Data Conversion (5.3) Learning Objectives PDF

Data Conversion (5.3) Learning Objectives 5.3.1.1 Identify analogue data (Level 1). 5.3.1.2 Identify digital data (Level 1). 5.3.2 Recall the basic operation and function of operational amplifiers (S). 5.3.2.1 Recall the operation of analogue to digital converters (Level 1). 5.3...

Data Conversion (5.3) Learning Objectives 5.3.1.1 Identify analogue data (Level 1). 5.3.1.2 Identify digital data (Level 1). 5.3.2 Recall the basic operation and function of operational amplifiers (S). 5.3.2.1 Recall the operation of analogue to digital converters (Level 1). 5.3.2.2 Recall the basic operation of digital to analogue converters (Level 1). 5.3.2.3 Recall the applications of analogue to digital converters (Level 1). 5.3.2.4 Recall applications of digital to analogue converters (Level 1). 5.3.2.5 Identify the analogue data inputs and digital data outputs of analogue to digital converters (Level 1). 5.3.2.6 Identify digital data inputs and analogue data outputs of digital to analogue converters (Level 1). 5.3.2.7 Recall the limitations of the various types of digital and analogue data (Level 1). 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 32 of 285 CASA Part 66 - Training Materials Only  Digital and Analogue Data Definitions At a practical level, the difference between analogue data and digital data is in how the data is measured. Analogue data is continuous and aims to identify every nuance of what is being measured, while digital data uses sampling to encode what is being measured. Another way to consider it is that analogue is the unfiltered raw data and digital is filtered data for practical use. Converting Between Analogue and Digital Analogue-to-Digital Converters (ADC) and Digital-to-Analogue Converters (DAC) are used to interface computers to the analogue world so that a computer can monitor and control a physical variable. A typical system may include: Transducer ADC Computer DAC Actuator. An understanding of Op-amps used as comparators is required to understand the operation of ADCs and DACs and will be introduced in the following section. Aviation Australia Analogue-to-Digital Converter (ADC) and Digital-to-Analogue Converter (DAC) 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 33 of 285 CASA Part 66 - Training Materials Only  Transducer The physical variable is normally a non-electric quantity. A transducer is a device that converts that physical variable into an electrical variable ADC The transducer’s electrical analogue output serves as the analogue input to the ADC. The ADC converts this analogue input into a digital output. The output consists of a number of bits that represent the analogue value. For example, the transducer may output an analogue voltage range of 800 to 1500 mV, which the ADC might convert to 01010000 (80) to 10010110 (150). Computer The digital representation from the ADC is processed by the computer. It may perform calculations or other operations and then give a digital output to manipulate the physical variable. DAC The digital output from the computer is converted to a proportional analogue voltage or current. For example, the computer may output a digital range between 00000000 and 11111111, which the DAC converts to a voltage ranging from 0 to 10 V. Actuator The analogue signal from the DAC is often connected to some device used to physically control or adjust the physical variable. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 34 of 285 CASA Part 66 - Training Materials Only  Operational Amplifiers The Op-Amp Operational amplifiers are often used to compare the amplitude of one voltage with another. In this application, the op-amp is used in the open-loop configuration, with the input voltage on one input and a reference voltage on the other. © Aviation Australia Operational amplifier The term operational amplifier, or op-amp, refers to a class of high-gain DC-coupled amplifiers with two inputs and a single output. The modern Integrated Circuit (IC) version is typified by the famous 741 op-amp. Some of the general characteristics of the IC version are: High gain, on the order of a million High-input impedance, low-output impedance Used with split supply (usually +/- 15 V) Used with feedback, with gain determined by the feedback network. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 35 of 285 CASA Part 66 - Training Materials Only  Zero Level Detection One application of an op-amp used as a comparator is to determine when an input voltage exceeds a certain level. Note in the illustration that the inverting input is grounded to produce a zero level and that the input signal is applied to the non-inverting input. Aviation Australia Zero level detection Because of the high open-loop voltage gain, a very small difference between the two inputs drives the op-amp into saturation, causing the output voltage to go to its limit. For example, consider an op-amp with a gain of 100 000. A voltage difference of only 0.25 mV between the inputs could produce an output voltage of 25 V if the op-amp were capable. However, since most op-amps have a maximum output voltage of +/- 15 V because of their DC supply voltages, the device would be driven into saturation. The wave shape illustration shows the result of a sine wave input voltage applied to the non-inverting input of the zero-level detector. When the sine wave is negative, the op-amp output is at its maximum negative level. When the sine wave input crosses zero (going positive), the amplifier is driven to its opposite state and the output goes to its maximum positive level. The zero-level detector can be used as a squaring circuit to produce a square wave from a sine wave. