Notes on Experiment #11 You should be able to finish this experiment very quikly. This week we will do experiment 11 almost A I. Your data will be the graphial images on the display of the sope. o, BRING GRAPH PAPER! m X m is best sine that is the atual sale of the sope display. You will be skething the transient response of a iruit. We will also take a look at the apaitor as an integrating devie. Part 1 Proedure et up the iruit as shown in Figure 1 (Page 81) of the experiment with C = 0.01uF and R =27K. et the amplitude of the square wave to 6 volts peak-to-peak. It is important that the frequeny of the 6 volt (peak-to-peak) be exatly 200 Hz. Do not trust the sales on the funtion generator. The sope sales are muh more aurate. o, do this: 1. et the time sale to 0.5mse/DIV. 2. Adjust the frequeny ontrol dial on the funtion gen. so that there is one omplete yle of the input and output on the sreen i.e. exatly the 10 horizontal divisions. (i.e. one yle is 5mse and therefore f = 200Hz.) 3. Draw a large (half page at least) aurate sketh of the input V (t) and output V C (t) (on the same sketh) just as you see it on the sope. 4. Repeat steps 1 to 3 with C = 0.02uF and C = 0.068uF. Now we will be estimating of the value of the time onstants (tau) for eah sketh of V C (t). The proedure is explained below. At time instant t=0, the supply voltage hanges from +3 to -3 V as shown in Figure 2. o we onsider the iruit to be as shown in Figure 1 for time t=0+. C V = -3V i v C R Applying KVL, 78 P a g e Figure 1
V or, V or, Ri v v ( t) VC (0) V or, v ( t) V dv dt dv v t [ V v 0 C dt (0) V ] e t The slope of the tangent line to v (t) an be found by taking the derivative of v (t) dv ( t) dt [ V C (0) V ] e t At t = 0 this beomes dv ( t) [ VC (0) V ] dt t0 o, for a vertial hange of (V C (0) V ), the horizontal hange is whih is the time onstant of the iruit or ζ. If you sketh the tangent line of v (t) from the point t = 0 to the -3 Volt line the the amount of horizontal hange must be ζ. Projet that amount of hange up to the t axis and you have graphially found the value of ζ. ee Figure 2. Figure 2. 79 P a g e
Part 2 Let R = 100K and C = 1uF. At 200 Hz V C will be very small ompared to V as required. Use only one trial of V (t) for this part: V (t) = 3os(400(pi)t) Is V C (t) approximately 1/ times the integral of 3os(400(pi)t)? Verify this by heking the amplitude and phase of V C (t). Part 1 Ciruit Analysis Use the iruit in Figure 1 of the experiment to find the general expression for V C (t). Calulate the expeted value of tau for eah apaitor. Part 2 how that if V C (t) is very tiny ompared to V (t) then V C (t) is approximately 1/ times the integral of V (t). (Hint: if V C (t) is very small then i C (t) is approximately V (t) /R ) Read and know the setup of this experiment and have fun! 80 P a g e
ECE 225 Experiment #11 Ciruits Purpose: To illustrate properties of apaitors and their operation in R-C iruits Equipment: Keysight 34461A Digital Multimeter (DMM), Keysight U8031A Triple Output DC Power upply, Keysight DO-X 2012A Osillosope, Keysight 33500B Waveform Generator, Universal Breadbox Universal Breadbox I. R-C step response et up the iruit in Figure 1 below with C = 0.01uF and R =27K. Adjust the funtion generator to provide a 200 Hz square wave, with zero DC offset, and 6 volts peak- to-peak. After these adjustments you an visualize the generator as the swithing iruit shown illustrated below the iruit. Figure 1. Connet the sope to display V C (t) on CH1 and V (t) on CH2. et the referene lines of both the hannels at the enter of the sreen. Then selet the DC presentation, and display V C (t) and V (t) simultaneously and with the same vertial sensitivity (VOLT/DIV) for eah hannel. Reord the input and output time funtions. Measure the time onstant by the method disussed in the notes, and ompare it with the value alulated from the values of R and C. In order to measure the time onstant aurately, you may have to alter the funtion generator's frequeny. Reord and omment upon your observations. Repeat the experiment with C = 0.02uF and C = 0.068uF. Notie that V (t) at the output terminals of the funtion generator is not a perfet square wave. Why? Reord the waveforms aurately, espeially the "imperfetion" in V (t). 81 P a g e
