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## Modern Instrumentation PHYS 533/CHEM 620

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**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.**Diagram of a subranging Flash built from two 4-bit flash**ADC**Factors in Converter Selection**• Speed • Conversion Time • Sampling Rate • Resolution • Noise Immunity • Ability to approximate an unsteady signal • Cost