 1991)

Introduction and motivation • How do we get a digital (bit stream) representation from an analog signal ? • How accurate is the representation ? • Does the digitizing system bias the digital data ? • What does ‘dynamic range’ mean and how must we interpret these numbers (e. g. 145 d. B) given by vendors ? • Why does a digitizer sample with 20 k. Hz (or more) ? • How can we measure the noise level (dynamic range) ? • What information about the recording system is useful or important for seismologists and needs to be stored as (SEED) metadata ? …. . 001101111010100001101011101001101111…… Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Digitizing theory Dynamic range of a N-bit digitizer Quantization: Variance of error: x, q(x) ∆ : smallest discrete step (LSB) q(x) x e +∆/2 -∆/2 t Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Digitizing theory Dynamic range of a N-bit digitizer Quantization: Variance of error: Quantization levels in a n-bit ADC: Data acquisition system – Reinoud Sleeman ∆ : smallest discrete step (LSB) 2 A: full scale input Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Digitizing theory Dynamic range of a N-bit digitizer Quantization: Variance of error: Quantization levels in a n-bit ADC: ∆ : smallest discrete step (LSB) 2 A: full scale input Sine wave (amp A): Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Digitizing theory Dynamic range of a N-bit digitizer Quantization: Variance of error: Quantization levels in a n-bit ADC: ∆ : smallest discrete step (LSB) 2 A: full scale input Sine wave (amp A): Dynamic range: (Bennett, 1948) Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Digitizing theory Dynamic range of a N-bit digitizer Quantization: Variance of error: Quantization levels in a n-bit ADC: ∆ : smallest discrete step (LSB) 2 A: full scale input Sine wave (amp A): Dynamic range: (Bennett, 1948) 6 d. B per bit Dynamic range digitizer: Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Oversampling PSD vs. sampling rate • In an ideal digitizer (assuming white digitizer noise) the quantization noise power is uniformly distributed between [0 – f. NYQ] Hz. • The noise power does not depend on the sampling rate. • For higher sampling rates the power spreads over a wider frequency range, so decreasing the power spectral density (and thus decreasing the quantization error) ! • Higher sampling rate improves the accuracy of the estimate of the (analog) input signal. Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Oversampling Ts = sampling interval (s) Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Oversampling Ts = sampling interval (s) noise power Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Oversampling Ts = sampling interval (s) noise power Theoretical expression for the (one-sided) PSD of quantization noise in a n-bit digitizer: PSD of quantization noise depends on the (initial) sampling rate, and so does the dynamic range ! Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Oversampling • oversampling factor 4 leads to increase of SNR of ~ 6 d. B (or 1 bit) Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Oversampling • oversampling factor 4 leads to increase of SNR of ~ 6 d. B (or 1 bit) • 1 -bit ADC with 256 x oversampling achieves a resolution of 4 bits Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Oversampling • oversampling factor 4 leads to increase of SNR of ~ 6 d. B (or 1 bit) • 1 -bit ADC with 256 x oversampling achieves a resolution of 4 bits • to achieve 16 bits resolution (96 d. B) you must oversample with factor 4^16 (~ 4000 000), and for 24 bits resolution this factor is 4^24 (~280 000 000 ); both can not be realized ! Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Oversampling • oversampling factor 4 leads to increase of SNR of ~ 6 d. B (or 1 bit) • 1 -bit ADC with 256 x oversampling achieves a resolution of 4 bits • to achieve 16 bits resolution (96 d. B) you must oversample with factor 4^16 (~ 4000 000), and for 24 bits resolution this factor is 4^24 (~280 000 000 ); both can not be realized ! • this problem is overcome by the delta-sigma modulator with the property of noise shaping, to enable a gain of more than 6 d. B for each factor of 4 x oversampling. Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Delta-Sigma Analog-Digital (A/D) Modulator (one-bit noise shaping converter) Inose and Yasuda, University of Tokyo, 1946 Comperator: Feedback: Integrator: Pulse train: Data acquisition system – Reinoud Sleeman ADC or quantizer average of y follows the average of x accumulates the quantization error e over time pulse density representation of x Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Delta-Sigma Modulator ei xi Data acquisition system – Reinoud Sleeman si ui q(ui) Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

Delta-Sigma Modulator ei xi ui si q(ui) noise shaping 2 -nd order: Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

