Coursehero >> California >> UCSD >> PHYS 2CL

Course Hero has millions of student submitted documents similar to the one below including study guides, homework solutions, papers, exam answer keys and textbook solutions.

#1 Experiment Using the laboratory instruments and software 1 Objective Learn to use the laboratory instruments and software that will be needed for the experiments. Refer to the notes of lecture #1 and to the Instruction Manual at the 2CL WEB site for additional description of the equipment and components. 2 Homework 1. Read through the Course Structure page on the course WEB site. 2. Study the Instruction Manual so that you are familiar with the controls on the three instruments and with the set up of the proto-board. 3. Read these instructions for experiment 1 so that you can follow them rapidly when working in the lab. 4. Review the mean and standard deviation and the probability table for the normal distribution function. 5. Review series and parallel combinations of resistors. For this lab, you will be graded by the TA s on your performance in the lab. This will be based upon your understanding of these instruments. 3 Description of the instruments 3.1 The multimeter The multimeter that you will use can measure DC voltage, AC voltage, DC current, AC current, resistance ( ), capacitance ( ), and frequency (Hz). The display indicates the measurement setting. For all measurement other than high current measurements the leads will be plugged into the COM and V connectors. 1 The multimeter can be used to measure voltages, currents, frequency (of an AC signal), resistance, and capacitance aswell as to test the . For voltages and currents it can measure both DC and AC. In the latter case it measures the Root Mean Square value (rms). In each function setting the scale is set automatically by the value you are measuring. The scale is shown in the LCD display as for example mV (milli-Volts), V (volts), pF (picoFarads, F (microfarads), etc. The multimeter has 3 input terminals. The black one is labeled com (for common ) and serves as the circuit s ground or common terminal. The meter will automatically sense the polarity of DC voltages or currents so that either wire may be connected to either input terminal. The sign will be indicated on the display. The terminal labeled V is the other input for all measurements other than large currents. The terminal labeled A is used only for measuring currents greater than 1 A. 3.2 The pin board ( proto-board ) Figure 1. Pin board with power supply connections to a 356 op-amp. The red lines indicate pin holes that are electrically connected. The pin board is a device that provides simple and rapid connection of circuits. Wires connected to circuit elements as well as pieces of wire to make connections can be 2 pushed into the holes where they make electrical contact to spring clips. The clips inside of the holes are connected as indicated in Figure 1. The stand up connector at the middle of the right end connects to the power supply that provides the +5, +12, -12, and GRND for the circuits assembled on the board. The pins at the right hand end of the board provide test points for these power supply voltages where you can measure the voltages with clip on connectors from the multimeter. 3.3 The signal generator Figure 2. The signal or function generator. The frequency is adjusted with the large round knob on the left and the range buttons in the middle section along the top. It is displayed by the LED s. The amplitude of the signal is adjusted by the ATT button and the small knob on the right end of the line of knobs. All output and input connections to the generator are BNC connectors. To monitor the output on the oscilloscope it will be most convenient to use a coax cable with BNC connectors on both ends. To connect the output to the amplifier that you will assemble on the protoboard you will want to connect a cable with clip leads on the end that you attach to the protoboard. 3 3.4 The oscilloscope Figure 3. The Tektronix 2225 oscilloscope. For full description see the Instruction Manual on our WEBCT site. The inputs are the leftmost two BNC connectors. 4 4 The Lab: Using the instruments All laboratory measurements must be recorded in your lab notebook and labeled. When appropriate, uncertainties in values must also be recorded and labeled. When a procedure is used to make a measurement, the procedure must be described. 4.1 Multimeter measurements 4.1.1 Voltage measurements Turn the meter to the V position to measure DC voltage. Connect the common lead from the meter to one of the pins labeled GND, in the second row at the top right hand end of the Proto-Board (Figure 1). Connect the other lead to the top row to measure the actual value of the 5 V supply. Now connect the clip lead to a +12 pin and then to a -12 V pin. Record the four significant digits of the values that you measure for all three quantities in your lab notebook. 