Data Acquisition and Filtering Exercise for Electrical Engineering Students, Study notes of Physics

Download Data Acquisition and Filtering Exercise for Electrical Engineering Students and more Study notes Physics in PDF only on Docsity! ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 1 Overview Computers allow for the automation of data acquisition at speeds that are difficult to comprehend. This is a good thing, but one must always bear in mind that computers are not intelligent. They do exactly what they are told, regardless of theoretical accuracy, without knowledge of physical practicality, and with no regard for safety. Many people are familiar with this behavior because they have family members who act this way, often while drunk (if you don’t have a family member like this, think carefully, you may be this member of your family!). Since computers perform only as well as the programmer programmed, it is wise to keep some basic concepts of data acquisition in mind so that you ensure the signals you work so hard to digitize are a faithful representation of reality. This lab will demonstrate and explore these concepts. By the end of the session you should be able to: • Understand the effects of DAQ resolution on your data • Prevent aliasing of your signal when collecting data • Analyze filtering circuits • Build both passive and active filters Suggested reading: Morris & Langari Chapter 6 (read online). Exercise 1 – Data Acquisition (DAQ) Resolution Background Computer data acquisition systems typically convert signals from analog to digital form. Since digital signals are discrete in both time and amplitude, the signal amplitude is approximated by one of a discrete and finite set of values and becomes quantized. The resolution, Vres, or minimum voltage that can be discriminated, of a DAQ system is determined by the voltage range it can measure, Vrange, and the number of bits for the DAQ, bits range res V V 2  . The resolution of a transducer, Tres, can be determined by multiplying Vres by the static sensitivity of the transducer, K. Before using a transducer to measure a variable, it is important that you know its resolution and range so that you pick the correct transducer for the application. In this exercise, you will observe signal quantization. Materials - cDAQ-9172 - some wire ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 2 Procedure Analysis 1. If the 12-bit NI 9201 analog input module is set to ±10 V, what is its resolution? Measurements 1. Open the LabView VI you created called DAQ OutPut input.vi 2. There is a good chance your DAQ Assistant Express VI will not work because it is set to be used with a different module. Double click the DAQ Assistant express VI, right click on “voltage channel”, and select change physical channel. Make sure your supported physical channel matches your current physical channel. If you need to change the channel, make sure you click ‘OK’ to exit the windows after the change, or it will not be saved! 3. Repeat this procedure for the second DAQ Assistant. 4. Connect the output channel of 201 is only on channel 9. your NI 9263 to the input channel of your NI 9201. Be sure to connect the common grounds. COM on the 9 5. Run the program with Amplitude 1 and Frequency 10.1 (your plots should look very similar) 6. Change your Amplitude to 0.1, 0.08, 0.06, 0.04, and 0.02 and comment on what begins to happen to the input voltage as you reduce the Amplitude to smaller and smaller values. 7. Zoom in on the y-axis of the input graph and estimate the minimum change in y-value observed in the data. How does this compare to your estimate for the DAQ resolution? 8. What happens if you choose an Amplitude of 0.002? ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 5 Exercise 3 – Filters Background There are two basic types of electrical signals that are produced when using electricity. These are direct current (DC) and alternating current (AC). An example of direct current can be seen in a battery where the voltage does not fluctuate with time. In instrumentation DC can be used to control a motor’s speed or used to control parameters such as start and stop functions on a machine. AC is the most common type of electrical signal that will be used in instrumentation and is a voltage that varies with time and is most commonly associated with a sine wave. Data obtained from your testing device are typically going to be a voltage or current that will vary with time due to the conditions that are applied to the device. This will result in a voltage that fluctuates with time, an AC signal. Examples of this can be seen when looking at the output signal of an accelerometer. When using AC signals you may find that there