Sistemas de Aquisição de Dados. Mestrado Integrado em Eng. Física Tecnológica 2016/17 Aula 4, 10th October

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1 Sistemas de Aquisição de Dados Mestrado Integrado em Eng. Física Tecnológica 216/17 Aula 4, 1th October

2 ADC Amplitude Quantization: ADC Digital Output Formats V REF +FS RANGE (SPAN) OR FS ANALOG INPUT N-BIT ADC MSB LSB DIGITAL OUTPUT N-BITS WHOLE NUMBERS: Number 1 = a N 1 2 N 1 + a N 2 2 N 2 + +a a 2 MSB LSB Example: = (1 2 3 ) + ( 2 2 )+ (1 2 1 )+ (1 2 ) = = 11 1 FRACTIONAL NUMBERS: Number 1 = a N a N a 1 2 (N 1) + a 2 N MSB LSB Example: = (1.5) + (.25) + (1.125) + (1.625) = =

3 Binary Coding of Quantised Numbers Unipolar Codes (4 bit example) BASE 1 NUMBER SCALE +1V FS BINARY GRAY FS 1LSB = +15/16 FS +7/8 FS +13/16 FS +3/4 FS +11/16 FS +5/8 FS +9/16 FS +1/2 FS +7/16 FS +3/8 FS +5/16 FS +1/4 FS +3/16 FS +1/8 FS 1LSB = +1/16 FS

4 Binary Coding of Quantised Numbers II Bipolar Codes (4 bit example) 2.1 C Q BASE 1 NUMBER SCALE +FS 1LSB = +7/8 FS +3/4 FS +5/8 FS +1/2 FS +3/8 FS +1/4 FS +1/8 FS 1/8 FS 1/4 FS 3/8 FS 1/2 FS 5/8 FS 3/4 FS FS + 1LSB = 7/8 FS FS ±5V FS NOT NORMALLY USED IN COMPUTATIONS (SEE TEXT) OFFSET BINARY TWOS COMP * ONES COMP. * ONES COMP SIGN MAG. * SIGN MAG.

5 How to connect ADC to the CPU (Two-Complement Binary Format) 12 bit bit x x x x Left align 16 bit Sign extend Verilog HDL Example: extended[15:] <= { {4{value[11]}}, value[11:] }; 5

6 Binary Coding of Quantized Numbers III BCD Codes (4 digit example) BASE 1 NUMBER SCALE +FS 1LSB = +15/16 FS +7/8 FS +13/16 FS +3/4 FS +11/16 FS +5/8 FS +9/16 FS +1/2 FS +7/16 FS +3/8 FS +5/16 FS +1/4 FS +3/16 FS +1/8 FS 1LSB = +1/16 FS +1V FS DECADE 1 DECADE 2 DECADE 3 DECADE 4

7 Analog-to-Digital Conversion a a1 a2... Mapping: R (finite set) T LSB Resolution 1 1/2 LSB 1 LSB = 1/8 1/4 3/8 1/2 5/8 3/4 7/8 FS ANALOG INPUT full scale 2 N, A LSB = V ref 2 N 7

8 Best resolution of a n-bit ADC (Value of a LSB) db F S = 2 log 1 ( 1 2 N ) 8

9 Anti-Aliasing Filters For a correct sampling we need to be sure that the image spectrum overlaps only at amplitudes lower than the ADC resolution log( F(f) ) Filter Cutoff Nth-Order LPF Slope = 6 N db/oct = 2 N db/dec The Bandwidth of the LPF + ADC system will always be inferior to the Nyquist Limit Fsamp /2 Dynamic range of ADC (db) -fs fs/2 fs log(f) Bandwidth 9

10 A-A Filter Examples ADC with fsamp= 1 bit Resolution: 6dB (see table in slide 8) 3rd Order Low Pass Filter: 6 db/dec fsamp/2=5 khz System s Analog Bandwidth BW= 5 khz

11 Bibliography Data Conversion Handbook, Chapter 2 Analog Devices Inc., 24 data_conversion_handbook.html Analog-to-Digital Conversion, Second Edition, Marcel J.M. Pelgrom, Springer 213

Sistemas de Aquisição de Dados. Mestrado Integrado em Eng. Física Tecnológica 2016/17 Aula 3, 3rd September

Sistemas de Aquisição de Dados Mestrado Integrado em Eng. Física Tecnológica 2016/17 Aula 3, 3rd September The Data Converter Interface Analog Media and Transducers Signal Conditioning Signal Conditioning