4.1.2 Resistance measurements Select three resistors from the parts cabinets. Two that are about 1000 (1 k) and one that is about 10000 (10 k). Set the meter to the position and connect the two clip leads to the two wires connected to each of the resistors. Record the four significant digits of the values that you measure for all three resistors in your lab notebook. Also record the nominal values that are specified by the manufacturer. 1. Accuracy of the resistors Resistors are provided by manufacturers with a variety of specified accuracies. A specified 5% accuracy would mean that the values measured for a large number of resistors of the same nominal value would fall on a normal distribution function with = 5% of the nominal value. (Review: what is a normal distribution and what is .) Using the table of probabilities for the normal distribution function, the nominal value of the resistor and, = 5%, determine what is the likelihood that you would find a resistor with a deviation from the specified value equal to or greater than what you measure? 2. Temperature dependence of the resistors While holding the resistor tightly between your fingers or against the palm of your hand watch for a slow drift of the resistor toward slightly smaller values. If you see any, measure the temperature coefficient of the resistors ( R/ T) assuming that room temperature is 70 F (21 C) and that your hand is 98.6 F (37 C). 3. Linearity of the meter. Connect the two 1k resistors in series using the proto-board and measure the sum of the two resistances. Record the value and compare to the sum of the values measured for them individually. 5 Connect the two 1 k resistors in parallel and measure the resistance. Compare to the calculated value for the two individually measured values. If the meter were non-linear, the value determined by the meter of known resistances would depend on the value of the resistance. For example, larger values might always read smaller than the known resistances and smaller values might read larger than the known values. Within what accuracy did the meter readings of the series and parallel combinations agree with the calculated values? Is the meter linear to the accuracy that it can be read (i.e. the least significant digit)? 5 The function generator, the scope and MATLAB 5.1 The oscilloscope The oscilloscope is used to monitor voltages that vary in time. If the scope is to be used for quantitative measurements, it must be calibrated. That means when the vertical scale is set to 1 Volt/division of the screen, a 5 volt change must be 5 divisions on the screen. When the horizontal sweep is set to .1 milli-seconds/division then a 5 millisecond pulse should be 5 divisions wide on the screen. In order to check the calibration you will need to use a standard signal, such as provided from the PROBE ADJUST peg on the oscilloscope front panel. a) Use a clip lead to connect the PROBE ADJUST signal to Channel 1 on your oscilloscope. Adjust the horizontal scale (time scale) and the vertical scale (voltage scale) until you see a square wave on the oscilloscope screen. Read the fine print underneath the PROBE ADJUST contact. It tells you the voltage and frequency of this calibration square wave. Record this information in your lab notebook, labeling it as the probe adjust calibration signal. b) Be sure the trace (the glowing line of the oscilloscope display) is well focused. Use the knob marked FOCUS on the far left of the control panel to adjust if necessary; Also, be sure the trace is not too bright. Use the knob marked INTENSITY on the far left of the control panel to adjust it to a reasonable brightness. Refer to the Oscilloscope reference in the Instruction Manual on the course web site if you need help in identifying the various dials and switches. c) Vary the scales to become familiar with the changes they make in the appearance of the pattern on the screen. Change the trigger SLOPE switch in the upper right section of the oscilloscope control panel. Record, in your notebook, the change that results from this adjustment. (The oscilloscope operates by sweeping an electron beam across a fluorescent screen at a rate determined by the time base knob. The beam is deflected in the vertical direction by an amount proportional to the input channel signal, thus producing an image of the time dependent signal. Unless the sweep frequency is exactly the same as the signal frequency, subsequent sweeps would show the signal at different positions along the horizontal axis of the display. The trigger is used to synchronize the sweep and the input signal so that the signal will appear fixed on the screen. Each sweep is initiated only when the signal level reaches the 6 value set by the trigger level knob, or at the magnitude and sign of the slope determined by the trigger slope adjustment.) d) Measure the peak -to-peak voltage of the square wave as well as the uncertainty