Analogue Interfacing. What is a signal? Continuous vs. Discrete Time. Continuous time signals

Size: px

Start display at page:

Download "Analogue Interfacing. What is a signal? Continuous vs. Discrete Time. Continuous time signals"

Opal Walton
5 years ago
Views:

1 Analogue Interfacing What is a signal? Signal: Function of one or more independent variable(s) such as space or time Examples include images and speech Continuous vs. Discrete Time Continuous time signals Defined at all instances in time (or other I.V.s) e.g. f(t) = sin(t)

2 Discrete time signals Defined only at a set of discrete (possibly infinite in number) times Time sequence {x[n], n = 0,±1,±2,.} e.g. x[n] = sin(2πn/n), n integer Not the same as digital which is discrete in the dependent variable as well e.g. a sampled continuous time signal with analog digital converter Signal level (voltage) represented by a binary number with limited precision (8, 10, 12, or 16- bit fixed point number) Often x[n] is a sampled version of x(t) at rate 1/T S (uniform spacing) x[n] = x(nt S ), n = 0,±1,±2, The world is analogue One of the key functions of many embedded systems is to control and react to events in the real world In digital systems we deal entirely with discrete signals The real world is temporally continuous and analogue Signals are not electronic: heat, pressure, light,.

3 Need to Convert signals of interest into electrical form suitable for electronic processing (sensing and transduction) Perform signal conditioning to amplify, filter and otherwise transform analogue signals Convert continuous-time, analogue signals to discrete-time sequence of binary numbers (or other digital form) Process the discrete signals, need to retain the relationship with physical properties Convert and digital outputs to analogue signals. May need to filter and condition. Convert electrical signals to heat, light, motion, pressure as appropriate (transduction, actuation) Physical Signal Sensing/ Transduction Signal Conditioning ADC Processing DAC Physical Signal Actuation/ Display Filtering/ Conditioning

4 Sensors and transduction Sensors Many sensors exist to convert a wide range of analogue signals to electronic form Temperature Pressure Speed or Displacement Acceleration Acidity Many others Example: Optical Encoder From

5 Ex: Analog Devices ADXRS300 Gyroscopic Sensor From Ex: Linear Variable Differential Transformer From

6 Example: Thermocouple Seebeck Effect: junction between two dissimilar metals creates temperature dependent voltage Basis for thermocouple, a common temperature sensor widely used in process control Typically convert signal of interest to analogue electrical signal Voltage or current varies monotonically with physical signal of interest Need to calibrate, amplify and filter Signal Conditioning

7 Signal Conditioning Amplification and level shifting Convert the range and mean value (offset) of a signal to fit the range of the analogue to digital converter Amplify Attenuate Level shift Filtering Remove unwanted frequency components in a signal (noise, interference ) Shape signal to account for effects of signal transduction and transmission (equalisation) Many filtering operations can be performed after conversion to digital form; some cannot (antialias filtering)

8 Linearisation, calibration Many sensors have nonlinear relationships between the physical signal and its electrical analogue Can be calibrated before (analogue) or after (digital) analogue to digital conversion Calibration before conversion allows faster processing; After is more precise, flexible and reconfigurable Inverting Non-Inverting Figures from Sedra and Smith Filter Differential Amplifier Buffer

9 Analogue to Digital Conversion Analogue-Digital Conversion Convert voltage (analogue signal) to time series of digital numbers Key considerations include resolution, dynamic range, sampling frequency and accuracy 8, 10, 12, 16-bit ADCs are common, higher resolutions available Acronyms ADC, A/D, ATD Typically, analogue signal is sampled by analogue sample and hold circuit Maintains a stable signal to convert HCS12 has two built-in 8/10-bit analogue-digital converters 8 channels can share each converter in time-multiplexed manner Interrupt-based interface possible

10 Quantization Error Representation as digital number Digital signal can only change as fast as least significant bit Changes are quantized to increments of the digital number. 12-bit ADC with linear mapping, each increment is 1/4096 of fullscale Causes numerical error between the true value and the digital representation (error range 0-1 LSB or +/-0.5 LSB) Sampling Error Sampling interval is a key consideration Limits temporal resolution Mean latency of 1/2 sample period from sampling alone Irregular sampling can cause distortion of the sampled signal Sampling rate should be controlled through timer circuitry

Effects of Irregular Sampling 12 10 8 6 4 2 0 0 2 4 6 8 10 12 12 10 8

11 Effects of Irregular Sampling True Analogue Delayed Analogue Irregular Digital

Temporal resolution limited by sampling rate Can up-sample to interpolate missing samples Makes assumptions about signal From Catsoulis Aliasing