PSD noise Assumption: quantization noise is white noise with feedback without feedback 0 100 output sample rate (Hz) 32000 initial sample rate The feedback loop in the quantizer shapes (differentiates) the quantization noise, with the result of smaller quantization noise at lower frequencies at the price of larger quantization noise at higher frequencies. Noise shaping does not change the total noise power, but its distribution. The downsampling (decimation) process uses digital anti-alias filters (FIR) which characteristics must be known by seismologists. Therefore the FIR coefficients must be part of the metadata. Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

Delta-Sigma Modulator / Modulator Decimation Delta-Sigma SEED Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Delta-Sigma Digitizer: summary • Oversampling: quantization noise PSD reduction • Feedback: noise shaping, quantization noise PSD reduction • Feedback order: higher order, improved noise reduction • Dithering: decorrelates signal and quantization noise (may reduce quantization noise) • Differential input: increases dynamic range (3 d. B) • Decimation decreases sample rate digital (FIR) filters characteristics Improved resolution (reduced quantization error) at a lower effective sampling rate Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Layout • introduction • digitizing theory (dynamic range, oversampling) • ADC - delta sigma modulator • decimation (SEED) • measuring instrumental noise • instrumental noise of today’s dataloggers • instrumental noise of the STS-2 Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Measurement of instrumental noise (dynamic range ) • 50 ohm shortened input recording (digitizer) • common input recording (digitizer or sensor) Ø Ø coherency analysis of 2 channels (Holcomb, 1989) coherency analysis of 3 channels (Sleeman et. al. , 2006) triplet method Holcomb, L. G. , A direct method for calculating instrument noise levels in side-by-side seismometer evaluations. U. S. Geol. Surv. , Open-File Report 89 -214 (1989) Sleeman, R. , A. van Wettum and J. Trampert. Three-channel correlation analysis: a new technique to measure instrumental noise of digitizers and seismic sensors. Bull. Seism. Soc. Am. , 96, 1, 258 -271 (2006) Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

2 -channel vs. 3 -channel model Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

Three-channel technique: § direct method for estimating instrumental noise and relative transfer functions (relative calibration!) based on the recordings only § no a-priori ð information required about transfer functions method not sensitive for errors in gain Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

The digitizer experiment Q 4120 STS-2 Q 4120 Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

PSD of self-noise Q 4120 measured with common STS-2 vertical signal (@ 20 sps) Power Spectral Density graph 143 d. B Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

Does the quantization error increases during quantizing a seismic signal ? Quanterra Q 4120 NO 139 d. B NARS datalogger (old model) slightly Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks Foz do Iguacu, Brazil, 13 -19 Aug 2010

The sensor experiment using STS-2 & Q 330 Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

( rel. to V 2 / Hz ) PSD in d. B extracted noise Wielandt (2 -channel technique) Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

( rel. to V 2 / Hz ) PSD in d. B extracted noise Wielandt Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

( rel. to V 2 / Hz ) PSD in d. B extracted noise Wielandt Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

( rel. to V 2 / Hz ) PSD in d. B extracted noise Wielandt Data acquisition system – Reinoud Sleeman Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

( rel. to V 2 / Hz ) PSD in d. B extracted noise Q 330 HR Data acquisition system – Reinoud Sleeman Wielandt Managing Waveform Data and Related Metadata for Seismic Networks do Iguacu, Brazil, 13 -19 Aug 2010 IRIS Workshop, 21 -26 Oct. Foz 2007, Kuala Lumpur - R. Sleeman

STS-2 self noise measurement needs Q 330 HR with pre-amp enabled ! STS-2 noise (Wielandt, 1991) Q 330 -HR pre-amp enabled

The Conrad Observatory Experiment • NERIES framework (TA 5) (funding) • Conrad Observatory (infrastructure, local conditions) • 4 STS-2 (same generation) • 4 Q 330 -HR, enabled pre-amplifier • Antelope ® acquisition

Q 330 -HR

Without thermal isolation Background noise LNM Wielandt (STS-2) Triplet (STS-2) 12 d. B !

With thermal isolation Background noise LNM Wielandt (STS-2) Triplet (STS-2) LH BH

Background noise LNM Wielandt (STS-2) Triplet (STS-2) no isolation thermal isolation

Seismic PSD Triplet (STS-2) julian day (2008)