and units of the The measurement. voltage is obtained by multiplying each 1cm division on the screen by the volts/div. number on the vertical channel knob. Note that each box is additionally divided into 5 sub-divisions. Therefore the resolution for reading a signal on the screen is 1/5 of a division plus any estimate that you can make of values between the small divisions. Use a vertical scale such that the square wave fills the largest portion possible of the screen. This will minimize the uncertainty of your voltage reading. e) Measure the period of the square wave (include uncertainty and units). This can be done either by spreading one period across the screen (use the time-base scale knob), or by measuring the time of several periods on the screen and then dividing by the number of periods. Record your measurements in your notebook, along with a clear statement as to what you actually measured. In your analysis, calculate the measured frequency from the measured period of the square wave. Propagate the uncertainty in the period to get an uncertainty in the frequency. In your conclusions, compare the measured frequency to the labeled value for the frequency of the square wave and compare your measured voltage to the labeled value of the calibration signal. If you find that your measurements of the PROBE ADJUST signal s amplitude and frequency agree with the given values, then you are done. If you find a significant discrepancy, you will need to adjust the calibration of the oscilloscope. This is done by turning the VAR knob on top of the corresponding (signal channel or time base) scale knob. Turn these knobs until your results agree with the given parameters for the supplied signal. When the calibration knobs are turned all the way counter clockwise and click, the oscilloscope is set to the factory calibration. A properly operating scope will be accurately calibrated at this setting. 5.2 The function generator Now use the oscilloscope to measure some signals from the function generator. a) Use a BNC coaxial cable to connect the output of the generator to channel 1 of the oscilloscope. A coax cable consists of two leads; a center wire conductor that carries the signal, and an outer braided conductor that is connected to ground . The coaxial geometry provides shielding from stray electromagnetic signals such as radio stations and power lines. b) Set the signal generator to a sine wave with a frequency of about 10 kHz. Record the frequency shown on the front panel of the signal generator and the uncertainty of the reading. If the reading is not fluctuating, use a 1-digit uncertainty in the least significant (last) digit of the readout. If the readout is drifting or fluctuating, be sure to increase the uncertainty accordingly. c) Adjust the horizontal and vertical scales of the scope until you have one full cycle of the sine wave on the oscilloscope screen. Use the position knobs to slide the 7 d) e) f) g) h) wave over to the right until the wave passes through zero at the left side of the screen. Try adjusting the level knob in the TRIGGER section in the upper right-hand section of the oscilloscope control panel. Describe the effect of adjusting the level . Try flipping the SLOPE switch again and describe its effect. Readjust the knobs and switches until you, again, have one full cycle of the sine wave on screen. Note: You can always locate the V = 0 position along the vertical axis by setting the switch under Channel 1 (or Channel 2, if that is what you are using) to the center position which is ground. That means that the input to the scope amplifier is shorted to ground so that no signal will appear. In this setting the trace will be a straight, horizontal line which you can set to any vertical position that you wish. If you anticipate signals with both positive and negative voltages it is often most convenient to set it at the center of the vertical scale. After completing this adjustment of the zero, set the switch under channel 1 back to AC or DC coupling. Now, use the vertical position knob to raise the wave so that its center is about 0.5 divisions above the central horizontal line on the oscilloscope screen. Later, when using ORIGIN to fit the data read off the screen to a sign wave, this vertical offset will be one of the fitting parameters. Be sure to record all relevant information about your settings in your notebook so that you could reproduce them if you needed to repeat any of the work below. Now record values of Voltage vs time by reading the data off the oscilloscope screen. Record 15 to 20 points of voltage vs. time in a table. Spread your readings evenly over the one cycle of the sine wave on the screen. Make certain that the columns of your table are labeled and that units and uncertainties are included. 