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 36 of 285 CASA Part 66 - Training Materials Only  Non-Zero Level Detection The zero-level detector can be modified to detect voltages other than zero by connecting a fixed reference voltage to the inverting input as shown in diagram (a) using a battery. A more practical arrangement is shown in diagram (b) uses a voltage divider to set the reference voltage. A Zener diode can also be used to set the reference voltage. Aviation Australia (a) Battery reference, (b) Voltage divider reference, (c) Waveform As long as the input voltage (Vin) exceeds the reference voltage (VREF), the output goes to its maximum positive voltage. Non-Inverting Amplifier An op-amp is connected in a closed-loop configuration as a non-inverting amplifier with a controlled amount of voltage gain. Non-inverting amplifier 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 37 of 285 CASA Part 66 - Training Materials Only  The input signal is applied to the non-inverting input (Vin +). The output is applied back to the inverting input (negative -) through the feedback circuit (closed loop) formed by Resistor input (R1) and Resistor feedback (R2). This creates negative feedback as follows. R1 and R2 form a voltage divider circuit which reduces Voltage out (Vout) and connects the reduced voltage to the inverting input. Inverting Amplifier The Inverting amplifier input signal is applied to the inverting input (2). The output is applied back to the inverting input (2) through the feedback circuit (closed loop) formed by Resistor input (R1) and Resistor feedback (Rf). This creates negative feedback using R1 and Rf as a voltage divider circuit. The voltage divider reduces Voltage out (Vout) and connects the reduced feedback voltage to the inverting input. Aviation Australia Inverting amplifier For equal resistors, the circuit has a gain of -1 and is used in digital circuits as an inverting buffer (also known an inverter). Therefore, an op-amp inverting amplifier with a gain of 1 serves as an inverting buffer. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 38 of 285 CASA Part 66 - Training Materials Only  Digital to Analogue Conversion Digital-to-Analogue Converters One common requirement in electronics is to convert signals back and forth between analogue and digital forms. Most such conversions are ultimately based on a DAC or D/A converter circuit. Therefore, it is worth exploring just how we can convert a digital number that represents a voltage value into an actual analogue voltage. Digital input values on 1, 2, 4, and 8 are input to the op-amp via weighted resistors. The resultant voltage from the resistors is applied to the inverting input of the op-amp. Aviation Australia Binary weighted resistor DAC circuit 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 39 of 285 CASA Part 66 - Training Materials Only  Binary Weighted Resistor DAC The illustrated circuit is the binary weighted resistor DAC shown in the previous section. It assumes a 4-bit binary number. The circuit uses +5 volts as a logic 1 and 0 volts as a logic 0. The circuit will convert the applied binary number to a matching (inverted) output voltage. In the following circuit, the digits 1, 2, 4 and 8 refer to the relative weights assigned to each input. Thus, 1 is the Least Significant Bit (LSB) of the input binary number, and 8 is the Most Significant Bit (MSB). Aviation Australia Binary Weighted Resistor DAC circuit If the input voltages are accurately 0 and +5 volts, then the 1 input will cause an output voltage of -5 × (4 k/20 k) = -5 × (1/5) = -1 V whenever it is a logic 1. Similarly, the 2, 4 and 8 inputs will control output voltages of -2, -4 and -8 V respectively. As a result, the output voltage will take on one of 10 specific voltages in accordance with the input BCD code. In the diagram below, the circuit is a binary weighted resistor DAC and truth table shows the conversion for a binary-weighted resistor DAC. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 40 of 285 CASA Part 66 - Training Materials Only  Aviation Australia Binary weighted resistor DAC and truth table 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 41 of 285 CASA Part 66 - Training Materials Only  R/2R Ladder DAC Binary weighted resistor DACs have some practical limitations. This is because there is a large difference in resistor values between the LSB and MSB. For example, in a 12-bit binary weighted resistor DAC – if the MSB resistor is 1 kΩ, then the LSB resistor will be over 2 MΩ. The problem is that when temperature varies, the resistance values over such a large range cannot maintain the correct ratios. The R/2R ladder overcomes this issue through its different circuit construction. The R/2R ladder uses only two resistance values and they are not greatly different. This means temperature variations have very little effect on the accuracy or the resistor ratios and therefore also have little effect on the voltage levels applied to the op-amp. © Aviation Australia R/2R ladder DAC (4-bit example) 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 42 of 285 CASA Part 66 - Training Materials Only  R/2R Ladder DAC Operation The following diagram, is an example of a 4-bit R/2R Ladder DAC circuit with the inputs labelled. O/P is the output. Aviation Australia R/2R ladder DAC with binary input 1000 The fundamental operating principle of the R/2R ladder is that two parallel resistors of equal value have an overall circuit resistance of one half of the value of an individual resistor. So two 2xR resistors in parallel have an overall resistance of 1xR. Selecting inputs as either five volts or zero volts determines the configuration of the resistive circuit. In the R/2R ladder illustrated has a binary input of 0001 where the one equals five volts on S1. S1 is the most significant bit (MSB) and S4 is the least significant bit (LSB) so the input of 0001 illustrated represents a binary value of 10002. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 43 of 285 CASA Part 66 - Training Materials Only  Analogue to Digital Conversion Analogue to Digital Conversion Methods Analogue to Digital Conversion (ADC) is a common interfacing process often used when a linear analogue system must provide inputs to a digital system. Many methods for ADC are available. We will cover the basic operation of two ADC types: Flash or simultaneous Digital-ramp or counter-type. The ADC process is generally more complex and time-consuming than the DAC process and many different methods have been developed. It may never be necessary to design or construct an ADC (they are available as complete packaged units). However, the techniques that are used provide insight into what factors determine an ADC’s performance. IN ADC OUT Creative Commons Analogue to digital converter 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 44 of 285 CASA Part 66 - Training Materials Only  Flash ADC To convert a digital code to an analogue voltage, we only had to find a way to effectively assign an appropriate voltage to each bit, and then combine them. Is there an equally easy way of finding the digital code that corresponds to a given analogue voltage? © Aviation Australia Flash ADC Consider the very simple requirement to determine whether an analogue voltage was closest to 0, 1, 2 or 3 volts. The result is stored as a 2-bit binary number. The first step in making this determination might be a set of three comparators, connected as shown below. As the analogue voltage increases, the comparators will, one by one from the bottom up, change state from false to true. Of course, additional digital circuitry will be required to encode these signals into the corresponding digital number. But this circuit forms the sensing array that will determine directly which code will be closest to the actual analogue voltage. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 45 of 285 CASA Part 66 - Training Materials Only  © Aviation Australia Flash ADC with encoder This approach will work and can be expanded to any number of steps for finer resolution of the analogue voltage. However, as you have probably already perceived, there is a problem with this approach in that the number of comparators required increases exponentially with the number of binary bits used to store the code. Using this approach to convert a 0 to 9-V range to a binary number will require nine comparators. A 4-bit binary number, counting from 0 to 15, requires 15 comparators. And a typical 8-bit circuit requires 255 comparators. This approach rapidly becomes too expensive for ordinary use, although it is practical if very high speed is required. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 46 of 285 CASA Part 66 - Training Materials Only  Aviation Australia Flash ADC number of comparators grows exponentially with increasing binary bits 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 47 of 285 CASA Part 66 - Training Materials Only  Flash ADC Encoder Due to the nature of the sequential comparator output states (each comparator saturating ‘high’ in sequence from lowest to highest), the same highest-order-input selection effect may be realised through a set of Exclusive-OR (XOR) gates. This allows the use of a simpler, non-priority encoder. The encoder circuit itself can be made from a matrix of diodes, demonstrating just how simply this converter design may be constructed. Not only is the flash converter the simplest in terms of operational theory, but it is the most efficient of the ADC technologies in terms of speed, being limited only in comparator and gate propagation delays. Unfortunately, it is the most component- intensive for any given number of output bits. Aviation Australia Flash ADC encoder An additional advantage of the flash converter, often overlooked, is the ability for it to produce a scaled output. For example, the diagram shows a float sensor in a fuel tank. Near the half-full point, the float moves almost vertically, giving a realistic readout of the contents. But at the extremities of close to full and empty, the float has more horizontal movement, giving a larger change in angle. This would result in a large change in the output voltage for little change in fuel level. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 48 of 285 CASA Part 66 - Training Materials Only  Aviation Australia Analogue fuel sender By adjusting the value of the resistors, each change of Binary 1 at the output would represent the same change in fuel quantity, no matter the fuel level. With equal-value resistors in the reference voltage divider network, each successive binary count represents the same amount of analogue signal increase, providing a proportional response. For special applications, however, the resistor values in the divider network may be made unequal. This gives the ADC a custom, nonlinear response to the analogue input signal. No other ADC design is able to grant this signal-conditioning behaviour with just a few component value changes. 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 49 of 285 CASA Part 66 - Training Materials Only  3-Bit Flash ADC Example Calculate the encoder inputs and digital outputs for the following analogue input voltage levels: Ex 1: VA = 2 volts Ex 2: VA = 4 volts Ex 3: VA = 5 volts Aviation Australia Flash ADC and truth table (3-bit digital output) 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 50 of 285 CASA Part 66 - Training Materials Only  Digital-Ramp ADC A slower but much less expensive approach involves the use of a DAC and a single comparator. One of the simplest versions of the general ADC uses a binary counter as the register and allows the clock to increment the counter one step at a time until the comparator output (Vax ) ≥ the ADC input (Va). It is called a digital-ramp ADC because the waveform at Vax is a step-by-step ramp. It may also be referred to as a counter-type ADC. It contains a counter, a DAC, an analogue comparator and a control AND gate. The comparator output serves as the active-LO (low) End of Conversion (EOC) signal. The ADC circuit output is represented by the Counter IC outputs. The digital values produced by the Counter represent digital or binary numbers. The output illustrated is sent to the DAC and would also be sent to a display device. Aviation Australia Digital-ramp ADC 2023-03-03 B1-05a Digital Techniques / Electronic Instrument Systems Page 51 of 285 CASA Part 66 - Training Materials Only