LAB #3: Virtual Instruments; Behavior of Second-Order Systems

LAB #3: Virtual Instruments; Behavior of Second-Order Systems Equipment: Dell Optiplex Gs+ Pentium computer National Instruments BNC-2140 signal connector box, PCI-4451 dynamic signal acquisition board, and VirtualBench virtual instrument library Multimeter (FLUKE 8050A) Function Generator (Tektronix CFG250) RLC Circuit Oscilloscope (Tektronix 2211) (Optional) Objectives: In this experiment, you will study the behavior of a second-order system represented by an RLC circuit. You will use a personal computer as an oscilloscope to acquire data. From this experiment, you should achieve a grasp of the concepts of natural frequency, damping, and frequency response. A secondary purpose of this experiment is to introduce you to virtual instruments. You should already be familiar with the basic operating principles of an oscilloscope and a PC. The virtual oscilloscope has some features that are not normally found on traditional oscilloscopes; these are described below. 1 VIRTUAL OSCILLOSCOPE The virtual oscilloscope (VI) used in this experiment is designed to emulate the functions of an actual four-channel oscilloscope and allow the user to exploit the versatility of a personal computer in manipulating acquired data. Essentially, a virtual instrument is software that enables a personal computer to act as a piece of hardware; in this case, it acts as an oscilloscope. The virtual oscilloscope was created by National Instruments as part of a Virtual Instrument Library called VirtualBench. Signals are brought into the computer through a National Instruments PCI-4451 dynamic signal acquisition and generation board. This board converts analog signals into digital signals, which can be manipulated by the computer. 1.1 Operations First, turn on the computer, if it is not already on, and log onto the system as a Guest. This is done by pushing the power button on the front of the machine and the power button on the monitor and following instructions. Double click on the Scope icon on the desktop. The front panel of the scope will be shown on the screen. This panel simulates the front panel of a traditional oscilloscope and contains a display area plus a variety of knobs and buttons. These are controls that can be manipulated with the mouse. There are also pulldown menus, where some of the settings are located, as well as file management controls and online help. To understand the operation of the VirtualBench Oscilloscope, let us begin with a discussion of the items on the front panel. 1.1.1 The display on the front panel looks very similar the display on a traditional two-channel oscilloscope, except that it also displays vertical divisions, the vertical position, and the timebase in the upper left hand corner of the display. Also, if any 1

measurements are requested, they are displayed below the trace(s) at the bottom of the display. Up to eight measurements can be displayed simultaneously. 1.1.2 Below the display are four push buttons and a slider bar, which is hidden if one of the buttons is depressed. If the Run button is depressed, the scope will acquire data continuously until the button is pressed again. If you press the Single button, the scope will acquire one frame of data and display it on the screen. If the Autosetup button is depressed, the software will determine the best setup for you. It is preferable if this feature is not used, and you determine the best setup yourself. The Mode button has two settings, Y-T and X-Y. If the Y-T mode is selected, the display will have voltage on the Y- axis, and time on the X-axis. If X-Y is selected, the X-axis will show the voltage of CH1 and the Y-axis will show the voltage of CH2. The slider bar, which is marked X<>, adjusts the point where triggering will occur. Normally, the slider bar, which moves the trace horizontally, is left in the left-most position. 