5.3 MATLAB and ORIGIN Laboratory data is now almost always obtained by electronic means so that it is either recorded automatically on a computer or is entered into a computer by the experimenter for analysis. In this course you will use the software package named MATLAB for analysis of data. Alternatively, you may use ORIGIN if you are familiar with it. Both should be available in the lab. 5.3.1 Start the program Login on one of the ACS (Academic Computing Service) computers in the lab using your UCSD user name and password. Load Matlab by clicking on its icon. The Command Window will open with a blinking cursor on the right side of the screen. 1. Type x=[] to open an empty table into which you can enter data. (Case is important and the type of parentheses is important) 2. At the bottom of the Command Window click on Workspace. This will open a window with headings Name Value Class. Double click on x and the array editor will appear. Enter the time data, that you read from the scope screen, in the first row of the table. 8 3. Close the workspace by clicking on the X in the upper right corner of the Workspace Screen (Not the entire MATLAB screen). In the command window, on the command line type y=[]. and again open the Workspace screen. Double click on y and enter the voltage data that you read from the scope screen. 5.3.2 Graph your data In the command window type Plot(x,y) (Remember case and parentheses type are important.) If the plot does not appear on your screen click on the window button of the main MATLAB screen and select Figure 1 at the bottom of the drop down menu. Your data will be plotted but do not print it until you have attempted to fit a sine wave to it. 5.3.3 Fit the data You will now fit the data to the function a*sin(b*x+c) + d. The parameters a, b, c, and d are the amplitude of the sine wave, its frequency, its phase, and the offset, respectively. The independent variable is the time, which we asked you to enter as, x. In the command window, type cftool. (Curve fitting tool). This will open a new window entitled Dats. On the drop down menu for x select your x data and on the drop down menu for y select y. Then click on Create data set. This will return you to the Curve Fitting Tool window. Click on the Fitting button. And another new window will open entitled Fitting. Click on New Fit. On the drop down menu for Type of fit select Custom Equations. Then click on New equation to open (yet another window entitled Create Custom Equation. Select General Equations since this allows entry of nonlinear equations such as sinusoidal functions.and type in the expression a*sin(b*x+c) + d Then click on the Apply button. The results of the fit will appear in the Results window and also plotted as a red line along with the data in the Curve Fitting window. If the fit does not appear good, click on Fit options in the fitting window and change the start point value for the parameters that you think are very far from what is required for the fit. A fit finds the parameters of a given function that provide the best match between that function and a set of data. The numerical fit is performed by changing the parameters until a quantity defined as the sum of the squared differences between the data points and the function evaluated at these points is minimized. This is called the method of least squares. For a fit to a linear function and a few other simple functions this can be done analytically but, in general, the procedure calls for an iterative solution, starting from some initial guess for the parameters. When the start point for the parameters a,b,c,d are within range the fit will proceed and yield a curve that appears to fit the data. The values of the parameters that provide the best fit will be in the Results window. You can print this plot with the best fit curve superimposed on the original data points by clicking on File in the Curve Fitting Tool window. In the drop down menu, click on Print to Figure. This will open the Figure 1 window where you can edit the plot to include axis labels and modify other properties of the plot. When finished, the figure can be printed or saved to a file in a variety of formats. 9 6 Data and results to report Your report should include a table with your raw data. For the fit to sine wave using MATLAB you should calculate the frequency obtained from the fitted parameter angular "b". Remember the difference between frequency in Hertz (cycles per second) and angular frequency (radians per second). In your conclusions, compare the fitted frequency to the frequency from the display on the signal generator, and the value you deduced from the scope screen and state whether they agree within your estimated measurement uncertainty and the estimate of the uncertainty yielded by the least squares fit. 10

Find millions of documents here - Study Guides, Homework Solutions, Papers, Exam Answer Keys and more. Course Hero has millions of course related materials that will enable you to learn better, faster and get an A in all your courses.
Below is a small sample set of documents: