CHEM3440Lec6F06 - CHEM*3440 Chemical Instrumentation Topic...

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Unformatted text preview: CHEM*3440 Chemical Instrumentation Topic 6 Digital Electronics Digital Data Domain An analog signal is continuously varying in time. A digital signal consists of discrete samples of an analog signal. It is discretized in both coordinates (time and signal amplitude). Sample Spectrum 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Sampling Event Signal Level (0,0) (1,1) (2,2) (3,4) (4,1) (5,2) (6,7) (7,2) (8,8) (9,2) (10,2) Digital Resolution This characterizes the number of different values into which the analog range is divided. Since modern computing is based on binary arithmetic, we invariably encounter powers of 2 as the number of resolution elements. Digital Bits 4 8 10 12 14 16 Resolution Elements 2 4 = 16 2 8 = 256 2 10 = 1024 10 12 = 4096 10 14 = 16384 10 16 = 65536 Percent Full Range 6.25% 0.39% 0.1% 0.025% 0.006% 0.0015% Size of a Resolution Step 1.25 V 78.1 mV 19.5 mV 4.9 mV 1.2 mV 305 ! V For a full range of ± 10 V. Effect on Accuracy An analog sine wave ±10 V in amplitude. Pink: Data digitized with 4 bit resolution (16 levels) Green: Data digitized with 10 bit resolution (1024 levels)-10-8-6-4-2 2 4 6 8 10 2 4 6 8 10 12 14 x-axis Voltage Largest error 3% (28%) 0.04% (0.5%) Fit Dynamic Range The incoming analog voltages should be amplifed to fll the range oF possible voltages. IF the amplifcation gain is too small, the eFFective resolution is decreased by not using the Full dynamic range. This is a ± 1V signal with a ± 10 V dynamic range.-2-1.5-1-0.5 0.5 1 1.5 2 2 4 6 8 10 12 14 x-axis Voltage Pink: 4 bit Green: 10 bit Gain Too Great IF the analog amplifcation is too large, the data is clipped at the limits.-20-15-10-5 5 10 15 20 2 4 6 8 10 12 14 x-axis Voltage Data is Forced into the limits oF the digital range, completely missing some oF the data. Sampling Frequency We choose how oFten to sample the signal. Too slow and we will miss inFormation. Too Fast and we have data-overload without gaining any additional inFormation. The digitization time defnes the maximum sampling Frequency. Too Little? 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Sampling Event Signal Level Too Much? 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Sampling Event Signal Level Fourier Theorem Every waveForm can be decomposed into a sum oF sine and cosine Functions. Here is an approximate square wave, Formed by adding the odd harmonics oF a sine wave whose amplitudes are the reciprocals oF their harmonic index....
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CHEM3440Lec6F06 - CHEM*3440 Chemical Instrumentation Topic...

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