12 Temporal resolution limited by sampling rate Can up-sample to interpolate missing samples Makes assumptions about signal From Catsoulis Aliasing Periodicity Periodic signals repeat regularly x ( t) = x( t + T) for some T and all t, fundamental period is the smallest such T, e.g. x( t) = sin( t) = sin( t + 2π ) = sin( t + 4π ) is periodic with period 2π Fourier theory states that we can compose arbitrary signals by combining sinusoids Periodic signals with Fourier Series Aperiodic signals with Fourier Transform But cannot represent all frequencies in an analogue signal in a sampled digital signal

13 if f 0 = 1 2, period N = 2, ω 0 = 2πf 0 then if x[n] = cos(nω 0 ) x[0] =1 x[1] = -1 x[2] =1 Alternates sign every discrete interval, obviously fastest alternation possible 5 e.g. ω0 = π, period N = then if x[n] = cos(nω 0) x[0] = 1 x[1] = 0 x[2] = 1 x[3] = 0 x[4] = 1 looks like ω 0 = 2π/5 or N =5 when one frequency is indistinguishable from another it is known as aliasing Nyquist Rate To be able to reconstruct a signal from a sampled digital signal unambiguously Need to sample at least twice the highest frequency in the signal Or need to limit the highest frequency in the signal to less than one half the sampling rate (anti-aliasing filter) Theoretical limitations, practically need to sample faster than Nyquist rate

14 Anti-aliasing filtering needs to be done before sampling Flash Converters In parallel, compare with voltage levels corresponding to all possible digital numbers Priority encoder chooses largest digital number less than input Very fast but expensive in circuitry (e.g comparators for 10- bit ADC) Can implement nonlinear converters easily

15 Successive Approximation Based on comparison with input Successively count up or down ADC digital number When digital number equals input, conversion is done from Successive Approximation Special counter: count first by mostsignificant bit and work to leastsignificant bit. Faster than standard count Example 10-bit Successive Approximation Converter

16 Successive approximation converters are typically slower than flash since they convert over multiple cycles Can compromise and estimate several bits at each cycle (pipelined converter) Sigma-Delta A 1-bit DAC suitable for high resolution, low measurement rate applications

Image acquisition Analogue signals are not only 1-D, for example images acquired by a CCD array are analogue Representation of analogue signals Engineering Units and Fixed Point Representations

17 Image acquisition Analogue signals are not only 1-D, for example images acquired by a CCD array are analogue Representation of analogue signals Engineering Units and Fixed Point Representations Physical signal expressed in standard unit: Watts, cd/m 2, N, Converted to voltage which is represented by a digital number (e.g for 8-bit converter) Often more useful to work in engineering units that represent physical units

18 Could represent as a floating point number with floating point support Slow in software Additional circuitry for hardware support in custom processor Hardware support may not be available or economical on chosen processor One can consider the digital number as a fixed point representation Can define the decimal point at any convenient bit position After bit zero gives standard integer representation Setting before most significant bit gives range 0 to 1 (actually one step less than one) Codecs Stands for coder/decoder Where paired coding and decoding of signals (eg ADC and DAC) occurs the device is called a codec Many different ways of mapping the signal to the code Linear Logarithmic Differential pulse coded

19 Digital to Analogue Conversion Digital to analogue conversion One approach: Sum up contribution of each bit set in digital number Weight each bit according to its place - 1, 2, 4, 8 This converts to analogue voltages but still need to handle time discretisation Zero-order hold: output is staircase like, switching at each sample Can filter to remove components above Nyquist rate and recover signal

20 PWM Pulse width modulation (PWM) can support a form of analogue output interfacing Control the duty cycle of a periodic binary signal If signal has high frequency, filtering with external filter or by a slow output device (e.g. an electric motor) can remove the high frequency switching Leaves lower frequency signal voltage is average over the cycle Variations in filtered signal reflect variations in duty cycle From Heath, 2003 Actuators, Motors and Displays

21 Interfacing with Actuators and Switching Power Switching large loads requires special interacing and protection circuitry Many options exist for switching/ controlling devices requiring large amounts of power; choice depends on Level and type of control desired Type of load Requirements for protection, isolation, EMC H Bridge circuits From Heath, 2003

Developer Techniques Sessions

1 Developer Techniques Sessions Physical Measurements and Signal Processing Control Systems Logging and Networking 2 Abstract This session covers the technologies and configuration of a physical measurement