is a frequency that is either not wanted or creating interference that creates errors in your data. To prevent this, frequency filters can be used to eliminate certain unwanted frequencies. Filters are also commonly designed to prevent aliasing by blocking frequencies greater than the Nyquist frequency. Filters come in four basic types: low-pass, high-pass, band-pass and band-stop. Each has its own filtering capabilities. Low-Pass: A filter that allows all frequencies below a set frequency. (Figure 1a) High-Pass: A filter that allows all frequencies above a set frequency. (Figure 1b) Band-Pass: A filter that passes all frequencies in a set range. (Figure 1c) Band-Stop: A filter that passes all frequencies except a set range. (Figure 1d) Such filters can only be used on AC signals because DC signals do not produce a frequency. Filters can be used in two different ways known as passive and active filtering. Of the two of these the passive filter is the most basic that can be built and uses resistors and capacitors to eliminate unwanted frequencies. Passive filters have a limitation in the amount of elimination of the surrounding frequencies but can be inserted into a circuit without the need of external power. Active filters are better at the elimination of the surrounding frequencies but require external power. LabVIEW Preparation Before we look at the effect filters have on signals, we must create a LabVIEW VI to help us visualize their effects. You may write the code yourself or use the pre-written Filters.vi. 1. Connect the cDAQ-9172 chassis to the computer ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 6 2. Use Measurement and Automation Explorer (MAX) to test if the DAQ is working properly 3. Open LabView. 4. Create a new .vi File>>New VI 5. Open the block diagram <ctrl+e>. 6. Create a DAQ Assistant to output two voltages with the following settings. Under timing setting change the Acquisition Mode to “N Samples”, Samples to Write to 100k and the Rate(Hz) to 100k. 7. Create a DAQ Assistant to input two voltages with the following settings. Under timing setting change the Acquisition Mode to “N Samples”, Samples to Read to 100k and the Rate(Hz) to 100k. 8. Place a Chirp Waveform.vi onto the block diagram. Function>>Sound and Vibration>>Generation>>SV Chirp Waveform.vi. 9. On the Chirp Waveform.vi find the nodes labeled Frequency Range, Sampling Info and Amplitude and create controls. 10. Create two copies of the chirp signal by adding Functions>>Express>>Signal Manipulation>>Merge Signals. Wire the output of the Chirp Waveform.vi to the top node of the Merge Signals.vi. Right-click the wire you just created and select “Create Wire Branch” and wire this to the bottom node of the Merge Signals.vi. 11. Wire the output of the Merge Signals.vi to the input of the analog output (AO) DAQ Assistant . 12. Place a Flat Sequence Structure around the analog output DAQ Assistant, Chirp Waveform.vi, and all controls and indicators connected to them. Functions>>Express>>Execution Control>>Flat Sequence Structure. 13. Place a new frame before the Flat Sequence Structure that was just created. To do this right- click on the left side of the border on the Flat Sequence and choose Add Frame Before. 14. Place a Wait (ms) function into the new sequence in the Flat Sequence Structure. Functions>>Programming>>Timing>>Wait (ms). Create a numeric constant on the Milliseconds to Wait node with the value of 25. 15. On the front panel create a graph indicator. Label the graph Chirp. 16. Return to the block diagram and split the signals from the analog input DAQ Assistant. Do this by placing a Split Signals Express VI , Functions>>Express>>Signal Manipulation>>Split Signals, on the block diagram. Wire the output of the analog input signal to the node on the left side of the Split Signals Express VI. Wire the top output to the Chirp graph indicator This Express VI allows the splitting of multiple signals so that in our case they are seen on one graph and connected to different inputs. 17. Place a Spectral Measurements Express VI (Functions>>Express>>Signal Analysis>>Spectral Measurements) onto the block diagram and use the following parameters. Under Selected Measurement select Magnitude Peak and Linear as the Result. Under Window choose None. 18. Wire the output of the analog input DAQ Assistant to the input of the Spectral Measurements Express VI. 19. Locate the FFT(peak) node on the Spectral Measurements Express VI and create a graph indicator. Label it FFT (Peak). ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 7 20. Place a Frequency Response Express VI onto the block diagram. Function>>Sound and Vibration>>Frequency Analysis>>Frequency Response. When the Frequency Response window comes up, select the Configuration tab and change the Window to None. Click Ok. 21. Wire the top output, which is connected to the Chirp graph, of the Split Signals Express VI to the Stimulus Signal input of the Frequency Response Express VI and the bottom output of the analog input DAQ Assistant to the Response Signal input. 22. Locate the Magnitude (Y/X) and Phase(Y/X) and create indicators. 23. Open the front panel and set the numeric controls to the following values: Start Frequency[Hz]=1.00, Stop Frequency[Hz]=10000, Fs = 50000, #s=100000 and Amplitude=10. 24. Place a Cursor Legend on the Magnitude (Y/X) graph indicator by right clicking on the graph and choosing Visible>>Cursor Legend. This creates a platform so that a cursor can be placed onto the graph. The coordinates of the cursor can then be changed so that values can be seen in the window provided. 25. Deselect Auto Scale X on all the graphs and make the range on the X-Axis 1-10K on the FFT (Peak), Magnitude (Y/X) and Phase (Y/X) graphs. Make the range on the Chirp graph 0-0.05. 26. Change the X-Axis representation to logarithmic on the FFT (Peak), Magnitude (Y/X) and Phase (Y/X) graphs by right-clicking on the graph and selecting X Scale>>Mapping>>Logrithmic. 27. Right-click on the numeric indicators to set their values as default. Data Operations>>Make Current Value Default. 28. Save the .vi as Filters.vi. ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 10 Measurements 1. Build the circuit in Fig. 1a on the breadboard. Using a 0.033 F capacitor and 10 k resistor. 2. Connect the AO0 of the NI-9263 to AI0 on the NI-9201. This will serve as the reference chirp signal output that is created by the .vi that will be used. 3. On the NI-9263 analog output, connect Vin of the circuit to AO1 and connect COM to the ground of the circuit. 4. On the NI-9201 analog input, connect Vout to AI1 and the circuit ground to AI9. 5. Open “Filters.vi” that was created earlier. 6. Right click the Chirp graph and select Visible Items>>X Scrollbar. 7. Run the .vi. 8. Notice the outputs on the graphs. Use the scrollbar created on the Chirp Graph to scroll through the waveform. See how the frequency changes with time. 9. Right click on the Magnitude (Y/X) graph and to show a Cursor Legend on the graph. Visible Items>>Cursor Legend. The y-axis has units of decibles while the x-axis as units of Frequency in Hz. 10. Right click in the cursor area and create a cursor by selecting Create Cursor>>Free. Use this cursor to find the decibel levels of attenuation at fc, 10* fc, and 0.1* fc. (You can either drag the cursors with the mouse or enter values in the legend to make the cursor jump). 11. Switch the resistor and the capacitor so that the circuit is like Fig. 1b and run the .vi again. 12. Save the changes to Filters.vi. 13. How do your circuits compare to the expected fc and 20 db per decade roll-off rate? Active Filters Active filters are different from passive filters in that there is an op-amp inserted after the filter to optimize the roll-off rate of the filter. For more regarding op-amps, please read Appendix B. The most basic active filter can be seen in Figure 2a and shows a single pole low- pass filter in series with an op-amp. A pole indicates the number of filters located in a circuit. The resistors R1 and R2 of an active filter determine the type of roll-off that the filter will create. Example filter types are Butterworth, Chebyshev and Bessel, and each has its advantages and disadvantages. The most commonly used filter, and the one we will be using, is the Butterworth. The Butterworth filter has a flat amplitude response, which is ideal, but is limited due to the non-linear phase shifting inherent with the design. Figure 2b and 2c show Sallen-Key filters which are two pole active filters with a roll-off rate of 40db per decade. This filter combines two poles, filters, to create a higher roll-off rate which helps separate the filtered from the unfiltered signal. Ideally, the ratio of R1/R2 = 0.586 for a two-pole Butterworth filter. If two Sallen-Key filters were placed in series an 80db roll-off would occur. In these filters it is easiest to make the values of Ra and Rb the same along with keeping Ca and Cb the same for simpler calculation of the cutoff frequency. The cutoff frequency for a two-pole Sallen-Key filter is, RCCCRR f baba c  2 1 2 1  when Ra = Rb and Ca = Cb. ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 11 a) Single-Pole Low-Pass Filter b) Sallen-Key Low-Pass Filter c) Sallen-Key High-Pass Filter Figure 2. Active filters ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 12 Experimenting with Active Filters In this exercise, you will build an active Sallen-Key filter and observe its roll-off characteristics. We will build a low-pass filter, so called because frequencies below fc pass through the circuit unattenuated while frequencies greater than fc are removed from the signal. Materials: - A/D Trainer - cDAQ-9172 - OP177 - 2 each 0.1 F capacitor - 2 each 3.3 k resistor - 1 each 1.5 k - 1 each 2.7 k Procedure Analysis 1. Determine the expected cutoff frequency for the Sallen-Key high pass filter shown in Figure 2c if Ra = Rb = 3.3 k, Ca = Cb = 0.1 F, R1 = 1.5 k, and R2 = 2.7 k. 2. Based on the values of R1 and R2, is this a Butterworth filter? Measurements 1. Build the circuit in Fig. 2b on the breadboard. Using the following values: Ra = Rb = 3.3 k Ca = Cb = 0.1 F R1 = 1.5 k R2 = 2.7 k 2. Connect the AO0 of the NI-9263 to AI0 on the NI-9201. This will serve as the reference chirp signal output that is created by the .vi that will be used. 3. On the NI-9263 analog output, connect Vin of the circuit to AO1 and connect COM to the ground of the circuit. 4. On the NI-9201 analog input, connect Vout to AI1 and the circuit ground to AI9. To avoid a ground loop, you must connect the DAQ ground to the power supply ground! 5. Don’t forget to power your Op-AMP. This is an “active” filter. 6. Open the updated “Filters.vi” that was created earlier. 7. Run the .vi. 8. Notice the outputs on the graphs. Use the scrollbar created on the Chirp Graph to scroll through the waveform. See how the frequency changes with time. 9. Right click in the cursor area and choose Create Cursor>>Free. Use this cursor to find the decibel levels of attenuation at . fc, 10* fc, and 0.1* fc. 10. Save the changes to Filters.vi. 11. How do your circuits compare to the expected fc and 40 db per decade roll-off rate? ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 15 To insert components into the breadboard, keep their pins straight and gently push into the holes. If the pins get bent and become difficult to insert, they can be straightened with a pliers. Always make sure components do not touch each other. The resistor (left) and capacitor (right) are inserted correctly, such that the leads are not short circuited by the breadboard. The transistor (middle), however, is improperly inserted such that the three leads are all connected to one another in the same column. TIPS ON USING YOUR BREADBOARD 1. If you are not sure of how to cut wires and strip insulation from them safely, see your instructor for assistance. 2. Insert components and integrated circuits (IC’s) into the appropriate breadboard area before inserting any wires. The leads of the IC’s will typically have to be bent slightly inward to match the spacing of the sockets on the breadboard. Check to make sure that the leads are inserted into the sockets correctly and that they are seated well. Be sure that any IC straddle the middle channel on the breadboard. If this is not done the leads can short circuit and ruin equipment. Note the position of pin 1 on the IC. 3. To remove an IC use an extraction tool, screwdriver, pliers or tweezers to avoid bending or breaking the leads on the IC. 4. Use only solid conductor wire (not stranded) with the size range of AWG20 to AWG 26. Wire larger than this can damage the spring clips in the breadboard. Use wire strippers to cut the wire to the correct lengths and check to make sure that the wire is not too large for the bread board (larger than AWG 20). Some wire strippers have measuring devices to determine the diameter or gage of the wire. Cut and restrip any wire that has frays, nicks, overly stressed or has any apparent damage. 5. It is possible to insert most wires by hand. In tight places, using the forceps or needle-nose pliers can make the job much easier. In either case, wires are easier to insert if they have been cut at an angle of approximately 45 degrees with respect to the axis of the wire. 6. When removing wires, be sure to pull perpendicular to the plane of the breadboard to avoid damage to the socket. 7. Route wires around components and IC packages, not over them. Occasionally, a component or an IC turns out to be defective. If wires have been placed over a component, you will have to remove them so that the component can be replaced. ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 16 8. It is best to wire a circuit in stages, beginning with power and ground connections. Add wires with the power switch OFF. Before turning the power ON, remove all hand jewelry and make sure that no foreign metal objects are near the circuit. Check every IC to make sure it is not overheating. If any IC is too hot to touch, immediately shut the power off and check all leads. (Be careful, because shorted ICs can become very hot and could leave a “brand” on your finger!) Also, make sure that no IC has been inserted backwards. 