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Q1: ليك 1.8 مة 1.6 1:4 1-2 0.8 0.6 0.4 0.2 0 -0.2 0.4 0.6 -0.0 61 Aut L graph 2 In で 917-88 Q R=47000 10-115 29 F 5 10 15 20 25 30 35 40 45 5f 60 A graph In (u) (V8) 2.0 1.6 7.4 1.2 1.1 QAI 0.8 (Inuy 0.6 0.4 0.2 0 0.2 -0.4 0.6 -8.8 10 28 ¥2 time Constat 470K 70 AT e = C= 5J 53x10 35 30 50 Gv 70 80 90 700 graph 66 2, 3 4,800 AT (S) ± 0,01 0,005 2,400 S S V +0,01 V 6, 24 1,83 5,84 1,76 5,49 1169 S 7,200 S 5,04 1,61 5 10,40 S 4,64 1,53 G 14,80 S 4,00 1,38 7 24,00 S 3,09 1,12 8. 31/60 S 2,40 0,875 q 1090 S1, 84 01604 10, 52.40 s 1136 01307 IL 83,20 01480 0,733 Note: when time is less than los (± is 0,001) AT (S) V (v) In U (v) ± 0,01 + 0,01 0,00 S 6,29 1,83 3355679 2 6,400 S 4,16 1,42 8,900 S 3,68 1,30 10,80 ما 3,12 1,13 12,90 S 2,80 1,02 19,00 S 2,56 0,940 18,00 S 2,00 0,693 24,00 S 1,36 0307 S 4 29,20 S 0, 960 10,0468 le 39/40 S 0,720 o so,980 -01328 01733 g 60 ار AT 0.6 1 .1.22 20-10 1.22 y₁ = 10 0.6 Y2 Je - Y 72-X .X2 /R 9- T T=RT == => = 20 C = R = 470000 1 -0.062 "/s 3297 7/22/ => र = 5/80 => 2² = 9 T -0.062 2 = RC " 16.1 S C h R 16.1 -5 3.42×10 = 470000 1&IC SOFT Fed Mad 20 30 3 6 v y₁ = 0.8, V₁ =37 g. = –0.4.4₂ = 74 70 80 90 100 66 graph A Ул ない 10.4-1.8 งา => 74-37 x2 Vi T R = 470000 TRC 18 10 C→F (sign) -00324 14 -1 -0.0324= 2 =) J0.0324 = 30.80 30.8 S = RC 30.8 - 47000 C 2012 470000 47000 -S C = 6.55x10 POF OPGE/n INVESTIGATION OF RC CIRCUIT BACKGROUND INFORMATION Before arriving at your lab session, you should read the background information and answer the pre-lab questions given below, in your logbook. • • Read the instructions for the practical carefully before you come, in particular the "Aims and Objectives" and "Experimental Procedure" sections. Make sure you can identify all of the equipment referred to - look these up in your notes or textbook if you are unsure of what you will need. If there are any words that you are not familiar with, look them up in a dictionary and ensure you understand what they mean. Make a note in your logbook of anything that you will need to remember. Think about the science behind the experiment. Do you understand the laws that are being investigated, and why it may be important to be able to carry out this experiment? PRE-LAB QUESTIONS After reading the background information for this experiment, complete the Pre-lab questions below in your logbook BEFORE the lab session. 1) What is the definition of the time constant in a discharging RC circuit? 2) Write down the equations for the time dependence of the voltage across the capacitor when it is discharging. 3) Sketch a discharge curve labelling key points. INTRODUCTION Capacitors are among the most-commonly used circuit elements in modern electronic devices. Your calculator and cell phone contain dozens or hundreds of them. Any two electrical conductors brought near each other form a capacitor. If a charge Q is transferred from one conductor to the other (so that one has a charge +Q and the other has charge -Q), then there will be a voltage difference V, which is proportional to the charge Q. The constant ratio Q/V is called the capacitance C. C = = The SI unit of capacitance is the farad (F). (1) A capacitor is a device which stores charge. If the two sides of a capacitor are connected across a battery of voltage Vo and then disconnected from the battery, each plate of the capacitor will carry a charge of magnitude QC V (one side has +Qo, the other has -Qo). The larger the capacitance, the larger the charge carried. If the two sides of this charged capacitor are then connected by a wire, there will be a large, brief current through the wire as the capacitor discharges. If we use a large resistance R, instead of a wire, to connect the sides of the charged capacitor, the capacitor will discharge much more slowly. The charge and the voltage on the capacitor will decrease exponentially in time, as shown in Figure1, with a time constant T = RC (T=Greek letter tau). Vo 0.37 Vo AIMS AND OBJECTIVES V τ Figure 1: Voltage vs time graph (discharging) in RC circuit ● Determine and compare the time constants (T₁ and T₂) associated with discharging stage of RC circuits. • Calculate the value of capacitance for both capacitors (C₁ and C₂). After completing the virtual experiment you must ensure you have completed the following: • A tabulated set of results, with correct units. • Identified sources of errors and stated precision of your instruments. Sketched discharging curves (exponential decay curves) of voltage vs time, labelling important features. • Plotted graphs of the corresponding In(V) vs time for the two capacitors. THEORY In this experiment, you will measure the voltage across a capacitor C that is connected in parallel to a known resistor R, by the use of a digital storage oscilloscope. By plotting graphs of voltage against time, you will be able to determine the time constant T of the circuit. This will allow you to calculate the value of the capacitor in the circuit. Consider the simple RC circuit shown below. The resistor R and capacitor C are connected to the battery Vo with switch S. Capacitor Resistor Switch Battery Figure 2: Schematic diagram of RC circuit If switch S is closed, the capacitor will be charged to a voltage Vo and will carry a charge Q₁ = C V If switch S is re-opened, a current i will flow through the resistor as the capacitor discharges. The current i, the charge q remaining on the capacitor, and the voltage v across the capacitor and resistor are related by the following equations: V = iR = Δα i =- At (2) (3) The negative sign in the second equation indicates that the charge q is getting smaller as the current i flows. Combining these two equations yields: Δα At 9 q RC τ (4) Where, we have written T = RC. Notice that T = RC has the units of time. With the initial condition q(t=0) = Q₁, the solution to this differential equation is q(t) = Qe 冷 The voltage v(t) is given by: V(t) = = (+)e (1) (1) =Ve (6) Taking the natural log of both sides of (6) yields In ln (V) τ + + In In (V) (7) (5) Hence, a plot of In(v) vs t should be a straight line with slope = -1/T PROCEDURE The circuit is assembled as shown in Figure 3 below. The circuit consists of a known resistor, R, of value 470 k with a tolerance of 5% and an unknown capacitor C. The experiment involves the charging and discharging of a capacitor. You need to first charge the capacitor. Once the capacitor is charged, investigate how the capacitor discharges by observing the trace of voltage against time on the oscilloscope. Switch 6V Battery LINI-T UTD2025C 200 Oscilloscope Po 000 Cursor Type Track Capacitor SALE VOLTSION Y Figure 3: Experimental set up of RC circuit FOBITION LEVEL CLOLD 470 ΚΩ Resistor Charging Process: ● Close the switch to charge the capacitor with V₁ = Vo. • Note that the charging process may happen quickly (almost simultaneously). Discharging Process: Open the switch and record time and the decaying voltage on the capacitor C₁ using the oscilloscope as shown in the figure 4 below. VIVEVEJU 25MMZ 250MS/s DIGITAL STORAGE OSCILLOSCOP Stop M Pos: 0.00us AT: 0.00s Vol: HZ Ta -36.00s Cursor Туре Track Tb: -36.00% Time AV. DOO a Va: 6.00V Voltage Vb: 6.00V CHI 2.00V CH2 MATH Off Off M 10.0s CH10.00mV Figure 3: Discharge curve • Record the voltage and time of 10 or more points along the exponential decay, including at least 5 or 6 points in the first part of the curve between the initial voltage V and V/3. Make sure your data points cover an appropriate range, otherwise you may not get the full curve similar to Figure1. Replace the capacitor C₁ with C₂ and repeat the above steps. LOGBOOK TASKS 1. Answer pre-lab questions. 2. Draw a fully labelled circuit diagram. 3. Sketch the discharging curves (exponential decay curve of voltage vs time) for C₁ and C2 on the same axes, labelling important features. 4. Using your data collected from the virtual experiment, plot the corresponding In(V) vs time graphs for both C₁ and C₂. a) This graph should be a straight line with slope -1/T.See Answer
