Electronics - PHYS 2371/2
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1 This course is primarily self-contained, it does not rely much on previous courses. REMEMBER it is not what you come in with, it s what you leave with 1
2 Calendar of Topics Covered Physics PHYS 2371/2372, Electronics for Scientists Don Heiman, Northeastern University, Fall 2018 Also see Course Description and Syllabus This is a schedule of the topics covered, but it may be modified occasionally (8/16/2018). Week Topics/Notes Lecture Topics (Chs.) I Sept 5-7 II Sept III Sept IV Sept Introduction Electronic Basics Time-Dependent Voltages AC Circuits Basic Concepts (Ch-2) Ch-16, Digital Multimeters Basic Circuit Analysis (Ch-3) Some Simple Circuits (Ch-4) Resistor/ Capacitor (Ch-47/48) The Oscilloscope (Ch-17) AC and Elements of Circuits (Ch-7/8) Step Function Analysis (Ch-12) Power Supplies (Ch-38) Step Func Analysis (LRC) (Ch-12) AC Circuit Analysis (Ch-9) Resonance (Ch-10) Due Wednesday, Sept. 26 Week-III HW (Chs. 7,8,12) Lab-3 report Homework (Ch-Problem) 2-8/9, 3-5/6, 4-4/8, 4-13/14 7-all, /2 12-3/4/5/6 Lab Experiments (always look for latest version) Lab-1 Electronic Basics (multimeter, voltage sources) Lab-2 Electronic Basics Report Template Lab-3, Oscilloscope and Time-Dependent Voltage (function generator, oscilloscope, RC filtering) Lab-4, AC Circuits (RC, RL, and RLC circuits) TODAY Quick Review-Basics Alternating Current, Ch-7 - RMS - problem 7-1 Elements of AC Circuits, Ch-8 - resistor, capacitor, inductors(l) - impedance (Z), reactance (X) (video break) Step Function Analysis, Ch-12 - RC circuit, LR circuit (LRC circuit next week) Power Supply, Ch-38 - diode rectifiers, filtering Lab-3, Time-varying Voltages - oscilloscope, RC circuit, - power supply filtering 2
3 Pope is happier with his smaller cell phone 3
4 Gustav Robert Kirchhoff ( ) Review Basics Kirchhoff s Basic Circuit Laws KCL Kirchhoff s Current Law Σ I = 0 at node conservation of charge KVL Kirchhoff s Voltage Law Σ V = 0 around loop conservative field Adding components R series = Σ R i, 1/R parallel = Σ 1/R i C parallel = Σ C i, 1/C series = Σ 1/C i Voltage Divider R 2 V 2=Vin R 1 +R 2 V V +V = R R +R He contributed to the fundamental understanding of electrical circuits. Kirchhoff formulated his circuit laws, which are now ubiquitous in electrical engineering, in 1845, while still a student. He completed this study as a seminar exercise; it later became his doctoral dissertation. In 1857 he calculated that an electric signal in a resistanceless wire travels along the wire at the speed of light. He proposed his law of thermal radiation in 1859, and coined the term "black body" radiation in R1 V in V 2 R2 0 4
5 Volltage Electronics - PHYS 2371/2 AC Alternating Current (Ch-7) Vp Sine wave V(t) = V p sin (ωt+φ) ω frequency, units---radians/s φ phase, units---radians 0 - Vp V PP Period T time f = ω / 2π T = 1 / f = 2π / ω V pp = 2 V p frequency, units--- Hz or cycles/s period, units---s peak-to-peak voltage How do you measure the power for AC? For DC, Power = I DC x V DC both I and V are constant With AC, I(t) and V(t) 5
6 RMS root mean square Averaging for AC signals (voltage or current) <V p > = 0 for sine wave 1 T 2 V RMS = V (t) dt T 0 RMS characterizes the average, independent of the waveform Power P = V RMS 2 / R For sine wave V RMS = V p / 2 = V p For square wave V RMS = V p For pulses V RMS < V p 6
7 Volltage Electronics - PHYS 2371/2 Prob. 7-1 wall plug f = 60 Hz V RMS = V Vp Period T = 16.7 ms 0 T = 1 / 60 = 16.7 ms V PP - Vp V p = 2 V RMS 170 V time 7
8 Basic Elements of AC Circuits R resistor carbon, carbon film, metal film ohm (Ω) C capacitor metal + ceramic or plastic film farad (F) L inductor coil of insulated wire henry (H) 8
9 Carbon composition Electronics - PHYS 2371/2 Resistors various types Carbon/metal film Wire wound 9
10 Capacitors various types Ceramic Electrolytic Variable 10
11 Inductors various types Simple Iron Core or Ferrite Toroidal 11
12 Inductor An inductor, also called a coil or reactor, is a passive two-terminal electrical component. It resists changes in current passing through it. When a current flows through it, energy is stored temporarily in a magnetic field in the coil. When the current flowing through an inductor changes, the time-varying magnetic field induces a voltage in the conductor, according to Faraday s law of electromagnetic induction, which opposes the change in the current that created it. (wikipedia) 12
13 Relation between Voltage and Current Time dependence of V(t) and I(t) I IP sin t Examples of Phase Shift V(t) and I(t) may not be in phase 13