9. To troubleshoot, start at a position in the circuit where the node voltage is known to be correct, and work outward from there. If a component or IC does not appear to produce the correct signal or voltage, check that power and ground are correctly connected to the IC; also check all inputs to the component. Finally, check that the output of the IC is not incorrectly connected to some other signal. 10. If you cannot get your circuit to work, bring it and a current circuit diagram or schematic to your instructor for help. WIRING GUIDELINES Wire is as critical an electrical component of you circuit as are devices such as resistors, capacitors, inductors, op amps and other ICs, etc. The following guidelines will help assure that your wiring is unflawed. 1. Use new wire. a. Spools of wire are provided. b. Old wire con break inside the insulation, causing incorrect circuit behavior that is difficult to troubleshoot. 2. Strip approximately 5/16 inch or 8mm of insulation off the ends of a wire. This is about the length of four breadboard holes. a. If you strip off too much insulation, the wires in adjacent breadboard columns can touch, causing a short circuit and most likely incorrect behavior of the circuit. b. If you don’t strip enough, the insulation can prevent the spring clips in the breadboard holes from closing properly around the uninsulated part of the wire that is inserted into the hole, creating an open circuit. 3. Wires should be routed less than ½ inch (12mm), above the breadboard. a. If the wires are too high, it will be difficult to trace signals through your circuit and easy to pull a wire out of the breadboard. b. If the wires are too low, be sure the stripped wire ends are seated firmly in the breadboard. Careful routing is essential for efficient troubleshooting. c. Avoid sharp bends in the wires. Sharp bends in the wire can cause the wire to break inside the insulation. 4. Run wires around or between chips and components rather than over them. a. Your chip or component may become defective or damaged while in use, and it is much easier to remove it for testing/replacement if you do not have to remove your wiring in order to remove the device. ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 17 b. When possible, leave two or three rows of breadboard between chips to allow room for signal wire to pass from one side of the IC to the other. 5. Make wire lengths from source to destination short. a. Route wires point to point, rather than squaring corners. b. Do not daisy-chain power and ground wires. Think parallel, not serial. 6. Wire from a complete schematic diagram. Be sure that the wiring to each chip’s pin number and that all of the component values match the component values shown in the circuit schematic and/or diagram. DIGITAL MULTIMETERS Digital multimeters are used for a variety of functions. They can measure AC and DC voltages and currents, resistance, capacitance, frequency and temperature. You should read the specifications of a multimeter before using them. A key point is that a digital multimeter often becomes a circuit element, similar to other circuit elements, and can inadvertently affect the circuit if care is not taken. Learning to use your digital multimeter correctly and safely is a critical aspect of becoming an excellent engineer. The following paragraphs provide an introduction to this topic. Leads The test leads of a multimeter connect to the jacks at the bottom of the multimeter. The color coded black test lead goes into the black jack labeled “COM”. When measuring voltage, frequency or resistance the red test lead goes into the red jack labeled “Hz”, ”V”, ”Ohm”, respectively. When measuring currents the red test lead goes into the jack labeled “mA”. Note that the “mA” jack is fused for 200mA max. Voltage To measure DC voltage, plug the red test lead into the appropriate red jack, as described above. Turn the multimeter dial to the DC voltage setting, which is denoted by the letter 'V' and a symbol consisting of a straight line with a dotted line beneath it. Then measure with the multimeter in parallel to the component for which you are measuring voltages. The input resistance of the meter in this mode is very high and, thus, should not affect the circuit unless the device being measured has a resistance of the same order of magnitude as the input resistance of the meter. The numbers under the DC voltage setting, indicate the upper Iimit of measurable voltage. If a letter is next to the number, it indicates a prefix for an order of magnitude. For example, a lower-case 'm' indicates milli- (for I0-3) and a 'k' indicates kilo- (for I03). If the measured voltage is larger than the upper Iimit of the instrument, then a ‘I' will be displayed in the left most digit, indicating overflow. ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 20 • the resistance of a resistor measures significantly below the tolerance specifications of that resistor The current input is fused with a 200 to 250 mA fuse. If the current reads zero and you are sure there should be a current flowing in the branch, the most likely problem is a blown fuse. The multimeter is delivered with a low-cost. short-life battery at the factory. When the battery voltage drops below a certain level, the DMM voltmeter does not measure accurately. It is not cost-effective to replace this battery either at the factory or at the distributor. It is recommended that you replace the battery with an equivalent long-life alkaline battery at least once every year. If you measure a population of resistors, the likelihood that the entire population is out of specification is essentially nil. Thus, if you determine that the mean of a population or resistors is out of specification, it is most likely that there is a calibration error associated with the resistance measurements of the multimeter. We have observed that when an old battery is used, the multimeter resistance readings will be low. Replacing the battery usually eliminates this effect. ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 21 Appendix B – Operational Amplifiers Overview Operational amplifiers (OP-Amps) are among the most widely used electronic devices today, being used in a vast array of consumer, industrial, and scientific devices. A partial list of uses for OP- Amps includes inverting amplifier, non-inverting amplifier, voltage follower, current-to-voltage amp, voltage-to-current amp, precision diode, integrator, differentiator, summing amplifier, differential amplifier, and comparator. Standard integrated circuit OP-Amps cost only a few cents in moderate production volume; however some integrated or hybrid operational amplifiers with special performance specifications may cost over $100 in small quantities. An OP-Amp is an integrated circuit device that is constructed with a relatively simple set of functional attributes (Figure 1). It has two inputs, called the Inverting Input and the Non-inverting Input, and an Output. It also requires a positive and a negative voltage power supply for its operation. The ±10 volt supplies indicated here reflect the use of the ±10 volt supplies on our units. The power supply could be higher or lower, depending on the nature of the power supply and the capacity of the OP-Amp. If an input voltage (Vin) is applied to an input, it will be amplified by the OP-Amp to produce a higher voltage at the output (Vout), and OP-Amps are designed to produce very high gain (gain = Vout/ Vin), which may be as high as 105. If we want to control the magnitude of the OP-Amp's gain at some more modest level, it is necessary to apply one additional component to this OP-Amp system. This component is an external wire connecting the output to the inverting input, and this wire creates a feedback loop that limits the gain of the system. The gain of an OP-Amp without feedback is called its open-loop gain. Figure 1. Typical Op-Amp symbol (left) and integrated circuit pin configuration (right). The behavior of most configurations of OP-Amps with external feedback can be determined by applying the "golden rules": 1. The output attempts to do whatever is necessary to make the voltage difference between the inputs zero (Voltage Rule) 2. The inputs draw no current (Current Rule) +12 volt supply (V+) -12 volt supply (V-) ESM 3444 Laboratory 2 – Filters Spring 2015 Due at start of labs the week of February 9 22 Example 1: Inverting Amplifier Figure B.1 below shows how a simple amplifier can be constructed from an OP-Amp in which the system gain is controlled by the resistance in the feedback loop. If the input voltage source (Vin) is attached between the Inverting input and ground (note, that the non-inverting input is attached directly to ground), then the OP-Amp forms an Inverting Amplifier in which the sign of the output voltage (Vout) is opposite to that of (Vin). The gain (gain = - Vout/ Vin) is determined by the relative size of resistors that limit current flow from the source (R1) and feedback current from the output (R2). For this configuration the Input Resistance of the circuit is equal to R1. Low values of R1 will limit the use of the inverting amplifier for measuring voltages from sources with a high source resistance. Figure B.1. Wire diagram for an op-amp configured as an inverting amplifier +12 volt supply (V+) -12 volt supply (V-)