Q2:1. To write down the system of equations based on Kirchhoff's laws for the initial scheme of branch currents 12, 13 etc. and to determine the electromotive force e1. Prepared in this way there is no need to solve the system of equations. 2. Calculate the required branch currents 12, 13, etc. according to the original scheme. and electromotive force e1 by the contour flow method. Check with the help of numerical values of branch currents and electromotive force found the correctness of the equations created in the previous point. 3. Find the distribution of potentials in the original circuit, with the potential of the grounded node read as zero ( 0 = 0 V). At the same time, redraw the original diagram and indicate it with arrows the actual (positive) directions of the branch currents and note the branch currents and numerical values of electromotive forces and potentials of nodes 1, 2, 3 and 4. 4. Prepare a capacity balance for the initial scheme. In order to calculate all consumers, electromotive force and current source capacities. 5. Calculate the readings of the voltmeters UV1 and U V2. 6. Find the current 12 of the second branch (elements of the second branch have index 2) of the equivalent generator method. 7. Calculate the input conductivity g 22 of the second branch and the second and third branches (where the elements have index 3) mutual conductivity g 23. Notes and recommendations: 1. The number of the scheme (variant) is chosen according to the list prepared in the study group, which is presented to the lecturer. 2. The numerical values of the parameters of the circuit elements are given in the table. Their choice determined by the supervising lecturer. 3. By solving the problem using the equivalent generator method (point 6), it is determined the electromotive force of the voltage generator e g in the condition of the second branch idling (the second branch is discontinued). At the same time, the distribution of currents in the remaining branches of the idle circuit should be find by the nodal voltage method. The input resistance R g of the equivalent generator is determined by the passive idle scheme with respect to the terminals of the second branch disconnected by conversion/nELEKTRIAHELADI ATE 3150. Kodutöö nr. 1. Alalisvoolu hargahel. Ülesanne: 1. Kirjutada välja võrrandsüsteem Kirchhoffi seaduste alusel algskeemi kohta otsitavate haruvoolude 12, 13 jne. ning elektromotoorjōu e, määramiseks. Sel viisil koostatud võrrandsüsteemi pole vaja lahendada. 2. Arvutada algskeemi kohaselt otsitavad haruvoolud 12, 13 jne. ja elektromotoorjõud e₁ kontuurvoolumeetodil. Leitud haruvoolude ja elektromotoorjōu arwäärtuste abil kontrollida eelmises punktis koostatud võrrandite õigsust. 3. Leida potentsiaalide jagunemine algskeemis, kusjuures maandatud sõlme potentsiaal lugeda nulliks (= 0V). Sealjuures joonistada uuesti algskeem ja näidata sellel nooltega haruvoolude tegelikud (positiivsed) suunad ning märkida haruvoolude ja elektromotoorjõudude numbrilised väärtused ja sõlmede 1, 2, 3 ja 4 potentsiaalid. 4. Koostada võimsuste bilanss_algskeemi kohta. Selleks arvutada kõikide tarbijate, elektromotoorjõudude ja vooluallika võimsused. 5. Arvutada voltmeetrite näidud U v₁ ja U v2. 6. Leida teise haru vool I 2 (teise haru elementidel on indeks 2) ekvivalentse generaatori meetodil. 7. Arvutada teise haru sisendjuhtivus g 22 ning teise ja kolmanda haru (kus elementidel on indeks 3) vastastikune juhtivus g 23. Märkusi ja soovitusi: 1. Skeemi (variandi) number valitakse vastavalt õpperühmas koostatud nimekirjale, mis esitatakse õppejõule. 2. Skeemi elementide parameetrite numbrilised väärtused on toodud tabelis. Nende valiku määrab juhendav õppejõud. 3. Ekvivalentse generaatori meetodil (punkt 6) ülesannet lahendades määratakse pingegeneraatori elektromotoorjõud eg teise haru tühijooksu olukorras (teine haru on katkestatud). Sealjuures voolude jagunemine tühijooksuskeemi allesjäänud harudes tuleks leida sõlmepingemeetodil. Ekvivalentse generaatori sisendtakistus Rg määratakse passiivse tühijooksuskeemi teisendamise teel katkestatud teise haru klemmide suhtes. Algandmed variant 3: r1=50 r2=50 г3=60 г4=50 гs=20 г6-20 ry=20 r8=20 i=2A i₁=4A e2=50 V e3=40 V e 4-30 V e 5 = 20 V e 6= 10 V Õppejõud: Aleksander Kilk 15. 2023/2024. Õppeaasta 7777 es ? e₁ De ⑦esSee Answer
Q3:3. The loading of a factory on a 1000 V, 50 Hz system includes: 20 kW heating (unity power factor) 10 kW (Pi) induction motors (0.7 lagging power factor) 5 kW lighting (0.85 lagging power factor) (a) Establish the power triangle for the total loading on the supply. (3 marks) (b) Determine the power-factor capacitor required to raise the power factor to unity.(4 marks) (c) Determine the change in supply current from the uncompensated to the compensated system. (3 marks)See Answer
Q4:2. Answer following questions: (a) Find the Thévenin equivalent circuit for the network to the left of terminals a - a' of the circuit given in Figure2. (4 marks) (b) What would be the impedance of the load that could absorb maximum power from the circuit when it is connected across a -a"? (2 marks) (c) What will be the reactive power absorb/supply by the load you have selected in 2b (2 marks) 51 R₁ ww 2 k R₂ w 1 ΕΩ E 1 + a L 8V20° -Thévenin R3 3.3 k Figure 2: Circuit for Question2 -odSee Answer
Q5: V IEE 3100 OPTIMIZING DESIGN USING MONTE CARLO SIMULATION This assignment involves finding the least cost combination of components to use in an electrical circuit to achieve a desired output voltage specification. The circuit for this assignment is shown below. R2 ww R1 99 R9 M R3 w R4 R5 ми The component values are: V = 175 V DC R1 = 150 OHMS, R2 = 100, R3 = 125 R4 = 100 R5 50 R6 50 R7 = 100 R8 = 75 R9 = 80 = The output voltage, Vout, which is the voltage drop across R7, has a quality specification that states it needs to be within +- 0.75 volts 95% of the time. Each component in the circuit, including the voltage source and all resistors have variability. Each component can be purchased with different levels of precision ranging from 1 to 20% tolerance with a different cost associated with a different level of tolerance. The cost structure is given by: R6 R7 27 R8 - мили Tolerance % Cost 1$12,000 2 3500 7 3 2000 4 1000 5 500 68129 300 11 200 150 125 10 100 37684 12345 80 70 60 50 19 45 20 67808 16 40 17 18 43322 35 30 27 25 For the voltage source the cost is determined by the tolerance percentage of the voltage source according to the following function: Cost of voltage source = $10/Tolerance^2. As an example assume a tolerance of 5%. The cost of this voltage source would then be 10/.05^2 = $4000. You have been asked to find the lowest cost combination of components that will meet the quality specification. You have been asked to do this for two variability assumptions. 1. Assume all components are normally distributed with a mean equal to the value given, and a std dev dependent on the precision level specified. 2. Assume all components are uniformly distributed with a mean equal to the value given and a range dependent on the precision level specified. Present your results in a report. The report must include an executive summary. The report must be well written with all tables and graphs discussed in supporting narrative. Your report should discuss the differences you observe between the normal and uniform assumptions.See Answer