14 What are I-V relationships for any time-dependent voltages R V IR I V / R ( volt / amp ) 1 C V dv C Idt I C dt ( farad coulomb / volt ) di 1 L V L I L Vdt ( henry volt s dt amp ) Impedance Z = V/I Z is a complex number containing the Resistance and the V-I phase difference (introduce i= -1) R C L I(t) = V(t)/R C dv(t)/dt -1/L V(t)dt V(t) = I(t) R 1/C I(t)dt L di(t)/dt Z = R -i/ωc iωl X = Z = R 1/ωC ωl φ 0 V lags I by 90 V leads I by 90 14
15 R, C, L - Voltages/Currents R C L I(t) = V(t)/R C dv(t)/dt -1/L V(t)dt V(t) = I(t) R 1/C I(t)dt L di(t)/dt Z = R -i/ωc iωl X = R 1/ωC ωl Φ = 0 V lags I by 90 Φ = π/2 V leads I by 90 Φ = + π/2 R, 1/ωC, ωl act like resistances (reactance) C and L only change the flow of current C and L do not dissipate energy, they store energy Φ = phase angle that the voltage LEADS the current in the circuit I ~ sin(ωt) V X ~ sin(ωt + φ) ELI the ICE man Inductor-L ELI voltage leads current Capacitor-C ICE current leads voltage 15
16 Example RC Circuit Impedance Series components (R,C or L) Z T = Z i = Z 1 +Z 2 Z = R -i/ωc iωl Reactance X = Z the magnitude of Z 16
17 Power Dissipated Power is dissipated (heat) in R only, C and L only store energy Power dissipated (heat) in R P = V 0 I total cos (θ) Power factor cos (θ) = R/X cos (θ) = 0 cos (θ) = 1 purely capacitive purely resistive In example cos(θ)=1.0/1.9 =
18 Combining Impedances Series components Z T = Z i = Z 1 +Z 2 Parallel components 1/Z T = 1/Z i = 1/Z 1 +1/Z 2 Z R = R ~ R Z C = -i /ωc ~ 1/C Series components R T = R i = R 1 +R 2 1/C T = 1/C i = 1/C 1 +1/C 2 Parallel components 1/R T = 1/R i = 1/R 1 +1/R 2 C T = C i = C 1 +C 2 18
19 Tesla Video Why is AC better than DC for power applications? AC allows for lower transmission losses, by increasing voltage and reducing current. Using a few assumptions, the power loss in transmission through power lines with resistance R is P = I 2 R. Thus, the power loss is proportional to ~ I 2. You can keep the delivered power (P=IV) constant by simply increasing the voltage by the factor, and reducing the current by the same factor of. So increasing the voltage by a factor of 2 and decreasing the current by a factor of 2, keeps the delivered power constant, but reduces the power loss in the power lines by a factor of 4. Auto Battery Automobiles increased the battery voltage from 6 VDC to 12 VDC in ~1955, in order to increase the current. POWER GRID GigaW Power plant Large substation Small substation street house Voltage kvac 26/69 kvac 13,800 VAC 4,000 VAC 120/240 VAC Power grids use voltages up to nearly 10 6 volts. This effect is only useful with AC, as it is very easy to step up and down the voltages with passive electrical transformers. 19
20 Step function analysis of RC circuit Electronics - PHYS 2371/2 Step Function Analysis (Ch. 12) 20
21 Step function analysis of LR circuit Electronics - PHYS 2371/2 21
22 Power Supply (Ch. 38) Want to: step up/down voltage; convert AC to DC C R 22
23 USB Power Supply What s inside? ipad charger teardown: inside Apple's charger and a risky phony Disassembly of the Apple USB Power Adapter 23
24 Lab Experiment Week-III The Oscilloscope and Time-dependent Voltages 24
25 General Circuit Instructions: (apply to this lab and all subsequent labs): (1) Draw the circuit diagram. This is important for any circuit you build, showing all instrument connections, as well as ground connections and other important information. (2) Place the elements physically on the breadboard to mimic the circuit diagram. (3) Make sure that all of the negative (ground/black) instrument connections are connected to the same point on the circuit whenever possible. Since the negative connections are usually connected together thru the power cables, they can short out a circuit component. Also, always set the scope display to enhance the visibility of the important data (for example, peak-to-peak voltages, phase shifts, cycles, etc.). 25
26 Lab-3, Oscilloscopes and Time-Dependent Voltages Physics PHYS 2371/2372, Electronics for Scientists Don Heiman, Northeastern University This lab allows you to explore the behavior of the circuit elements, resistors/capacitors/inductors, to timevarying voltages. The following lab (Lab-3) examines more combinations of circuit elements to AC signals. You will need: Oscilloscope, Function Generator, BNC-to-Banana adapters I. The Oscilloscope In this exercise you will become familiar with the digital scope. Using a 5 V peak sine wave, view the waveform on the scope. 1. View the waveform for a frequency of 60 Hz. 2. Using the Measure function of the scope, find the peak-to-peak and RMS voltages of the waveform, the frequency and the period. Compare these to expected values. 3. Without changing the amplitude of the function generator, repeat for a frequency of 3 MHz, and discuss any differences. Videos on Oscilloscopes
