Theoretical 1 Bit A/D Converter

Transcription

1 Acquisition 16.1 Chapter 4 - Acquisition D/A converter (or DAC): Digital to Analog converters are used to map a finite number of values onto a physical output range (usually a ) A/D converter (or ADC): Analog to Digital converters are used to convert continuous physical signals (usually ) into equivalent or binary numbers. Theoretical 1 Bit A/D Converter Digital (Binary) Output 1 Theoretical 3 Bit A/D Converter Digital (Binary) Output V -3.75V -.5V -5V +5V +.5V +3.75V +5V Analog Voltage -5V -3.75V -.5V 1-5V +5V +.5V +3.75V 11 +5V Analog Voltage 1 1 Offset Binary 3 Bit A/D Converter -5V -3.75V -.5V Digital (Binary) Output -5V V +.5V +3.75V V Analog Voltage Bits: The number of digits in a binary number. A 1 bit binary number is either or 1, a bit binary number is either, 1, 1, or 11, etc. An N bit binary number can have different values. Binary: Binary numbers are in base, only allowable digits are and 1. 1 Hex (or hexadecimal): Digital values expressed in base 16. Note that 1 hex digit is exactly 4 binary digits

2 Acquisition 16. Range: The difference between the min and max analog voltages that can be accurately converted to binary. Common ranges are volts ( range), to +1 V (1 V range), and volts ( V range). Resolution: Amount of analog voltage equivalent to a single binary bit = range / N resolution of 1 bit A/D with a + 5 V range ADC Formulas - Bipolar Bipolar input: - V REF < V IN < + V REF midpoint or nominal voltage, digital value V nom ( V REF) n V REF ( V REF) the resolution is centered about the nominal value, so 1 1 V REF ( V REF) V in = Vnom resolution Vnom n ADC Formulas - Unipolar Example #1 Unipolar input: < V IN < + V REF midpoint or nominal voltage, V digital value V nom n REF the resolution is centered about the nominal value, so 1 1 VREF V in = Vnom resolution Vnom n Given a 1 bit, + 5V ADC, what is the nominal voltage for a digital value of 1? What range of input voltages would all be converted to the digital value of 1? Example # Given a 1 bit, to 1 V ADC, what is the nominal voltage for a digital value of 763? Example #3 Given a 1 bit, +1V ADC, what digital value would V in = +5.43V convert to? What range of input voltages would all be converted to the digital value of 763? Given an 8 bit, to 5V ADC, what digital value would V in = 34V convert to?

3 Acquisition 16.3 Multiplexer: a switching" device to connect different analog signals to the same ADC 8 or 16 different analog inputs common, single-ended ended or differential inputs used, inputs often amplified near multiplexer All 16 inputs must have the same ground (common) Single-Ended Multiplexer Differential Multiplexer Typical DAQ System Connect inputs here + E - E Must be careful with these All 8 inputs can have different grounds (commons) (inside computer) National Instruments PCI-61 M-Series M Board 16 bit resolution (~.3 mv/bit) accuracy specs on manufacturer s datasheet +1 volts full scale input (bipolar) offset binary coding 8 channel differential input multiplexer maximum single or multi-channel sampling rate of 5 ks/s (5, samples/sec) Sources of Additional Info Omega Transactions on Acq. analogio.html Locally stored at 36 website (Weblinks( Weblinks) CyberResearch cyberresearch.com/members/.com/members/dadesign.html EE Lab at University of Pennsylvania ee.upenn.edu/rca/software/ /software/labview/ daqlvoverview.html

4 Acquisition 16.4 Chapter 5 Discrete Sampling and Analysis Signal Express - Configuration What should you set these values to? Sampling rate affects rad/s,, Hz Hz Hz samples rad/s,, Hz 15 rad/s,, Hz 1 Hz 15 Hz samples 1 Hz samples

5 Acquisition rad/s,, Hz 5 rad/s,, Hz Hz 5 Hz samples 3 Hz samples rad/s,, Hz Hz Hz samples How fast should you sample? Nyquist Theorem: as fast as the highest frequency component of your input signal! or you will get - samples of a high frequency signal look like a low frequency In In many (but not all!) applications, sample times the highest frequency component of input signal! How do you prevent aliasing? (at least x highest frequency in input) can lead to too much data! to attenuate (or reduce) amplitude of high frequency signals a simple RC low-pass filter is often included on data acquisition boards! Magnitude, db Anti-aliasing Filters 1st order nd order 3rd order 4th order Frequency,, rad/sec

6 Acquisition 16.6 Signal Express - Configuration Brief Intro to Spectrum Analysis Total_sample_time analysis relates time and frequency domains Any Any (time domain) can be represented by sine and cosine waves (frequency domain) Where is spectral analysis used? monitoring roller bearing faults will generate vibration signals at characteristic multiples of the shaft speed spikes in the frequency domain often indicate system s natural frequencies generally want to avoid exciting the system at these frequencies Sample Set #1 14 data points collected at 1 Hz sampling rate (using A/D converter) Amplitude Hz sine 3 Hz + 1 Hz sine Magnitude Valid Invalid Magnitude.9.7 alias of the ~3 Hz signal.6 appears at ~97 Hz.5.3 alias of the ~1 Hz signal. appears at ~9 Hz

7 Acquisition 16.7 Sample Set # 14 data points collected at 1 Hz sampling rate (using A/D converter) Hz Magnitud First Set, 14 1 Hz Folding Frequency or Nyquist Limit of 5 Hz Valid Invalid Magnitud First Set, 14 1 Hz alias of the ~3 Hz signal appears at ~97 Hz alias of the ~1 Hz signal appears at ~9 Hz Magnitud Lower Half of FFT First Set, 14 1 Hz most of the original signal is a sine wave at ~3 Hz some of the original signal is a sine wave at ~1 Hz noise and artifacts from FFT process