Q6: EXPERIMENT E1 Resistors and logic circuits 1.0 Introduction An electric circuit is a complete path from the positive terminal to the negative terminal of a power source. If the elements of the circuit are arranged in such a way that only one path exists for current flow (i.e. the current is identical for all elements), then the circuit is a series one. If an identical voltage exists across a number of alternative current paths then the circuit is a parallel one. Most practical circuits involve various combinations of series and parallel components. Of course components can be connected so that they are neither in series or parallel. Answer the following questions books: 1. If voltages are identical, then how are the components connected? 2. If currents are identical, then how are the components connected? 2.0 Series circuits 2.1 Series circuit theory your lab A typical series circuit is shown in Figure 2.1, this circuit having four resistors and a power source R1 R2 Vs R4 R3 Figure 2.1 The total resistance R, in the circuit may be calculated by a simple summation of the individual resistors: R=R₁+ R₂+R3+ R4 This may be extended for n number of resistors. From Ohm's Law, the total current in the circuit may be calculated. V, IR, or I, V₁/R₁ An important requirement of a series circuit is that the current is identical throughout the circuit. This feature will be observed in this experiment. 2.2 Requirements for series connection test Select the resistors 1k2, 82002 and 68092, and use the DMM set as an ohmmeter to measure their values. Record your results in Table 2.2, which is to be drawn in your lab book. 680-673 680 Rnom- x100 Rmea X100% Ruam Nominal Resistance Measured Resistance % Difference R₁ = 6802 673 1.03% R₂ = 820л 803-4♫ 2.02% R₁ = 1000 986 Series Rot=2500 J 2462 A 1.4% 1.5.4% Table 2.2 Connect the resistors in series on your breadboard, and measure the total resistance, Riot (do not connect the DC power supply yet, and do the % calculations outside lab time). 2.3 Voltage tests Draw Table 2.3 in your lab book. 15x 680г 2500 R₁ VR, = Vsx Rtot Quantity Measured value from Theoretical values using % Difference nominal values for V, and R DMM Vs 15.1 V Riot 2462.2 VRI 4-127 V VR2 4.9276 V VR3 6.047V IA 6.132X103 A 18 6-132X10 A Ic 6.132X10 A ID 6.192x-3A 13= 10-3 6.132 x 10 15V 2500 4-08 V 9-667% 1-504% 1-15% 4.92 v 0-154% 6 V 0-71% 0806A 2-15% 0-006A 2-15'1 4.0060 2-15% 0-006 A 2-15% Table 2.3 red V=15V R1-6800 D EQ DMM COM black B R2=82002 R3 = 1k0 Figure 2.3 Connect the variable DC power supply and, using the DMM in voltmeter mode, adjust the output to 15V. Measure and record the actual value from the DMM into Table 2.3. It is essential that this voltage remains unchanged at the recorded value for the entire series test. Figure 2.3 shows the meter connections for measuring the voltage across R₁. You will need to reconnect the red and black wires to measure the voltages across the other resistors. 2.4 Current tests The next part of the experiment is to measure the current at various points in the circuit. Use the DMM set up in ammeter mode to measure milliamps through the four points A, B, C and D. Note that it will be necessary to break your circuit and remake it in order to insert the ammeter. Record your results in the appropriate fields in Table 2.3 in your lab book. 2.5 Comments and conclusions Discuss the reasons for any differences in Table 2.2. Use Ohm's Law to calculate the current flowing in the circuit I, and hence calculate the voltage drop expected across each resistor (e.g. voltage drop across R₁ is calculated as VRI = IR₁, etc). Use the nominal values for the power supply voltage and resistances. Compare these theoretical values with the measured values and express them as percentage differences using the following formula: (Measured value - Theoretical value)/Theoretical value × 100 List the possible reasons for any differences. If any difference is greater than 5%, there could be a serious problem with either your calculations or tests, and checks will be needed. Comment on the sum of the three measured resistor voltages. Is this result consistent with expectations? Also comment on your current measurements. 3.0 Parallel circuits 3.1 Theory for parallel circuits DMM AMMETER mA COM RA Re red black Figure 3.1 A typical parallel circuit is shown in Figure 3.1. Parallel circuits have more than one path for current flow and there must be the identical voltage across all parallel paths. Two such paths exist in the example circuit as shown. The identical voltage appears across all the resistors in the circuit and the current through each arm is inversely proportional to the circuit resistance (from Ohm's Law). The total current in the circuit is given by I, la+Is (from Kirchoff's current law). Note the 'break-then-remake' method in order to measure the current using an ammeter. By Ohm's Law: L=V, RA I=V,/RB These can be substituted into Kirchoff's Current Law equation to give: I-V(1/R+1/RB) -V.((RA) + (RB)) =V(RARB)/[RA+ RB]) The term RRB / (R₁+ Rs) expresses the total value of resistance (R, V./I) in the circuit. In practice the inverse form, (R.)"' = (Ra) + (Ra)", is often simpler to work with as a calculator's inverse button (r) can be used thus reducing the amount of resistance data inputting. In addition this inverse form is directly extendable to any number of resistors. 3.2 Requirements for parallel tests The following table is to be drawn in your lab books. Quantity Measured DMM Value from Theoretical Values Calculated V₁ 10-03 v lov VRA 10-03 V OV VRS 10-03V lov VR6 NO-03V lo V =→/ 37-2 mA 0.0369 A Ib 14.9 MA I 12-5 CI 10-17 MA Riot 267.1 V=IR 0.0147 A 10 = Ix271 G-0122 A 0-01 A 10 = I 2717 271 Table 3,1: Parallel Circuit - 3 Resistors 680 1000 Select the resistors R4, Rs and R6 (k2, 82002 and 6802 respectively) as used in section 2.2. Use the DMM to measure their values and record your results. 3.3 Tests on three resistors in parallel b V₁-10V R₁ Rs Re 9 Figure 3.3 Connect the circuit as shown in Figure 3.3. Use the DMM to measure the total resistance, Riot and record it in Table 3.1. Then, using the DMM connected in the correct configuration, measure and record all the currents and voltages associated with this circuit, recording your results in your lab books in Table 3.1. 3.4 Comments and conclusions Comment on the relation between your measured V and I results and the voltage and current principles of the parallel connection./n 1. In the first part of the lab you will investigate the series circuits with resistors. a. Connect the resistors in series on your breadboard, and measure the total resistance Rtot (do not connect the DC power supply yet, and do the % calculations outside lab time). b. Voltage Tests: Connect the variable DC power supply and, using the DMM in voltmeter mode, adjust the output to 15V. Measure and record the actual value from the DMM into Table 2.3. It is essential that this voltage remains unchanged at the recorded value for the entire series test. Figure 2.3 shows the meter connections for measuring the voltage across R₁. You will need to reconnect the red and black wires to measure the voltages across the other resistors. c. Current Tests: the next part of the experiment is to measure the current at various points in the circuit. Use the DMM set up in ammeter mode to measure milliamps through the four points A, B, C, D. Note that it will be necessary to disconnect your circuit and remake it in order to insert the