1.1.3 To the right of the display are several areas that contain buttons and knobs. The Channels section contains buttons for switching on and off the different traces. For example, if the button for Ch 1 is green in the center, the trace for the signal should be seen on the display. If the button is not green in the center, the trace will not be be shown on the display. Each trace can be displayed in a different color. To the right of the Channels section are two knobs and a channel-selector switch. The switch is used to select an active channel that you want to adjust using the two knobs. The first knob is for adjusting the scale of the trace by changing the volts/division of the display for that trace. This setting is displayed at the top-left corner of the display area. The second knob is for adjusting the vertical position of the trace on the display. Note that a colored triangle at the right edge of the graph area indicates the vertical position of the zero-voltage level for each active trace. The Timebase knob adjusts the (horizontal) time scale of the display by changing the number of seconds per division. This setting is listed just above the graph area. The Measure indicator box is used to determine which channel s data is to be used in computing the requested measurements to be listed at the bottom of the display. Some of the selected measurements are not displayed if the cursors are active. The Cursors section is used to provide cursors on the display for making measurements. If the cursors button is not depressed, the cursors will not be seen on the display. When the cursors are active, two cursors will be attached to the selected trace, and the coordinates, as well as the spacing between them will be displayed with the measurements at the bottom of the display. Large adjustments to the cursor location can be made by simply using the mouse to move the line attached to the cursor. The four cursor arrow buttons can be used for making fine adjustments. The bottom selector in the Cursors section allows the user to set the location of the trigger cursor. The mouse may also be used to move the trigger cursor. The last section on the front panel is the Trigger controls section. Depending on which trigger mode is selected, other boxes will appear in the trigger control section. You should only need to use the NORMAL mode, or no trigger at all (NONE). For all types of trigger modes, except NONE, the slope box will be available, and the trigger crosshair cursor will be available for setting the trigger level and trigger delay. For the NORMAL mode you will also need to select the trigger channel. Two trigger settings are made from outside this trigger menu area: the trigger level and trigger delay are set by moving the trigger cross-hair cursor, labeled T; and the trigger sensitivity is set in the manner described in Sect. 1.1.4 below. 1.1.4 There are also controls for the oscilloscope found under the Edit-Settings pull-down menu option. This option provides a dialog box with tabbed pages that contain some of the controls. The most important page is the GENERAL page. The options you will be interested in are the Trigger Sensitivity, the Sample Rate, and the Buffer Size. The trigger sensitivity adjusts the change in level of the signal required before the signal will be 2

acquired. This is determined in fractions of a division. The buffer size is the number of samples contained in the displayed signal when the signal is frozen on the screen, and the sample rate is the number of samples taken in one second. The MEASUREMENTS page can be used to select up to eight measurements and calculations that you wish to display on the front panel display. The CHANNELS page can be used to choose AC or DC coupling for each channel, as well as determine a vertical offset for the trace. (Note that this vertical offset is not the same as the vertical position setting, which is controlled by one of the knobs on the front panel.) You need not be interested in the attenuation, and you will not need to change the color of the trace. 1.1.5 The trace shown in the Display can be saved to a spreadsheet-compatible file by clicking File-Save Waveform option on the pull-down menus. A dialog box will appear that will ask you which waveform you wish to save. You also have the option of indicating the users name, comments, and the measurements in the file as well. When you click OK the windows save dialog box appears where you can select a file name and location. You will want to save your files on a floppy disk for later use in writing your report. 1.1.6 Try Help-Pop-up Help to obtain information about one or two of the scope s features, e.g., the Timebase knob. 1.2 Test Drive the Virtual Oscilloscope Before beginning the experiment, it will be useful for you to take the VirtualBench Scope for a test drive in order to get comfortable with all of the controls. 1.2.1 From the Edit-Load Settings menu, recall the file lab4a.set. Set the Trigger Mode to NONE and set the Ch 1 COUPLING to AC. Set the Time Base to 2 msec/div and the vertical scale to 500 mv/div, and select Ch 1 as the active trace on the display. 1.2.2 Use a BNC-BNC cable to connect the Main output of the function generator to Ch 1. Set the function generator to give a sine wave of 100 Hz. Turn the function generator on, and then turn the amplitude knob to the 12 o clock position. (NOTE: The usable signal range of the PCI-4451 dynamic signal acquisition board is ± 42.4 V (30 V rms ). The BNC-2140 has excitation overload protection of ± 42.4 V, so any signal out of this range will be clipped.) 1.2.3 Start acquiring data by clicking the Run button below the display. You should then see a 100 Hz sine wave on the plot display. Adjust the output of the function generator to give a 2 V peak-to-peak amplitude. Adjust the Ch 1 V. Position knob and note the change in the Y-axis values. 1.2.4 Halt the continuous-acquistion mode by clicking the Run button again. A trace should remain on the screen. Re-acquire the trace by pressing the Single button. 1.2.5 Save the trace to a file by pulling down the File menu and clicking Save Waveforms. Enter a filename and any other information you wish, and click OK. Then select a location and save the file. 3

1.2.6 Use the Cursors, and the Measurements to confirm the frequency of the sine wave. Experiment with the VirtualBench Scope until you are comfortable with it. If you would like to do so, input the same signal to the Tektronix scope and the VirtualBench Scope and compare the settings required with each. 2 FREQUENCY RESPONSE OF A SECOND-ORDER SYSTEM 2.1 Calculate the undamped natural frequency of the LC circuit using the nominal values of L and C. 2.2 From the Edit-Load Settings menu, recall the file lab4b.set. 2.3 Using a tee, connect the output of the function generator to Ch 1 and to the to switch input to the RLC circuit. Connect the to scope output of the RLC circuit to Ch 2. Activate both Ch 1 and Ch 2. Set the circuit damping resistance to minimum (i.e., to full CCW). 2.4 Set the function generator to give a sine wave output of about 100 Hz with 0.5 V peak-to-peak amplitude. Also set the Trigger SOURCE to Ch 1 and set the COUPLING of both channels to AC. Using the Vertical Position knob, offset Ch 1 by -1.0 V and Ch 2 by +0.5 V so the traces will not be overlaid. 2.5 With the Cursors off, gradually increase the driving frequency from about 100 Hz to about 1 khz and observe how the system output changes in amplitude and phase angle, particularly as you pass through the resonant frequency range and on to higher frequencies. Acquire enough data to plot amplitude ratio (V o /V I ) vs frequency and phase angle vs frequency for a frequency range that includes the resonant frequency. Take amplitude and phase data for at least ten frequencies, starting around 200 Hz below resonance and including several frequencies near the resonant frequency. You will have to modify the Volts/div setting for Ch 2 when you are near resonance. NOTE: Since the output from the function generator may vary with frequency, it is wise to measure both the input amplitude and the output amplitude at each frequency. You will also need to measure the phase angle between the output signal and the input signal. 2.6 Calculate the resistance to give critical damping (ζ=1.0). Using the multimeter, set the resistance potentiometer for ζ = 0.7, and take the data necessary to determine frequency-response amplitude and phase curves (i.e., amplitude vs frequency and phase versus frequency) for this second-order system. 3 RESPONSE TO A SQUARE-WAVE INPUT 3.1 Return the resistance potentiometer to the full CCW minimum-damping setting. Set the COUPLING on Ch1 and Ch2 to DC. Set the function generator to produce a square wave with amplitude of 1.0 V pk-pk and a frequency of 100 Hz. Obtain 4

plots of the input signal (Ch 1) and the output signal (Ch 2) for this square-wave input, and save these waveforms to include as plots in your report. 3.2 Exit the VirtualBench Scope and turn off your computer. 4 HOMEWORK (to be incorporated in your Formal Report 1) 1. If the tolerance of the capacitor is ± 10%, and that of the inductor is ± 10%, what is the absolute uncertainty in your calculated undamped natural frequency? 2. From your frequency-response data, determine the values of damped natural frequency ω d and damping factor ζ for the experiments of Sects. 2.4 and 2.5. 3. Explain the differences, observed in Part 3.1, between the square-wave input and the corresponding output from the second-order system. 5 REFERENCE PCI-4451/4452 User Manual, National Instruments, Austin, TX, April 1998. RC: 3/98, 2/99, 6/99; PDF 11/99. 5

Front Panel of VirtualBench Scope 6

Specifications Dynamic Signal Acquisition and Generation Data Acquisition Dynamic Signal Acquisition and Generation (PCI-445x) Typical for 25 C unless otherwise stated Analog Input Channel Characteristics Number of channels... 2 (PCI-4451) or 4 (PCI-4452), simultaneously sampled Input configuration... True differential Resolution... 16 bits Type of ADC... Delta-sigma, 128-times oversampling Sample rates... 5 ks/s to 204.8 ks/s in increments of 190.735 µs/s Frequency accuracy... ±100 ppm Input signal ranges... Software-selectable Gain Full-Scale Range (Peak) Linear Log 0.1-20 db ±42.4 V 0.316-10 db ±31.6 V 1 0 db ±10 V 3.16 +10 db ±3.16 V 10 +20 db ±1.00 V 31.6 +30 db ±0.316 V 100 +40 db ±0.100 V 316 +50 db ±0.0316 V 1000 +60 db ±0.0100 V FIFO buffer size... 512 samples Data transfers... DMA, programmed I/O, interrupt Transfer Characteristics INL relative accuracy... ±2 LSB DNL... ±0.5 LSB typ, ±1 LSB max,no missing codes Offset (residual DC) Gain Max Offset -20 db ±30 mv -10 db ±10 mv 0 db ±3 mv +10 db ±1 mv +20 db ±300 µv +30,+40,+50,+60 db ±100 µv Gain (amplitude accuracy)... ±0.1 db, fin = 1 khz Amplifier Characteristics Input impedance... 1 MΩ in parallel with 50 pf (+ and each to AIGND) Frequency response Gain 0, +10, +20, +30, +40 db... ±0.1 db, 0 to 95 khz, 204.8 ks/s, DC coupling -20, -10, +50, +60 db... ±1 db, 0 to 95 khz, ±0.1 db, 0 to 20 khz -3 db bandwidth... 0.493 fs Input coupling... AC or DC, software-selectable AC -3 db cutoff frequency... 3.4 Hz Common-mode range Gain 0 db... Both + and should remain within ±12 V of AIGND Gain < 0 db... Both + and should remain within ±42.4 V of AIGND Overvoltage protection... ±42.4 V, powered on or off (±400 V guaranteed by design, but not tested or certified to operate beyond ±42.4 V) Inputs protected... ACH0, ACH1, ACH2, ACH3 Common mode rejection ratio (fin < 1 khz)... 90 db, Gain 0 db; 60 db, Gain < 0 db Input noise spectral density... 8 nv/ Hz (achievable only at Gain = +50 db or +60 db) Dynamic Characteristics Alias-free bandwidth... DC to 0.464 fs Alias rejection... 80 db, 0.536 fs < fin < 63.464 fs Spurious-free dynamic range... 95 db THD... -80 db; -90 db for f in < 20 khz or signal < 1 Vrms IMD... -100 db (CCIF 14 khz + 15 khz) Crosstalk (channel separation)... -100 db, DC to 100 khz Phase linearity... ±1, Gain 0 db; ±2, Gain < 0 db Interchannel phase... ±1, Gain 0 db; ±2, Gain < 0 db (same configuration all input channels) Interchannel gain mismatch... ±0.1dB, for all gains (same configuration for all input channels) Signal delay... 42 sample periods, any sample rate (time from when signal enters analog input to when digital data is available) Onboard Calibration Reference DC level... 