ISAT 300 Computer-Based Instrumentation (part 2) Sampling and A/D Converters 11/14/01

Sampling (In the context of polling) Filter input first      

Sampling (In the context of polling) Then sample      

Sampling of Time-Varying Signals (Measurands) When using a computerized data acquisition system, measurements are only made at a discrete set of times, not continuously. For example, a temperature or voltage reading (called a sample) may be taken every 0.1 s or every 2 min, and no information is taken for the time periods in between the samples.

Sampling of Time-Varying Signals (Measurands) a) time-varying signal (e.g., voltage) b) signal being sampled c) the sampled points (dots) d) signal can be reconstructed by connecting the dots

Sampling of Time-Varying Signals (Measurands) The rate at which measurements are made is known as the sampling rate, expressed in samples/sec or Hz. Incorrect selection of the sampling rate can lead to misleading results.

The problem of aliasing 10 Hz input sampled at 11 Hz Output looks like 1 Hz !

The problem of aliasing (continued) 10 Hz input sampled at 9 Hz Output looks like 1 Hz

The problem of aliasing (continued) 10 Hz input sampled at 8 Hz Output looks like 2 Hz

The problem of aliasing (continued) 10 Hz input sampled at 12 Hz Output looks like 2 Hz

The alias frequency 10 Hz input sampled at 11 Hz Output looks like 1 Hz

When does aliasing happen? 10 Hz input sampled at 11 Hz Output looks like 1 Hz

Another pathology 10 Hz input sampled at 5 Hz Output looks like 0 Hz (dc) Beware if

Avoiding aliasing To avoid aliasing, sample your signal at greater than twice the maximum frequency of interest. This is a minimum X the maximum frequency of interest would be better. Another way to state this rule is the Nyquist criterion:

The A/D converter--produces binary numbers

A one-bit A/D converter V in V in > 5 V  output = on “1” V in < 5 V  output = off “0” Input Output

A two-bit (unipolar) A/D converter 10.0 V 7.5 V 5.0 V 2.5 V 0 V 0d0d 1d1d 2d2d 3d3d N = 2 Output has 2 N possible values (error on page 78?) Input Output Range? Span?

A two-bit (unipolar) A/D converter 10.0 V 7.5 V 5.0 V 2.5 V 0 V 0d0d 1d1d 2d2d 3d3d N = 2 (V ru - V rl ) / 2 N How big is each input bin? Input Output

Input resolution error = Quantization error 10.0 V 7.5 V 5.0 V 2.5 V 0 V 0d0d 1d1d 2d2d 3d3d N = 2  0.5 (V ru - V rl ) / 2 N

Sampling and A/D Conversion a) An analog signal has been sampled and then converted to digital (2’s complement). b) This quantization results in error.

Saturation 10.0 V 7.5 V 5.0 V 2.5 V 0 V 0d0d 1d1d 2d2d 3d3d N = 2 V in = 12 V Input Output

A two-bit (bipolar) A/D converter 5.0 V 2.5 V 0.0 V V V 0d0d 1d1d -1 d -2 d N = (V ru - V rl ) / 2 N Input Output (2’s complement)

Choosing an A/D converter--resolution National Instruments model 16E-4 National Instruments model 16XE bits 16 bits

Choosing an A/D converter--speed National Instruments model 16E-4 National Instruments model 16XE kS/s 20 kS/s (kiloSamples/second)

Choosing an A/D converter--input range National Instruments model 16E-4 National Instruments model 16XE-50  10 V

Calculating the digital output To estimate the digital output of an A/D converter, see page 81. E.g., for a simple binary A/D converter: V in = analog input voltage V ru = upper value of input range V rl = lower value of input range N = number of bits D o = digital output (as a decimal number!)

Calculating the digital output Example: 8-bit, simple binary A/D converter Range is 0 to 5V. Input is 3.15V. Find output.