ammeter. Record your results in the appropriate fields in Table 2.3 in your lab book. 2. In the second part you will investigate the parallel circuits with resistors. a. Parallel circuits have more than one path for current flow, and there must be an identical voltage across all parallel paths. The identical voltage appears across all the resistors in the circuit, and the current through each resistor is inversely proportional to its resistance (from Ohm's Law). The total current in the circuit is given by I₁ = la + lɓ (from Kirchoff's current law). Note the 'break-then-remake' method in order to measure the current using an ammeter. b. Tests on 3 resistors in parallel: Connect the circuit. Use the DMM to measure the total resistance Rtot and record it in Table 3.1. Then, using the DMM connected in the correct configuration, measure and record all the currents and voltages associated with this circuit, recording your results in your lab books in Table 3.1. You should download the logbook Excel file from the VLE, and enter your measurements into the Excel file. You will use your logbook (and guidance from the Key Questions) to write a lab report. The lab report will be submitted on the FC312 Physics VLE page, via a Turnitin link in the Module and Assessment tile. Guidance: For this assessment you should make use of the following materials: • Resistors lesson notes Core textbook: AQA Physics A Level, Year 1 13.1-13.5 and Year 2 23.1 Please note: This is an individual assessment so you should not work with any other student. Your tutor will also ask for a draft copy of your report and provide written feedback. Before you submit this assessment, you will have an opportunity to receive feedback from your peers (other students in the class). Your tutor will arrange a time for you to share and discuss your progress with your classmates. You do not have to act on their feedback, but you may find it useful to enhance your final submission. Kaplan International Pathways 2 kaplanpathways.com Structure: Your lab report should contain the following sections: • • • ● • • • • Introduction. You should give a brief overview of the main theories behind the experiment. What is the background to this experiment? Aim. Clearly state the aim of the experiment - what are you trying to determine? Materials and methods. You should explain how the experiment was carried out. You should give enough detail so that another person can repeat the experiment in the same way you did. Results. You must include all your results. Results tables should be clearly labelled. All measurements must include units. If graphs are required, they should be an appropriate size and clearly labelled. Discussion. You need to explain what your results mean. You should link your results to relevant theories and explain how they fit together. You must use in-text citations where appropriate. Any unexpected results should be explained. Conclusion. State what has been learned from this experiment. Have you met the aim of the experiment? Errors. What may have affected your results? This section should include errors such as systematic, parallax and human errors ones that cannot be avoided. References. You should list all sources used. - Appendix. The raw data tables and the detailed calculations should be included here. Theory and/or task resources required for the assessment: You should refer to the appropriate chapters in the key texts as well as the lecture materials for the topic relevant to your experiment. Referencing style: You should refer to a minimum of 5 relevant sources for your report. You must include a Harvard style reference list at the end of your report. Expected word count: The lab report usually contains 1500-2000 words, excluding references. In each section you should include around the following number of words: • Introduction & Aim: 300-500 words Materials and methods: 300 words Results: 200 words Discussion: 500-600 words • Conclusion & Errors: 200 words Learning Outcomes Assessed: Apply good laboratory practice to the conduct of experiments, and to measure, record and interpret outcomes accurately using a lab report format Submission Requirements: You must include the following paragraph on your title page: I confirm that this assignment is my own work. Where I have referred to academic sources, I have provided in-text citations and included the sources in the final reference list. Kaplan International Pathways 3 kaplanpathways.com You must type your assessment in Arial font 11, with single spacing. You must submit the assessment electronically via the VLE module page. Please ensure you submit it via Turnitin. Assessments submitted after the submission deadline may incur penalties or may not be accepted. Addition submission information - check you have done the following: Formatting Consistent font, spacing, page numbers, formatting and subheadings Citations Correct format and location throughout the report Referencing Harvard referencing system used correctly in the reference list Summarising Paraphrasing Spell check Proof-reading Grammar Summarising the results of research Paraphrasing the contents of research findings Spell check the report Proof-reading completed Grammarly has been used to check the report How will this assessment be marked? Lab Report - (80% of assessment score) Experimental Procedure and Plan of experiment (10%) We will be looking for: • • • • • • Clearly defined aim of experiment Appropriate theoretical context Hypothesis with reasons List of equipment and consideration of safety procedures Clear explanation of method Clearly labelled diagram showing the equipment set-up Methodical practical skills (instructions followed correctly) Appropriate safety precautions Data Handling - Results (Tables, graphs, calculations) (15%) We will be looking for: • Good quality results with units • Recognition of outliers, repeat measurements to reduce uncertainty Equations, structural formulae • Correct mathematical manipulation in calculations, including units • Units on graph axes and/or table headings • Results quoted to correct precision, with consideration of errors Data Handling – Results (Uncertainty & Errors) (10%) We will be looking for: Identification of errors and discrepancies • Analysis of impact on results Kaplan International Pathways 4 kaplanpathways.com Discussion and Conclusion (30%) This will mainly be found in the Introduction, Discussion and Conclusion sections. We will be looking for: Clear explanation of the science underlying your observations Interpretation of results and graphs • Explanation of all results • • Confirmation (or otherwise) of hypothesis and/or aims Well-explained links to theory with equations Overall structure and quality of presentation (10%) We will be looking for: Attractive, clear layout with title page, headings, sub-headings • Neat, well laid-out tables with column headings • • • Neat graphs with titles, labelled axes and well-spaced, numbered scales Correctly formatted chemical and mathematical equations Calculations that are well laid out and easy to follow References correctly formatted and attributed • • Correct use of academic English: О Good English sentence structure Correct English spelling ○ ○ ○ 3rd person passive voice used correctly throughout lab report Paragraphs for each new section Academic integrity (5%) Information from sources is appropriately paraphrased/summarised rather than relying on quotes • Any direct and indirect quotations are clearly marked and acknowledged with correct citations • References match the citations and are correctly formatted • Data/facts presented are genuine and accurate Practical Skills - (20% of assessment score) Hazard identification video task - (10%) Health & Safety VLE quiz – (10%) The overall mark will be a percentage (0-100%). How will you get feedback? Your tutor will mark the assessment and provide you with a written feedback sheet. You can use this feedback to guide your further learning on the module. Kaplan International Pathways 5 kaplanpathways.comSee Answer