5.000 V ±2.5 mv Temperature coefficient... ±5 ppm/ C max Long-term stability... ±15 ppm/ 1000 h Analog Output (PCI-4451 only) Channel Characteristics Number of channels... 2 simultaneously updated Output configuration... Balanced differential Resolution... 16 bits Type of DAC... Delta-sigma, 64-times oversampling Sample rates... 1.25 to 51.2 ks/s in increments of 47.684 µs/s Frequency accuracy... ±100 ppm/ Output signal range... software-selectable Gain Full-Scale Range Linear Log 1 0 db ±10.0 V 10 20 db ±1.00 V 100 40 db ±0.100 V FIFO buffer size... 512 samples Data transfers... DMA, programmed I/O, Interrupt Transfer Characteristics Offset (residual DC)... ±5 mv max, any gain Gain (amplitude accuracy)... ±0.1 db, f out = 1 khz Voltage Output Characteristics Output impedance... 22 Ω between + and DACxOUT, 4.55 kω to AOGND Frequency response... ±0.2 db, 0 to 23 khz, 51.2 ks/s -3 db bandwidth... 0.492 fs Output coupling... DC Short-circuit protection... Yes (+ and may be shorted together indefinitely) Outputs protected... ±DAC0OUT, ±DAC1OUT Idle channel noise... -91 db fs, DC to 23 khz measurement bandwidth Dynamic Characteristics Image-free bandwidth... DC to 0.450 fs Image rejection... 90 db, 0.550 fs < fout < 63.450 fs Spurious-free dynamic range... 90 db, DC to 100 khz THD... -80 db; -90 db for fout < 5 khz or signal < 1 Vrms IMD... -90 db (CCIF 14 khz + 15 khz) Crosstalk (channel separation)... -80 db, DC to 23 khz Phase linearity... ±1 Interchannel phase... ±1 (same configuration both output channels) Interchannel gain mismatch... ±0.1 db, for all attenuations (same configuration both output channels) Signal delay... 34.6 ±0.5 sample periods, any sample rate (time from when digital data is expressed to when analog signal appears at output terminals) Digital I/O Number of channels... 8 input/output Compatibility... 5V/TTL Digital logic levels Power-on state... Input (High-Z) Data transfers... Programmed I/O Timing I/O Number of channels... 2 up/down counter/timers, 1 frequency scaler 320 National Instruments Phone: (512) 794-0100 Fax: (512) 683-8411 info@natinst.com www.natinst.com

Specifications Dynamic Signal Acquisition and Generation (continued) Triggers Analog Trigger Source PCI-4451... ACH<0..1> PCI-4452... ACH<0..3> Level... ± full-scale Slope... Positive or negative (software selectable) Resolution... 16 bits Hysteresis... Programmable Digital Trigger Compatibility... 5V/TTL Response... Rising or falling edge Pulse width... 10 ns min Bus Interface Type... PCI Master/Slave Power Requirement Power (PCI-4451)... +5 V, 1.7 A idle, 2.0 A active +12 V, 100 ma typical (not including momentary relay switching) -12 V, 40 ma typical +3.3 V, unused Power (PCI-4452)... +5 V, 2.2 A idle, 2.5 A active +12 V, 120 ma typical (not including momentary relay switching) -12 V, unused +3.3 V, unused Available power... +4.65 to +5.25 VDC at 0.5 A (analog I/O connector) Available power... +4.65 to +5.25 VDC at 1.0 A (digital I/O connector) Physical Dimensions (not including connectors)... 10.65 by 31.19 by 1.84 cm (4.19 by 12.28 by 0.73 in.) Digital I/O connector... 50-pin VHDIC female type Analog I/O connector... 68-pin VHDIC female type Environment Operating temperature... 0 to 40 C Storage temperature range... -25 to 85 C Relative humidity... 10% to 95%, no condensation Calibration Calibration interval... 1 year Certifications and Compliances CE Mark Compliance BNC-2140 Accessory Input Capacitance 1 Current Excitation On Off DIFF mode 85 pf 75 pf SE mode 150 pf 145 pf Current excitation Level... 4 ma Accuracy... ± 1.015% Temperature coefficient... ± 127 ppm/ C Voltage compliance... 24 V Excitation overvoltage protection... ±42.4 V (30 Vrms) powered on or off Power Consumption... 400 ma at +5 VDC (from DSA board) Dimensions... 14.0 by 11.2 by 3.8 cm (6.0 by 4.4 by 1.6 in.) I/O connectors I/O signals... 6 BNC connectors DSA board... 68-pin 0.8 mm VHDC1 female connector 1 Includes the effects of the BNC-2140 with a 1 m SHC68-C68-AI analog cable. Dynamic Signal Acquisition and Generation Data Acquisition National Instruments Phone: (512) 794-0100 Fax: (512) 683-8411 info@natinst.com www.natinst.com 321