Modern InstrumentationPHYS 533/CHEM 620 Lecture 8 Analog to Digital (A/D) & Digital to Analog (D/A) Converters Amin Jazaeri Fall 2007
Types of Signals • Analog Signals (Continuous-Time Signals) • Discrete Sequences (Discrete-Time Signals) Signals that are continuous in both the dependant and independent variable (e.g., amplitude and time). Most environmental signals are continuous-time signals. Signals that are continuous in the dependant variable (e.g., amplitude) but discrete in the independent variable (e.g., time). They are typically associated with sampling of continuous-time signals.
Types of Signals (cont.) • Digital Signals Signals that are discrete in both the dependant and independent variable (e.g., amplitude and time) are digital signals. These are created by quantizing and sampling continuous-time signals or as data signals (e.g., stock market price fluctuations).
What is DSP? • Changing or analyzing information that is measured as discrete sequences of numbers • The representation, transformation, and manipulation of signals and the information they contain
Unique Features of DSP • Signals come from the real world • Need to react in real time • Need to measure signals and convert them to digital numbers • Signals are discrete • Information in between discrete samples is lost
Processing Real Signals • Most of the signals in our environment are analog such as sound, temperature and light • To processes these signals with a computer, we must: 1.convert the analog signals into electrical signals, e.g., using a transducer such as a microphone to convert sound into electrical signal 2. digitize these signals, or convert them from analog to digital, using an ADC (Analog to Digital Converter)
Processing Real Signals (cont.) • In digital form, signal can be manipulated • Processed signal may need to be converted back to an analog signal before being passed to an actuator (e.g., a loudspeaker) • Digital to analog conversion can be done by a DAC (Digital to Analog Converter)
Typical DSP System Components • Input lowpass filter (anti-aliasing filter) • Analog to digital converter (ADC) • Digital computer or digital signal processor • Digital to analog converter (DAC) • Output lowpass filter (anti-imaging filter)
DSP System Components • Analog input signal is filtered to be a band-limited signal by an input lowpass filter • Signal is then sampled and quantized by an ADC • Digital signal is processed by a digital circuit, often a computer or a digital signal processor • Processed digital signal is then converted back to an analog signal by a DAC • The resulting step waveform is converted to a smooth signal by a reconstruction filter called an anti-imaging filter
Advantages of DSP • Versatility • Digital systems can be reprogrammed for other applications • Digital systems can be ported to different hardware • Repeatability and stability • Digital systems can be easily duplicated • Digital systems do not depend on strict component tolerances • Digital system responses do not drift with temperature
Advantages of DSP (cont.) • Simplicity • Some things can be done more easily digitally than with analog systems (e.g., linear phase filters) • Security can be introduced by encryption/scrambling • Digital signals easily stored on magnetic media without deterioration
Disadvantages of DSP • DSP techniques are limited to signals with relatively low bandwidths • The point at which DSP becomes too expensive will depend on the application and the current state of conversion and digital processing technology • Currently DSP systems are used for signals up to video bandwidths (about 10 MHz) • The cost of high-speed ADCs and DACs and the amount of digital circuitry required to implement very high-speed designs (> 100 MHz) makes them impractical for many applications • As conversion and digital technology improve, the bandwidths for which DSP is economical continue to increase
Disadvantages of DSP (cont.) • The need for an ADC and DAC makes DSP not economical for simple applications (e.g., a simple filter) • Higher power consumption and size of a DSP implementation can make it unsuitable for simple very low-power or small size applications
A/D and D/A converters • These are the means by which a signal can be converted from analog to digital or from digital to analog as necessary. • The idea is obvious but implementation can be complex. • There are certain types of D/A and A/D that are trivially simple. • We will start with these and only then discuss some of the more complex schemes. • In certain cases one of these simple methods is sufficient.
Why is an A/D Converter Used? • Provides a link between the analog world of transducers and the digital world of signal processing and data handling. • This allows for: • Data storage • Numerical and graphical displays • Computer or logic circuit processing • Transmission
Limitations of Digital Techniques • The real world in mainly analog. • To deal with analog inputs, three steps must be followed: • Convert the real-world analog inputs to digital form(analog-to-digital converter, ADC) • Process (operate on) the digital information • Convert the digital output back to real-world analog form (digital-to-analog converter,DAC)
A/D and D/A converters • Analog to digital and, to a lesser extent, digital to analog conversion are common in sensing systems since most sensors and actuators are analog devices and most controllers are digital. • Most A/Ds required voltages much above the output of some sensors. • Often the output from the sensor must be amplified first and only then converted. • This leads to errors and noise and has resulted in the development of direct digitization methods based on oscillators (to be discussed later).
Where are A/D Converters Used (sensors)? • Strain Gages • Thermocouples • Data Acquisition Devices • Load Cells • Microphones (voice circuitry)
Threshold digitization • In some cases, an analog signal represents simple data such as the presence of something. • For example, in chapter 5 we discussed the detection of teeth on a gear using a hall element. • Suppose the signal obtained at the output of a sensor (which is quite small), looks more or less like a sinusoidal function. • We are only interested in the part of the signal that is above a certain threshold.