Q7: CALIFORNIA STATE UNIVERSITY, FULLERTON DEPARTMENT OF ELECTRICAL ENGINEERING EG-EE 203L Experiment 4 CIRCUIT ANALYSIS AND THEOREMS I. BACKGROUND The purpose of this experiment is to allow the student to experimentally verify certain circuit analysis techniques and circuit theorems that have been discussed theoretically, in EG-EE 203. In order to do this you will make use of the circuit shown in Fig. 1. -Vs.+ ww Rs www R3 Az' Iz E + V4 www Z x' x -V2+ www R2 FIG. 1 The circuit contains four pairs of terminals w-w', x-x', y-y', and z-z'. As shown in Figure 1, the terminals of each of these pairs are shorted together with a short link. Any link may be removed, and either a voltage source or a milliammeter may be inserted in its place. Every time a voltage source is inserted, let its positive terminal be connected to terminal w, x, y, or z and its negative terminal to terminal w', x', y' or z'. In order to do the experiment you will need sources of 5 VDC and 10 VDC. You will be expected to set up your PS 503A power supply to serve for both sources. Except where otherwise stated you will be expected to use the DM502 to make the voltage measurements required. (Read the equipment notes on the DM502 digital multimeter). The Simpson multimeter may be used to measure currents. 47 II. PREPARATION A. Let R2=2 KQ, R3= 3 K2, R4=4 K, and R5= 5 KQ. 1. Assume that the 10V source is inserted at x-x'. Predict the values of V2 and V3. 2. Assume instead that the 5V source is inserted at y-y'. Predict the values of V2 and V3. 3. Assume that the 10V source is inserted at x-x' and the 5V source is inserted at z-z'. Predict Iy and V2. 4. Assume that the 5V source is inserted at x-x'. Predict the values of Iz. 5. Assume that the 10V source is inserted at x-x' and the 5V source is inserted at y-y'. Using superposition and the results obtained in parts II.A.1 and II.A.2 predict the values of V2 and V3. 500 KQ B. Let R2=200 KS2, R3= 300 K2, R4= 400 KS, and R5= 500 KN. 1. Assume that the 10V source is inserted at w-w' and the 5V source is inserted at y-y'. Predict the values of V2 and V5. C. Calculate the Thévenin equivalent of all the circuit of Part II.A.3 except R2. egalov a ro gefiov a smit III. IN THE LABORATORY A. Set up the circuit of Fig. 1 with the values given in Part II.A. In each of the following steps find the percent difference between the experimental and predicted values. 1. Verify the predictions made in Part II.A.1. 2. Verify the predictions made in Part II.A.2. 48 3. Test the superposition theorem by inserting both the 10V source at x-x' and the 5V source at y-y'. Measure V2 and V3 and verify the predictions made in part II.A.5. 4. Verify the predictions made in Part II.A.3. 5. Verify the prediction made in part II.A.4. Insert milliammeter at z-z' 6. The Reciprocity theorem says that, in a bilateral network if you interchange the positions of the voltage source and the milliammeter, the milliammeter reading will be unchanged. Make this change in the circuit of Part II.A.4. and verify the theorem. B. Set up the circuit of Fig. 1 with the values given in Part II.B. 1. Measure V2 first with the DM502 and then with the Simpson multimeter. Compare your measurements with the prediction made in Part II.B.1. Summarize the results in the following table and explain the results. Note: For DM502, RM=10MQ TDS For Simpson RM=20KQ/VDC. To find RM, 20K has to be multiplied by the voltage scale being used. Table for V2 large time com Calculated II.B.1 DM 502 Simpson 260 The Amy 2. Measure V5 first with the DM502 and then with the Simpson multimeter. Compare your measurement with the prediction made in Part II.B.1. Do these results compare in a manner similar to what was found in Part III.B.1? Summarize the results in the following table and explain the results. Table for V5 Calculated II.B.1 DM 502 Simpson 260 49 C. Set up the circuit shown in Fig. 2 using the values calculated in Part II.C. Measure V2 and compare with the value obtained in Part III.A.4. RTH www Voc FIG. 2 + R2 = 2K D. What conclusions do you draw from this experiment? R-300 Predic EV 50See Answer
Q8: California State University, Fullerton Department of Electrical and Computer Engineering EGEC 203L-08 Electric Circuits Laboratory Assignment 8 RLC Circuit: Impedance Measurement Submit only copy per team Before submitting, verify that your submitted files are readable • • Read all parts before your start Part A Spring 2024 RLC circuits and preparation Make yourself familiar with RLC circuits. Read the relevant sections in the lab manual and the circuits textbook. Review background information on capacitive reactance, inductive reactance, resistance, and impedance. Review phasor diagrams. Complete Part I of Experiment 7 in the Lab Manual (Page 61) Complete Part II ((A, B and C) of Experiment 7 in the Lab Manual (Page 61-62) (Lab) Complete parts A and B in the manual (pages 62 and 63). Part B • Turn in a completed and filled copy of this handout on Canvas showing all relevant calculations, data and results (in PDF format). All of these must be included in the report as well, in the relevant sections. Do not omit any details in the report. • Also turn in an informal report via Canvas in PDF format. Your report shall include: 1. Title page. This page must include the title of the assignment, the full names of the team members and date of report completion 2. Introduction 3. Theoretical background. Use information from multiple sources, at least two. List those sources in the report. 4. Tools and Equipment 5. Procedure 6. Observations, Calculations, Measurements and Results 7. Discussion 8. Conclusions CALIFORNIA STATE UNIVERSITY, FULLERTON ELECTRICAL ENGINEERING EG-EE 203L Experiment 7 VOLTMETER MEASUREMENT OF AN UNKNOWN IMPEDANCE I. BACKGROUND The purpose of this experiment is to show how the value of an impedance can be determined with a minimum of instrumentation. At the same time a study is made of the behavior of a particular simple circuit. The circuit to be used for determining an unknown impedance, Z, is as shown in Fig. 1. The magnitudes of Vs, VR and Vz can be measured with the Digital Voltmeter. Vs + VR - w R Zt +1 Vz FIG. 1 Knowing R, the magnitude of Z can now be calculated. By means of a graphical construction of the related phasor diagram, or of the equivalent trigonometrical calculation, the magnitude of the phase angle can be found. The sign of the phase angle can be determined from the knowledge that an inductive impedance will increase if the frequency is increased slightly, whereas a capacitive impedance will decrease if the frequency is increased slightly. The three things thus found completely determine Z. II. PREPARATION A. Sketch a typical phasor diagram showing the relationship between Vs, VR and Vz for each of the following cases. Place Vs in the horizontal position pointing to the right. 61 1. Z is equivalent to the series combination of an inductance and a resistance. 