B. Equipment. Advanced Lab
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- Agnes Howard
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1 Advanced Lab Measuring Periodic Signals Using a Digital Oscilloscope A. Introduction and Background We will use a digital oscilloscope to characterize several different periodic voltage signals. We will take time to be the independent variable, but the same waveform descriptions and parameters apply to cases where the independent variable is something else, such as position. An important class of time-varying signals is the periodic signal. A periodic signal V(t) satisfies the equation V(t) = V(t + nt) for n = 1,2,3... where T is the period of the signal. Some of the periodic signals we will study are shown in Fig. 1. B. Equipment 1. Teachspin Teachscope Signal Generator-- The Teachscope is a device that generates twelve different voltage signals. The chosen signal is available on both a BNC connector (see below) and on an insulated terminal. Output impedance is 1000 ohms. 1
2 2. Tektronix TDS1002 Digital Oscilloscope A user s guide to the Tektronix TDS1002 two-channel digital oscilloscope is available at your lab station. A brief guide is furnished in Appendix A. (You should read through the appendix before beginning the measurement procedure unless you are an experienced oscilloscope operator.) The oscilloscope has an input resistance of 1 MΩ in parallel with an input capacitance of 20 pf. The measurement bandwidth is DC - 60 MHz in DC Coupled mode and 10 Hz 60 MHz AC Coupled. The block diagram below shows the functions of the oscilloscope and their relationship to each other. This scope has two channels, named CH1 and CH2. Each channel can be configured as to scale factor (Volts/div) and coupling (AC, DC, or Ground). Make sure that the COUPLING is set to DC if the DC level of a signal is to be measured. A key feature is the synchronization of the start of the trace with a specific waveform condition; this is done by the TRIGGER system. A TRIGGER can be derived from the input signal itself (for instance, when it reaches a specified voltage) or from an external signal. 3. BNC Coaxial Cable We will often use coaxial cables with BNC connectors to connect signals to measuring instruments. Coaxial cables contain two electrical conductors: a wire center conductor and a coaxial cylindrical outer conductor made of braided wire or metal foil. The outer conductor, also known as the shield, is electrically isolated from the center conductor. The outer conductor of the coaxial cable is usually held at ground, i.e. at zero electric potential, while the varying signal voltage is fed through the center conductor. Since coaxial cables contain two conductors, they are terminated at each end with a connector having two terminals most commonly, a BNC connector, with a Bayonet twist-lock. The sleeve of the BNC connector is always tied to the shield of the coaxial cable, while the cable center conductor passes through the center pin of the connector. The BNC cables we use have negligible resistance and a capacitance of approximately 100 pf/meter. 4. Oscilloscope Probe The oscilloscope probe has a switch with 1X and 10X positions; we will use the 10X. Attaching the 10X probe to the signal source results in an effective input resistance of 10 MΩ and a total capacitance of only 16 pf. The oscilloscope scale factor readout can take into account the factor of 10 attenuation produced by the probe. C. Procedure Attach Input Channel 1 of the TDS1002 oscilloscope to the BNC output connector of the Teachscope box using a BNC cable. Please note that every Teachscope box is different, so it is important to record on your data sheet the unit number of the box you use (this is a one-letter, one-number combination shown on the Teachscope panel; e.g., C3). Turn the Teachscope Channel selector to 1; this will produce a sine wave with a peak-to-peak amplitude of about 5.4 V and no offset (no DC voltage component). Adjust the trigger level control to get a stable display. (You should have already set the zero position on the scope vertical axis using the method of Appendix A). 2
3 Next, complete the measurements shown on the data sheet for the sine wave signal obtained with the Teachscope selector switch on position 1. In most cases, you can use the automatic measurement capabilities listed under the scope s MEASURE menu to get the needed results. You can measure up to five quantities simultaneously. (Signal frequency is always measured separately, to good precision, with the result shown at the bottom of the display). Probably the most useful automatic measurements are peak-to-peak volts and volts RMS, both of which are measured over one cycle of the waveform. The Mean measurement s usefulness is limited because the mean voltage is averaged over the entire record ; i.e., over the entire contents of the display screen. If the display does not show an integral number of cycles of the wave, then the indicated mean will not correspond to the mean over one cycle (and we usually want the one-cycle mean). You will probably have to read the DC voltage from the waveform itself without automatic help. Be sure to include units, and also include uncertainties when requested. The uncertainty levels are determined as follows: Random Uncertainty: If the measurement reading fluctuates, the (sample) standard deviation characterizes the random uncertainty. (Often the average absolute deviation is just as good.) If you average several repeated measurements, then you would of course use the sample standard deviation of the mean to characterize the uncertainty. You will probably find the random uncertainty in these measurements to be negligible compared to the systematic uncertainty. Systematic Uncertainty: You can usually look at the equipment manufacturer s accuracy specifications to determine the systematic uncertainty. For the Tektronix TDS1002 scope we have Vertical Resolution: 8-bits; DC Vertical Accuracy:±3% on all models (Affects voltage measurement) Time Base Accuracy: 50 ppm (Affects time and frequency measurements.) Switch the Teachscope selector to position 2 and make the measurements on the square wave signal. Then, switch the selector to position 3, adjust the trigger controls for a stable display (you may need to switch the Trigger mode to normal if it is in the auto position), and determine which of the signals from the data sheet you have. Make the indicated measurements (see notes below if you have a pulse) and record the results in the appropriate section of data sheet, along with the channel number (3) where you found the signal. Follow this same procedure for Teachscope selector positions Notes on Pulse Measurements and Probe Use. When you look at the pulse waveforms, you will probably find they look more like triangles than rectangular pulses. This is because the capacitance of the coaxial cable combines with the output impedance of the signal source to form an RC circuit which must be charged and discharged, thus limiting the rate of voltage change. You can use the scope probe (on the 10X setting) to minimize the load capacitance. You first need to check and possibly adjust the probe tuning. Attach the probe to the scope s Channel 1 BNC. Then, press the probe check button and follow the directions on the screen. Try looking at the pulses with the probe connected to the Teachscope probe terminals (main probe clip on out terminal, probe ground wire on gnd terminal). You should probably make your measurements of pulse width and height using the probe without the BNC cable attached to the Teachscope BNC output. Measurement of pulse characteristics can be tricky, especially when the time between pulses is very long compared to the pulse width. You may need to change trigger slope and trigger coupling for best results. D. Documentation/Report When you have completed the data sheet, tape/paste it into your lab notebook. 3
4 Teachscope Model # Measured Value Uncertainty Sine wave (no offset, approx. 5.4 volts peak-peak) Channel number 1 Square Wave (with offset): Channel number 2 Sine wave (one half-cycle clipped, no offset) Positive or neg. half-cycle clipped? +5 V DC AC pk-pk (noise) level Ground (with low level noise spikes) Sawtooth (long repetition time, positive offset) Triangle wave (positive offset) 4
5 Measured Value Uncertainty Sine Wave (positive offset) TTL pulse (short duration, long repetition time, ground-to-positive pulse) Pulse width TTL pulse (moderate duration, long repetition time, positive-to-ground pulse) Pulse width Differentiated square wave (no offset) TTL pulse (short duration, moderately short repetition time) Pulse width 5
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