A/D Conversion Process 1) Quantizing: • Partitioning analog signal range into a number of discrete quanta. • Matching the input signal to the correct quantum.
A/D Conversion Process 2) Encoding: • Assigning a unique digital code to each quantum. • Matching the digital code to the input signal. • Binary System: • Range containing an even number (2n) of consecutively numbered quanta. • Code consist of binary bits (1 or 0) corresponding to the binary number of the signal quantum.
A/D Conversion Process • Example: • Sample analog signal with range of 0-15 V • Partition into a range of 16 quantization levels. • Using 4-bit binary encoding.
Basic Operation of ADCs • START command initiates the operation. • Control unit modifies the binary number stored in the register. • The binary number in the register is converted to an analog output VAX by the DAC. • The comparator compares VAX with the analog input VA. As long as VAX < VA, the comparator output stays HIGH. When VAX exceeds VA by at least an amount equal to VT, the comparator output goes LOW ad stop modifying the register number. • The control logic activates the end-of-conversion signal, EOC.
Digital-Ramp ADC • Also known as a counter-type ADC. • Uses a binary counter as the register and allows the clock to increment the counter one step at a time until VAX >= VA. • Example 10-13A,B.
Resolution • Smallest change in input which will result in a change in the digital input. • Resolution = VFS/2n • VFS assumes analog input in volts. • n = number of bits in digital output. • 2n = number of states. • Accuracy increases as n increases.
A/D Resolution and Accuracy • Source of error: step size of the internal DAC. • Quantization error: difference between the actual (analog) quantity and the digital values assigned to it. • Accuracy is dependent on the accuracy of the circuit components. • Example 10-14.
Sampling Rate • Frequency with which the A/D converter “checks” the analog signal. • Minimum sampling rate should be at least twice the highest data frequency of the analog signal.
Accuracy Comparison • Increased accuracy results with greater resolution (y-axis divisions) and higher sampling rate (x-divisions). Low Accuracy Improved Accuracy
Conversion Techniques • Comparator • Most Basic A/D Converter • 2 Inputs (Signal, Reference), 1 Output • Output = 1 if signal > reference • Output = 0 if signal < reference
The simplest form of ADC uses a resistance ladder to switch in the appropriate number of resistors in series to create the desired voltage that is compared to the input (unknown) voltage Converting Analog into DigitalElectronically
The output of the resistance ladder is compared to the analog voltage in a comparator When there is a match, the digital equivalent (switch configuration) is captured Converting Analog into DigitalElectronically
Converting Analog into DigitalComputationally • The analog voltage can now be compared with the digitally generated voltage in the comparator • Through a technique called binary search, the digitally generated voltage is adjusted in steps until it is equal (within tolerances) to the analog voltage • When the two are equal, the digital value of the voltage is the outcome
Converting Analog into DigitalComputationally • The binary search is a mathematical technique that uses an initial guess, the expected high, and the expected low in a simple computation to refine a new guess • The computation continues until the refined guess matches the actual value (or until the maximum number of calculations is reached) • The following sequence takes you through a binary search computation
Initial conditions Expected high 5-volts Expected low 0-volts 5-volts 256-binary 0-volts 0-binary Voltage to be converted 3.42-volts Equates to 175 binary Binary Search Analog Digital 256 5-volts Unknown (175) 3.42-volts 2.5-volts 128 0 0-volts
Conversion Techniques • Direct/Flash Conversion • Fastest n-bit Conversion Technique • Compares input signal to set of reference signals representing all amplitudes using comparators. • Uses priority encoder to match parallel digital output to corresponding comparator output states.
Conversion Techniques • Integrating Conversion • Uses analog integrating circuits. • Converts average input values into trains of pulses to be encoded by digital counters or processors. • Feedback Conversion • Uses a n-bit DAC to compare DAC and original analog results. • Comparison changes digital output to bring it closer to the input value.
Types of ADC • Successive-Approximation (Sampling) Converter • Flash Converter • Dual-Slope Converter • Voltage-to-Frequency (V/F) Counting Converter • Sigma-Delta Converter • RC Converter • Pulse-width modulation (PWM) Converter
Subranging Flash ADC • Pure Flash ADC is very expensive for large bits. • Subranging Flash ADC is Hybrid between successive approximation and flash. • AD7280 or ADC0820 uses two 4-bit flash ADC to build an 8-bit subranging Flash ADC. • Figure next page: Upper 4-bit (MSB) flash ADC finds coarse MSB digital output, then converts into approximate analog level by a 4-bit DAC, the lower 4-bit flash ADC finds the fine 4-bit (LSB) digital code.
Factors in Converter Selection • Speed • Conversion Time • Sampling Rate • Resolution • Noise Immunity • Ability to approximate an unsteady signal • Cost