27 II. Time Response of an RC circuit Here you will explore the response of an RC (resistor/capacitor) circuit to a voltage pulse. Construct a circuit consisting of a C=0.1 μf capacitor and an R=2 kω resistor in series, and connect to the function generator. Use the TTL output from the function generator to obtain a square wave with voltage alternating between +5 V and 0 V. Note that this is equivalent to switching a DC voltage on and off. View the voltage across function generator on chnl-1 of the scope and the voltage across the capacitor (V C ) on chnl-2. Make sure you consider that the scope has a single ground (outer contact on the BNC connector), so you don t short out one circuit element. 1. First, compute the time constant C =RC and frequency f o =1/(2π τ C ). View the voltage waveforms, V C (t), for three frequencies f determined by the relations, f << f o, f ~ f o, and f >> f o. Make sure V in is always +5 V to 0 V. Adjust the scope settings to display all the important quantities. Capture the scope waveform in Excel. Make a plot of all 3 waveforms. Print out and discuss the results. 2. At one frequency, where f < f o, determine the circuit time constant, τ C, from the time it takes for the capacitor voltage, V C (t), to drop to 1/e of any starting value. Compare the measured time constant to RC, including the uncertainties in R and C. Videos on Function Generators
28 IV. Power Supply Filtering An RC circuit is useful for filtering the AC waveform into a DC waveform in a power supply. The circuit diagram shows a simple circuit to change the input sine wave voltage from AC to DC. The diode selects only the positive half of the sine wave which appears across the load resistor. Make this circuit on the protoboard with a standard diode and R=1 MΩ resistor. Use the Output connection of the function generator set to f=60 Hz sine wave to supply the input to the diode. 1. First, using the two scope channels, view and copy (to Excel) the sine wave waveforms across the function generator and the resistor. 2. Add a C=0.01 μf capacitor across the resistor. View and copy the scope waveform across the capacitor and discuss. 3. Replace the capacitor with a large C=10-22 μf capacitor. 4. Plot all 4 waveforms (function generator, no capacitor, small capacitor and large capacitor) on the same graph. 5. Compare the mean voltage and waveform for the two capacitors in III-2 and III-3. Discuss. Surf Youtube for tutorials 28
29 Drawing Circuits (free) Circuit Diagram - (download/save png file, drag or copy/paste file into document) CircuitLab (can only copy whole screen page) Digikey XCircuit SmartDraw Teach logic gates and build circuits - (useful for digital circuits) 29
30 Lab Reports - Important Things to Consider Purpose of reports communication, documentation (you may also learn something while writing) Printing 4-page MAXIMUM. Use 11 or 12 pt font (for Arial use 11 pt). Use supplied Template, or equivalent. Abstract 4-7 sentences only; keep it simple Say specifically: (1) what you did and (2) what you found. List important results (values). Example We investigated the current-voltage relationships of a resistor, diode and light bulb. The resistor showed linear ohmic behavior, but the diode and light bulb were nonohmic. Using the rule for a simple voltage divider, we explored series resistors and series capacitors. We measured the input impedance of a DVM to be 10.2 MΩ; while the internal impedance of an unregulated power supply was found to be 23 Ω. Procedures you can shorten the procedures, be brief Bullets use them sparingly Circuit Diagrams Include all circuit diagrams. They should be small, ~1-2 wide. You can draw them using: Circuit Diagram - (download/save file as png then drag or copy/paste into document Equations List all important formulas - Generally, numbered equations should go on a separate line. When computing an answer, give the formula and the input values. Do not show all the math steps. Final values should go on a separate line or in a table of values. Plots Give a Title and Figure number: Example: Figure 3: I-V Plot for Standard Diode Label axes: Example I (ma) and V (V). Connect data points with a curve. Small figures Figures should not be larger than approximately 3-4 wide Place figures along with the text wrap the text around the figure. ROI plot only the important region of interest. Data Tables When you have a plot, don t include the data table (or put the table into an Appendix at the end). Shorten-Shorten-Shorten the Text Let the figures and math tell the story. You don t need to say. the voltage across V 2 was found to be volts. Simply write.v 2 = V. (get used to using subscripts and superscripts). 30
31 Ende 31
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