II. An iruit as an integrator Using the same iruit from part I, if V C (t) is muh less than then V R (t) is almost equal to V (t) and therefore i C (t) is almost equal to V s (t)/r. how that under this ondition, V C (t) = 1/ times the integral of V (t). Thus the iruit ats as an integrator. Use a square wave of frequeny 200 Hz and amplitude 4 V peak-to-peak, and use C = 1 uf. Are the approximations mentioned above valid under these onditions? Display V (t) and V C (t) simultaneously on the sope as in part 1, exept that sine V C (t) is muh smaller than V (t) you will have to use different vertial sensitivities (VOLT/DIV) for the two hannels. Try the sinusoidal and triangle waveforms. Reord your observations. Comment on the quality of this iruit as an integrator. What is the integral of a square wave? Of a sinusoidal wave? Of a triangle wave? (Hints: the square wave is a suession of onstants; what funtion g(t) is the integral of the onstant funtion f(t) = +3? f(t) = -3? The sinusoid is easy, from a basi alulus ourse. The triangle wave resembles the funtion f(t) = K 1 *t + K 2 ; what funtion g(t) is the integral of that?) 82 P a g e
General Lab Instrutions The Lab Poliy is here just to remind you of your responsibilities. Lab meets in room 3250 EL. Be sure to find that room BEFORE your first lab meeting. You don't want to be late for your first (or any) lab session, do you? Arrive on time for all lab sessions. You must attend the lab setion in whih you are registered. You an not make up a missed lab session! o, be sure to attend eah lab session. REMEMBER: You must get a sore of 60% or greater to pass lab. It is very important that you prepare in advane for every experiment. The Title page and the first four parts of your report (Purpose, Theory, Ciruit Analysis, and Proedure) should be written up BEFORE you arrive to your lab session. You should also prepare data tables and bring graph paper when neessary. To insure that you get into the habit of doing the above, your lab instrutor MAY be olleting your preliminary work at the beginning of your lab session. Up to four points will be deduted if this work is not prepared or is prepared poorly. This work will be returned to you while you are setting up the experiment. NOTE: No report writing (other than data reording) will be allowed until after you have ompleted the experiment. This will insure that you will have enough time to omplete the experiment. If your preliminary work has also been done then you should easily finish your report before the lab session ends. Lab reports must be submitted by the end of the lab session. (DEFINE END OF LAB EION = XX:50, where XX:50 is the time your lab session offiially ends aording to the UIC CHEDULE OF CLAE.) Eah student should submit one lab report on the experiment at the end of eah lab session. If your report is not omplete then you must submit your inomplete report. If you prepare in advane you should always have enough time to omplete your experiment and report by the end of the lab session. 3 P a g e
A semester of Experiments for ECE 225 Contents General Lab Instrutions... 3 Notes on Experiment #1... 4 ECE 225 Experiment #1 Introdution to the funtion generator and the osillosope... 5 Notes on Experiment #2... 14 ECE 225 Experiment #2 Pratie in DC and AC measurements using the osillosope... 16 Notes on Experiment #3... 21 ECE 225 Experiment #3 Voltage, urrent, and resistane measurement... 22 Notes on Experiment #4... 29 ECE 225 Experiment #4 Power, Voltage, Current, and Resistane Measurement... 30 Notes on Experiment #5... 32 ECE 225 Experiment #5 Using The ope To Graph Current-Voltage (i-v) Charateristis... 33 Notes on Experiment #6... 37 ECE 225 Experiment #6 Analog Meters... 40 Notes on Experiment #7... 42 1 P a g e
ECE 225 Experiment #7 Kirhoff's urrent and voltage laws... 44 Notes on Experiment #8... 56 ECE 225 Experiment #8 Theorems of Linear Networks... 52 Notes on Experiment #9... 55 ECE 225 Experiment #9 Thevenin's Theorem... 57 Notes on Experiment #10... 56 Operational Amplifier Tutorial... 63 ECE 225 Experiment #10 Operational Amplifiers... 72 Notes on Experiment #11... 78 ECE 225 Experiment #11 Ciruits... 81 Notes on Experiment #12... 83 ECE 225 Experiment #12 Phasors and inusoidal Analysis... 88 2 P a g e