2. Z is equivalent to the series combination of a capacitance and a resistance. B. Calculate literally (with letters, not numbers) the value of Z in terms of R and the voltages. C. Show how to determine the magnitude of the phase angle of Z from the phasor diagram: 1. Show the phase angle in the phasor diagrams sketched in Part II.A. 2. Calculate the magnitude of the phase angle trigonometrically in terms of the voltages. III. IN THE LABORATORY For each individual measurement made, connect the unknown impedance in a circuit as shown in Fig. 1, set the frequency of Vs using the frequency counter, set Vs approximately to 5 volts, and adjust R so that Vz is approximately equal to VR in magnitude. Do not waste time trying to be exact with the voltage settings. Then record R and make good measurements of Vs, VR and Vz with the digital voltmeter. Finally, test to see whether Z is inductive or capacitive. A. Use the series combination of a 200 ohm resistor and a 10 mH inductor as the unknown impedance Zt. XL = WL 1. Make the above measurements at a frequency of 7000 Hz. 2. Calculate Zt. 217500 Vs 3. Draw a large phasor diagram carefully to scale based on your data. Measure the phase angle of Zt. 4. Calculate the phase angle of Zt trigonometrically. Compare the value obtained graphically with the calculated value. B. Construct the circuit shown in Fig. 2 using the same elements for Zt as in part III.A. Consider that the circuit between the two left-hand terminals is one equivalent unknown impedance, Ze. 62 CALIFOR DEPARTM 500 Ω Ze- 0.05 µF Zt FIG. 2 C 1. Using the value of Zt determined in parts III.A.2 and III.A.4, calculate the value of Ze at 7000 Hz. Ze=700 2. Determine Ze experimentally. Compare with the calculated value. Z=610See Answer
Q9:ZBP2 J2. IN OUT J1. 0 HDR1X2 Speaker HDR1X3 Audio Input Jack Battery XFG1 9V C3 JE 100pF C1 HH 0.1µF R3 10kQ 30 % Key A Volume C6 C7 0.1μF 01 10µF 3- C4 470pF LM386 C2 0.1uF R1 R6 10kQ Key-A Gain 50 % R2 10kQ 100 C5 10µF C8 北 1000μF Tektronix SC1/nAudio Amp LM386 Audio Amplifier Audio Input Jack Volume 10K ww C7 0.1 uF Battery HH www.circuitbasics.com C4 100 uF https://www.circuitbasics.com/build-a-great-sounding-audio- amplifier-with-bass-boost-from-the-Im386/ HF C5 0.1 uF LM386 5 3 Good technical info on the LM386 https://www.apogeeweb.net/circuitry/Im386- internal-circuit.html C3 10 uF Gain 10K 0.1 uF C6 R2 R1 470 pF 10K 10R C8 10 uF C1 1000 uF Speaker +/n Need detailed explanation of the Circuit on how it work and how each part work also what is does. Need names of each Part and how Lm386 works. IF calculation is required then do for the parts. From the Multisim Image, Explain why we use the Bode Plotter, Function Generator, and Oscilloscope.See Answer
Q10:Activity 3 For a transmission line, the characteristic impedance Zo and the propagation coefficient y are given by 2,= R+jesL VG+jac = √(R+ jesL)(G+ju) x= Given R 250 L=5x10 H. G 80x100 siemens, C = 0.04x10°F and w 2000 π rad/s determine in Polar form and exponential form impedance Zo and propagation coefficient y (Use De-Moivre's Theorem to solve).See Answer
Q11:Problem 3: Transform the following NMOS Common Drain Amplifier to the AC equivalent Circuit. (5 point) VDD www www Rsi www www +See Answer
Q12:Problem 1: Given input voltages, compute the output voltages of the following circuit. (2 point) V2 ° IDI DI D₂ ID2 R ww -o Vo V₁ = 0.7V 1 V₁ (V) V2 (V) Vo (V) 0 0 4 0 0 4 4 4See Answer
Q13:2. For the circuit below, If 10k Ohm resister is removed calculate the current through each resistor and voltage drop on each resistor, redraw circuit diagram. (35) 12 www 1KQ I 100V IS IS ww + ww I 2KQ 10ΚΩ IG I, ΣΑΚΩ 3KQ I u HI H ILSee Answer
Q14:Q.3: Give brief answers: [Marks:5] a) Two resistances of value 402 and 602 are connected in parallel of 2mA current source. Find power dissipated across 42. b) How are three quantities related in Ohm's law?See Answer
Q15:Q.2: Identify and label each node and using the Nodal analysis, find out Voltage value at each node and Current for 5KQ in circuit given below. [Marks:10] 10ΚΩ 20ΚΩ Www- -w- 5KQ 1 2mA 30ΚΩ www 12VSee Answer
Q16:Homework #2 - Part III DESIGN A 3-bit BCD SYNCHRONOUS COUNTER Objective: 3 Bit up/down synchronous Counter Problem Statement: To design and implement 3-bit UP and Down, Controlled UP/Down Synchronous Counter using MS-JK Flip-flop. Inputs: The counter will have one main input "X". When "X" = '1' the counter will up-count, otherwise when "X" = '0', the counter will down-count. Up Counter: The up counter counts binary form 0 to7 i.e. (000 to 111). It counts from small to large number. Its Output goes on increasing as they receive clock pulse Down Counter: This down counter counts binary from 7-0 i.e. (111-000). It counts from large to small number. Its Output goes on increasing as they receive clock pulse • Draw the State Diagram (any representation), State Table, and the Excitation Table of this circuit. • Provide the excitation equations (simplify your circuit using K-maps) • Sketch the circuit.See Answer
Q17:Homework #2 - Part II Sequence detector: The machine has to generate z = 1 when it detects the sequence 1011. Once the sequence is detected, the circuit looks for a new sequence. The signal E is an input enable: It validates the input x, i.e., if E = 1, x is valid, otherwise x is not valid. resetn x 011011011 01101101101011010101 x E clock FINITE STATE MACHINE E Z Draw the State Diagram (any representation), State Table, and the Excitation Table of this circuit with inputs E and x and output z. Is this a Mealy or a Moore machine? Why? Provide the excitation equations (simplify your circuit using K-maps) Sketch the circuit.See Answer
Q18:1. The circuit of Figure 1 contains an independent voltage source VDD = (5000+a) mV and two MOSFETs whose parameters are as follows: Vin (500+ẞ) mV, μnCox = (300+y) μV/A², (W/L) = 6 µm/1 μm, λ = 0 V-¹; Vtp = -(500+5) mV, μpCox = (100+) μV/A², (W/L) = 2 µm/1 μm, p = 0 V1. (i) Calculate the current /D1 and the voltage Vos1. (10 points) (ii) Use LTSpice to calculate ID1 and VDS1. (5 points) (iii) If the results from (ii) are different from those in (i), explain why. (5 points) M2 VDD + D1 V DS1 M1 Figure 1See Answer
Q19: ECE 220 Laboratory 5 Step Response and Frequency Response Michael W. Marcellin Please follow all rules, procedures and report requirements as described at the beginning of the document entitled ECE 220 Laboratory 1. Always wear your safety glasses when performing your lab experiments. Prelab Part 1 Consider the RC circuit shown below in Figure 1. We will examine the step response and natural response of this circuit. Recall the FIFE equation from class: x(t) = x(∞) + (x(t₁) − x(∞))e-(t-to)/T vi(t) 1 ΚΩ + 1 μFvc(t) Figure 1. RC step response and natural response. Suppose to = 0, vc (to) = 0 V, and v¿(t) = 5 V for t ≥ to. a) Write an equation for vc (t) for t≥ 0 (step response). b) About when will vc (t) reach its final value? Now assume to = 10 ms, vc(to) = 5 V, and v¿(t) = 0 V for t ≥ to. c) Write an equation for vc (t) for t≥ 10 ms (natural response). d) About when will vc (t) reach its final value? Now, assume that vi(t) is the square wave shown in Figure 2 below. 5 V ↑ Vi(t) 10 ms 20 ms 30 ms 40 ms t Figure 2. Square wave. Assume vc (0) = 0 V. Then your equation from a) above is good for 0 ≤ t < 10 ms. Now, from your answer to b) above, vc (t) reaches 5 V well before 10 ms. So, your equation from c) above is good for 10 ≤ t < 20 ms. We will verify this using PSpice. Start a new project as usual, and draw the circuit shown below in Figure 3. We use a new part in this circuit called VPULSE to generate the square wave of Figure 2. This part can generate a very general periodic pulse sequence. Set the parameters as shown in the figure. The meanings of the parameters are as follows: PER is the period V1 is the "first" voltage V2 is the "second" voltage (usually higher than V1) TD is the Time Delay before switching from V1 to V2 PW is the Pulse Width (time voltage stays at V2 before returning to V1) TR is the Rise Time (time voltage takes to transition from V1 to V2) TF is the Fall Time (time voltage takes to transition from V1 to V2) Λ V10 V2=5 V1 TD = 0 TF = 1n TR = 1n PW = 10m PER = 20m R1 w 1k HH C1 1u 152 Figure 3. RC circuit with square wave input. Double click carefully on the capacitor symbol itself (not the label or value). The property editor spreadsheet opens. Scroll left or right until you find the column labeled IC. This is the initial condition for the capacitor voltage. Set the cell below IC to 0. Click on the tab labeled PAGE 1 to return to your schematic. Create a new simulation profile and set Analysis Type to Time Domain (Transient). Set the parameters as follows: Run to time: 40 m Start saving data after: 0 Maximum step size: 0.1 m Add voltage markers as shown in the figure and run your simulation. Verify that the resulting curves agree with your answers to a)-d) above. e) print your graph. Prelab Part 2 Consider the RC circuit shown below in Figure 4. a) Use complex phasor analysis to calculate the steady state output voltage vo(t) for three different values of f. Specifically, ƒ = 10 Hz, f = 1 kHz, and ƒ = 100 kHz. == Don't forget that w = 2πf, so that the three different inputs are v¿(t) = cos(20πt), vi(t) = cos(2000πt), and v₁(t) = cos (200000πt). If you have done this correctly, you should get something fairly close to vo (t) = cos(20πt), v,(t) = 1½ ½ cos (2000πt - 45°), and v₁ (t) = 0.01cos (200000πt – 90°), for the three different inputs, respectively. + vi(t) = cos(2Пft) V 15.7 ΚΩ w 10 nF vo(t) Figure 4. Steady state response for RC circuit. Note that the only thing that changed in your three calculations is the frequency of the cosine input (10 Hz, 1 kHz, 100 kHz). In particular, the circuit is exactly the same in all three cases. From your calculations, we can see that the 10 Hz cosine passes through the circuit essentially unaltered. On the other hand, the 100 kHz cosine essentially does not pass through the circuit. From this, we conclude that the circuit is a "low pass" filter. That is, low frequency sinusoids pass through the circuit, while high frequency sinusoids are "filtered out." We will verify your results for the f = 1 kHz case using PSpice. Start a new project and draw the circuit of Figure 5. As in previous labs, use the part VSIN to generate the input voltage v¿(t). This part generates sin (2πft) by default. We can get cos (2лft) by setting the parameter TD = 1/1/ For the example here with f 4f = 1 kHz, we need TD = -1 4000 = −0.25 ms. To set this value, click carefully on the VSIN part (not the labels or values). The property editor spreadsheet opens. Scroll left or right until you see the column labeled TD. Enter –0.25 m in the cell below TD. To understand this choice for TD, see the appendix. Create a new simulation profile. Set the Analysis Type to Time Domain (Transient), and enter the following parameters: Run to time: 6.5 ms Start saving data after: 5 ms Maximum step size: 1 us (don't forget that u means “micro” in PSpice) The parameters above will collect 1.5 ms of data starting at time t = 5 ms. We wait until 5 ms have elapsed before collecting data so that the circuit is in steady state (transient response has died away). VOFF = 0 VAMPL = 1 FREQ=1000 AC = R1 ww 15.7k V1 C1 10n Figure 5. PSpice RC circuit. Place voltage markers as shown in the figure to measure the input voltage and output (capacitor) voltage. Run the simulation. The resulting figure should show two sinusoids. Verify that they appear as expected. Checking the amplitudes is easily done by inspection. The phase of the output voltage is a little trickier. We can obtain it as follows: First note that the input voltage crosses through 0 V (with negative slope) at 5.25 ms. The output voltage passes through 0 V (with negative slope) a short time later. You can determine this time fairly accurately using the PSpice cursor. Click Trace->Cursor->Display Now, in the lower left corner of the graph (the black part of the screen) is a legend which shows symbols for the two voltage curves (traces). Click carefully on the legend symbol (not the label next to it) for the output voltage curve. Now, click anywhere on the graph to initially place the PSpice cursor. Then, drag the cursor left/right with the mouse (or use the left/right cursor keys on your keyboard) to move the PSpice cursor to the place where the output voltage is closest to 0 V. Hint: Watch the values in the cursor window in the lower right corner of your screen. Once you have the cursor in the correct place, Click Plot->Label->Mark This will label the (x, y) coordinates of the PSpice cursor on the screen. As an example, Figure 6 below shows what this looks like for the first zero crossing of the input voltage. Your task is to mark the first zero crossing of the output voltage. b) print your graph showing the appropriate mark. Temper at ure: 27.0 C:\Users\ mwm Desktop\ 2201 220 I abs\ ab 5\ ps pi ce\ Freq_Response\fre Steady St at e active) Profile: "SCHEMATI C1- Steady St at e" Dat e/ Ti me run: 08/26/12 09: 59: 40 Г (A) 1. OV 0. 5V- ov- -0. 5V- 785m - 1. Ov 5. Oms 5. 2ms 5. 4ms V(V1: +) V( C1: 2) A1: (5. 2506m - 3. 8785m) Date: August 26, 2012 A2: (5. 0000m 1. 0000) 5. 6ms 5. 8ms Ti me 6. Oms 6. 2ms 6. 4mb 6. 6ms DI FF( A) : (250. 617u, - 1. 0039) Page 1 Ti me: 10: 02: 41 Figure 6. Voltage marking example. Now, back to calculation of the output voltage phase. As mentioned above, and as shown in Figure 6, the input voltage crosses through 0 V at 5.25 ms. Your graph shows the time at which the output voltage crosses through 0 V a short time later. The difference between these two times is the time delay, At. You can find the phase delay of the output voltage, relative to the input voltage, using unit analysis, as 40 (degrees) = At (seconds) × f cycles \second/ × 360 degrees cycle c) Calculate 40. Verify that your answer agrees with your calculations from part a). Prelab Part 3 We discovered above that changing the frequency of the input cosine changes both the magnitude and phase of the output cosine. That is, the magnitude and phase of the output cosine are both functions of frequency, say A(f) and 0 (f), respectively. The function A(f) is called the magnitude response of the circuit, while the function 0 (f) is called the phase response of the circuit. We now consider making plots of these two functions. From the resulting graphs, we can easily see how the magnitude and phase of the output cosine will behave as a function of the input cosine frequency. We could create these graphs by computing/nLab report 5 (rubric) Lab part 1 Pulse response circuit: (5 points) Write the equation for V(t) for t≥0. Write the value of V(t) when t = 0, t=5. Write the equation for V(t) for t≥ 10ms and value of V(t) when t = 10ms Lab part 2 Low pass filter: (5 points) Error analysis Vpeak-peak of V.(t) and phase difference ASee Answer
Q20: ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer Michael W. Marcellin Please follow all rules, procedures and report requirements as described at the beginning of the document entitled ECE 220 Laboratory 1. Always wear your safety glasses when performing your lab experiments. Prelab Part 1 In Lab 2, we built a simple volt meter using a d'Arsonval panel meter. We found that the main problem with this simple meter is that its Thevenin resistance is rather small. Because of this, it tends to load the circuit being measured, changing the value of the voltage to be measured. Here, we consider an improved volt meter that uses a 1 mA d'Arsonval panel meter and an op amp as shown in Figure 1. In this figure, assume power rails of +7 V, and −2 V. a) Calculate the value of R required so that id = 1 mA when v₁ = 5 V. b) For the value of R calculated above, write an expression for iɖ as a function of vi. Observe that your equation in b) results in a linearly increasing needle deflection as a function of v¿, with full (100%) deflection at 5 V. Specifically, the current through the panel meter is of the form id = ẞv₁. That is, the op amp and resistor form a voltage-controlled current source with the panel meter as its load. An important feature of this circuit is that neither the value that you calculated for R, nor your equation for ia depend on the internal resistance of the panel meter. Vie Figure 1. Improved volt meter. In Lab 2, we used your simple meter to measure the voltage at terminals a and b in Figure 2 below. We discovered that your meter performed poorly when RT was not small. Specifically, we saw a large %error for the case of Rh = 4.7 k§. This is because the input (Thevenin) resistance of your meter was not very large compared to 4.7 kQ. Recall that an ideal volt meter has infinite input resistance. The input resistance looking into the input of the improved volt meter of Figure 1 is very large. In class, we would model it as infinity. In reality, it is "only" many Meg-Ohms. This results in the %error of the improved meter being negligible for values of Rh up to at least 1 MQ. We will now verify this via a PSpice simulation. RTh w VTh b a Figure 2. Thevenin equivalent circuit. Start a new project in PSpice and draw the circuit shown below in Figure 3. This figure represents the use of the improved meter of Figure 1 attempting to measure Vɑð in Figure 2. The 155 resistor is used to model the panel meter, although this resistance value is unimportant as noted above. As in Prelab 3, use uA741 for the op amp. We have not used the Vcc labeling trick this time, and have just allowed wires to cross. Note carefully that PSpice includes a red dot (node) where wires connect. There is no such connection where the negative power supply wire crosses the feedback path. Note also, that this time we have included two parameters (variables). Each of them is created using the new property button in the property editor spreadsheet for the part PARAM, as before. You do not need two copies of PARAM. You will just create two different properties (columns) within the same instance of PARAM. Finally, note that the (default) values of the two parameters should be chosen as Vrh = 5 V and RTh 1 MQ. Remember that in PSpice, we use "meg" in place of "M." = {VTh} PARAMETERS: RTH = 1 meg VTH=5 R4 U17 www {RTh} 3 V+ 6 OUT V2 2 4 OSTO UA741 V- R2 www 155 R7 Put your calculated value of R here No connection here www www R6 2k Figure 3. PSpice schematic. Perform a linear sweep of RÃ from 1 kÔ to 1 M in increments of 1 k. Note that và will R5 7k V3 9Vdc (automatically) stay at its default value of 5 V throughout this sweep. Use a current marker, as shown in Figure 3, to measure the current through the panel meter. The resulting graph will show this current, iɖ, as a function of Rh. Ideally, it should be constant at 1 mA, corresponding to 100% needle deflection, since the voltage that the meter is trying to measure is 5 V. In reality, ia will decrease very slightly as Rä increases due to the loading effect. c) What value of Rh (among those tested) yields the maximum error between id and its ideal value of 1 mA? d) For this value of Räh, calculate the %error in iɖ· e) print your graph. Now edit the simulation profile and redo the sweep. This time we will sweep và from 0 to 5 V in increments of 0.1 V. The value of RTh will (automatically) stay at its default value of 1 M throughout the sweep. You may have to add the current marker again after you edit the simulation profile. Ideally, the graph of the current through the panel meter, id, should rise linearly from 0 to 1 mA, corresponding to a linear needle deflection from 0 to 100%. Your graph should (essentially) show this desired behavior. f) print your graph. Prelab Part 2 In class, we discussed an op amp comparator circuit as shown below in Figure 4. For this circuit, whenever V¡ > Vref, V goes to the positive power rail. Else, v goes to the negative power rail. Throughout this part, assume that the power rails are +5 V. Vi νο Vref Figure 4. Comparator circuit. Now consider the circuit of Figure 5. a) Which LED will be turned on when v₂ = 1 V? Which LED will be turned on when vi = -1 V? Vi 200 Ω. 200 Ω LED 1 LED 2 Figure 5. Comparator with LEDS. Now consider the circuit of Figure 6. b) Write an equation for v₁ as a function of the pot setting F. Assume F = 0 corresponds to the slider being all the way up. 5 V+ 01 vi(t) 1 ΚΩ + n(t) 5 VC + Figure 6. Input signal. = To make things more interesting, we add some “noise” to v₁. The resulting “noisy” signal is v¡(t) = v₁ + n(t). Assume that the noise n(t) is a square wave of amplitude vp = 0.1 V (Vpp 0.2 V) and frequency f = 2 Hz. Figure 7 shows a graph of vi(t) for a pot setting F = 0.4. Make sure that you understand this figure. Changing the pot setting F will raise or lower the level of the signal in Figure 7. As another example, when F 0.5, the square wave will be oscillating above and below 0 V, rather than above and below 1 V as shown in Figure 7. = 1.0 V ^vi(t) $0.2 V 0.5 1.0 2.0 (seconds) Figure 7. "Noisy" signal. Consider now connecting v₂ (t) in Figure 6 as the input to the circuit of Figure 5. Like the improved volt meter, the input resistance of the comparator is very high. Thus, we do not need to worry about the loading effect. c) What do you expect the LEDs to do for a pot setting of F = 0.4? How about F = about F = 0.6? 0.5? How In class, we also talked about the Schmitt trigger (comparator with hysteresis) which reduces "chattering" due to noise. A Schmitt trigger circuit is shown below in Figure 8. Again, assume power rails of ±5 V. d) What is the threshold T for the Schmitt trigger as shown? Note that this threshold is larger than Vpp of the noise in the example above. Thus, any chattering in the example should be eliminated by replacing the comparator with the Schmitt trigger. We will verify this in the lab. Vi 20 ΚΩ w 300 ΚΩ w νο Figure 8. Schmitt trigger. Prelab Part 3 In this part, we use an RC circuit together with a comparator to build a simple timer. Figure 9 below shows an RC circuit with a step input of 3 volts at time t = 0. Assume that the initial capacitor voltage is 0 V. In Chapter 7, we will learn the theory for RC circuits. For now, just use the fact that vc(t) = 33e-t/RC V. a) Let C220 µF and calculate the value of R required so that the capacitor voltage passes through 2.5 V at time t 8 seconds. That is, vc (8) = 2.5 V. = 3 V t=0 R + C. VC Figure 9. RC step response. The circuit of Figure 10 below shows the RC circuit from Figure 9 connected so that the/nLab report 4 (rubric) Lab part 2 Comparator circuit: (3.5 points) Draw the noisy signal V,(t) when the DC offset is 1 V, 0 V, and -1 V. What is the output V.(t) when the DC offset is 1 V, 0 V, and -1 V. Explain the behavior of LED 1 and LED 2 you observed in the lab for those different DC offset values. Schmitt trigger: (3.5 points) Explain how the Schmitt trigger helps eliminate chatter? Perhaps use a representative diagram showing how the threshold you computed helps eliminate chatter. Lab part 3 Timer circuit: (3 points) When does the capacitor charge? At what time did the LED turn on? How can you change the time the LED turns on?See Answer

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