Electronics - PHYS 2371/2

Transcription

1 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 Power Supply, Ch-38 - diode rectifiers, filtering HWs due on Fridays HW (Chs. 7,8,12) due this Friday, Sept. 23 Lab-3 report due Wednesday, Sept. 28 Lab-3, Time-varying Voltages - oscilloscope, RC circuit, - power supply filtering

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3 Review Basics Kirchhoff s Basic Circuit Laws KCL Kirchhoff s Current Law Σ I = 0 at node KVL Kirchhoff s Voltage Law Σ V = 0 around loop 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 V 2-out = V in R 2 /(R 1 +R 2 ) Gustav Robert Kirchhoff ( ) - Born in Königsberg, East Prussia (now Kaliningrad, Russia) graduated from the Albertus University of Königsberg, moved to Berlin, then received a professorship at Breslau (now Wroclaw, Poland). 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 gave a proof in He also investigated spectroscopy and the emission of blackbody radiation by heated objects. He coined the term "black body" radiation in 1862.

4 Volltage Electronics - PHYS 2371/2 AC - Alternating Current (Ch-7) Vp Sinewave V ( t) V sin ( t ) frequency, units rad/s phase, units radians P 0 V PP Period T - Vp time f 2 T= 1 f V PP 2V P 2 frequency, (Hz or cycles/s) period 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 RMS root mean square Averaging for AC signals (voltage or current)

6 Volltage Electronics - PHYS 2371/2 Vp Period T = 16.7 ms 0 V PP - Vp time

7 Basic Elements of AC Circuits R-Ohm (Ω) C-Farad (F) L-Henry (H)

8 Carbon composition Resistors various types Carbon/metal film Wire wound

9 Capacitors various types Ceramic Electrolytic Variable

10 Inductors various types Simple Toroidal Iron Core or Ferrite

11 Inductor An inductor is a passive two-terminal electrical component which resists changes in electric 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 current that created it. (wikipedia)

12 Relation between Voltage and Current Time dependence of V(t) and I(t) Examples of Phase Shift V(t) and I(t) may not be in phase

13 What are I-V relationships for any time-dependent voltages 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 Series components Z T = Z i = Z 1 +Z 2 Reactance X = Z the magnitude of Z

15 Power Dissipated Power is dissipated (heat) in R only, C and L only store energy

16 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

17 Video From the Tesla video last week, what do you think about: (1) transmitting power through the air; (2) giving it for free (how to charge people)?

18 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 2 2 = 4. Auto Battery Automobiles increased the battery voltage from 6 VDC to 12 VDC in ~1955, in order to decrease 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 Step function analysis of RC circuit Electronics - PHYS 2371/2 Step Function Analysis (Ch. 12)

20 Step function analysis of LR circuit

21 Power Supply (Ch. 38) Want to convert AC to DC C R Surf Youtube for rectifier tutorials

22 USB Power Supply What s inside?

23 Lab Experiment 2 The Oscilloscope And Time-dependent Voltages Prepare for Prelab Quiz on Friday

24 General instructions: (apply to this lab and all subsequent labs): 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. Place the elements physically on the breadboard to mimic the circuit diagram. 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 in the instrument, 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 Lab-3, Oscilloscopes and Time-Dependent Voltages Physics PHYS 2371/2372, Electronics for Scientists Don Heiman, Northeastern University, 09/19/2016 This lab allows you to explore the behavior of the circuit elements, resistors/capacitors/inductors, to time-varying 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

26 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. 3. Next, for f ~ f o view the voltage on the resistor with the scope, V R (t), by exchanging the capacitor and resistor. Explain what you observe. Why is the voltage positive and negative? Videos on Function Generators

27 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 Drawing Circuits (free) Digikey CircuitLab (Export as png file) XCircuit SmartDraw Teach logic gates and build circuits -

29 Ende