Fundamentals of Electrical Engineering I © Don Johnson

Total Page:16

File Type:pdf, Size:1020Kb

Fundamentals of Electrical Engineering I © Don Johnson Fundamentals of Electrical Engineering I © Don Johnson This work is licensed under a Creative Commons-ShareAlike 4.0 International License Original source: The Orange Grove http://florida.theorangegrove.org/og/items/c7d013ec-2b4d-6971-65f9-b1a6af2d9092/ 1/ Contents Chapter 1 Introduction ..................................................................................................1 1.1 Themes ................................................................................................................................1 1.2 Signals Represent Information ........................................................................................2 1.2.1 Analog Signals..........................................................................................................3 1.2.2 Digital Signals...........................................................................................................4 1.3 Structure of Communication Systems .............................................................................5 1.4 The Fundamental Signal ...................................................................................................7 1.4.1 The Sinusoid ............................................................................................................7 Exercise 1.4.1 ............................................................................................................8 Exercise 1.4.2 ............................................................................................................8 1.4.2 Communicating Information with Signals............................................................8 1.5 Introduction Problems.......................................................................................................9 1.6 Solutions to Exercises in Chapter 1 ................................................................................10 Chapter 2 Signals and Systems ...................................................................................11 2.1 Complex Numbers ...........................................................................................................11 2.1.1 Definitions ..............................................................................................................11 Exercise 2.1.1 ..........................................................................................................13 Exercise 2.1.2 ..........................................................................................................13 2.1.2 Euler's Formula......................................................................................................13 2.1.3 Calculating with Complex Numbers....................................................................14 Exercise 2.1.3 .....................................................................................................15 Example 2.1 ............................................................................................................16 2.2 Elemental Signals..............................................................................................................16 2.2.1 Sinusoids ................................................................................................................16 2.2.2 Complex Exponentials ..........................................................................................17 2.2.3 Real Exponentials ..................................................................................................18 2.2.4 Unit Step.................................................................................................................18 2.2.5 Pulse........................................................................................................................20 2.2.6 Square Wave ..........................................................................................................20 2.2.7 Signal Decomposition ...........................................................................................21 Example 2.2 ............................................................................................................21 Exercise 2.3.1 ..........................................................................................................21 2.3 Discrete-Time Signals ......................................................................................................21 2.3.1 Real-and Complex-valued Signals .......................................................................22 2.3.2 Complex Exponentials ..........................................................................................22 2.3.3 Sinusoids ................................................................................................................23 2.3.4 Unit Sample............................................................................................................23 2.3.5 Symbolic-valued Signals .......................................................................................24 2.3.6 Introduction to Systems .......................................................................................24 2.3.6.1 Cascade Interconnection...........................................................................25 2.3.7 Parallel Interconnection .......................................................................................25 2.3.8 Feedback Interconnection....................................................................................26 2.4 Simple Systems ................................................................................................................27 2.4.1 Sources ...................................................................................................................27 2.4.2 Amplifiers ...............................................................................................................27 2.4.3 Delay .......................................................................................................................28 2.4.4 Time Reversal.........................................................................................................28 Exercise 2.6.1 ..........................................................................................................28 2.4.5 Derivative Systems and Integrators ...................................................................29 2.4.6 Linear Systems.......................................................................................................29 2.4.7 Time-Invariant Systems ........................................................................................30 2.5 Signals and Systems Problems .......................................................................................32 Problem 2.1: Complex Number Arithmetic ................................................................32 Problem 2.2: Discovering Roots ...................................................................................32 Problem 2.3: Cool Exponentials ...................................................................................32 Problem 2.4: Complex-valued Signals .........................................................................33 Problem 2.5: ...................................................................................................................34 Problem 2.6: ...................................................................................................................35 Problem 2.7: Linear, Time-Invariant Systems .............................................................36 Problem 2.8: Linear Systems ........................................................................................37 Problem 2.9: Communication Channel .......................................................................37 Problem 2.10: Analog Computers ................................................................................38 2.6 Solutions to Exercises in Chapter 2 ................................................................................38 Chapter 3 Analog Signal Processing ...........................................................................40 3.1 Voltage, Current, and Generic Circuit Elements ...........................................................40 Exercise 3.1.1 ..................................................................................................................41 3.2 Ideal Circuit Elements .....................................................................................................41 3.2.1 Resistor...................................................................................................................42 3.2.2 Capacitor ................................................................................................................42 3.2.3 Inductor ..................................................................................................................43 3.2.4 Sources ...................................................................................................................44 3.3 Ideal and Real-World Circuit Elements ..........................................................................44 3.4 Electric Circuits and Interconnection Laws....................................................................45 3.4.1 Kirchhof's Current Law .........................................................................................46 Exercise 3.4.1 ..........................................................................................................47 3.4.2 Kirchhof's Voltage Law (KVL) ................................................................................47
Recommended publications
  • Glossary Physics (I-Introduction)
    1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay.
    [Show full text]
  • Chapter 2 Basic Concepts in RF Design
    Chapter 2 Basic Concepts in RF Design 1 Sections to be covered • 2.1 General Considerations • 2.2 Effects of Nonlinearity • 2.3 Noise • 2.4 Sensitivity and Dynamic Range • 2.5 Passive Impedance Transformation 2 Chapter Outline Nonlinearity Noise Impedance Harmonic Distortion Transformation Compression Noise Spectrum Intermodulation Device Noise Series-Parallel Noise in Circuits Conversion Matching Networks 3 The Big Picture: Generic RF Transceiver Overall transceiver Signals are upconverted/downconverted at TX/RX, by an oscillator controlled by a Frequency Synthesizer. 4 General Considerations: Units in RF Design Voltage gain: rms value Power gain: These two quantities are equal (in dB) only if the input and output impedance are equal. Example: an amplifier having an input resistance of R0 (e.g., 50 Ω) and driving a load resistance of R0 : 5 where Vout and Vin are rms value. General Considerations: Units in RF Design “dBm” The absolute signal levels are often expressed in dBm (not in watts or volts); Used for power quantities, the unit dBm refers to “dB’s above 1mW”. To express the signal power, Psig, in dBm, we write 6 Example of Units in RF An amplifier senses a sinusoidal signal and delivers a power of 0 dBm to a load resistance of 50 Ω. Determine the peak-to-peak voltage swing across the load. Solution: a sinusoid signal having a peak-to-peak amplitude of Vpp an rms value of Vpp/(2√2), 0dBm is equivalent to 1mW, where RL= 50 Ω thus, 7 Example of Units in RF A GSM receiver senses a narrowband (modulated) signal having a level of -100 dBm.
    [Show full text]
  • The Basics of Power the Background of Some of the Electronics
    We Often talk abOut systeMs from a “in front of the (working) screen” or a Rudi van Drunen “software” perspective. Behind all this there is a complex hardware architecture that makes things work. This is your machine: the machine room, the network, and all. Everything has to do with electronics and electrical signals. In this article I will discuss the basics of power the background of some of the electronics, Rudi van Drunen is a senior UNIX systems consul- introducing the basics of power and how tant with Competa IT B.V. in the Netherlands. He to work with it, so that you will be able to also has his own consulting company, Xlexit Tech- nology, doing low-level hardware-oriented jobs. understand the issues and calculations that [email protected] are the basis of delivering the electrical power that makes your system work. There are some basic things that drive the electrons through your machine. I will be explaining Ohm’s law, the power law, and some aspects that will show you how to lay out your power grid. power Law Any piece of equipment connected to a power source will cause a current to flow. The current will then have the device perform its actions (and produce heat). To calculate the current that will be flowing through the machine (or light bulb) we divide the power rating (in watts) by the voltage (in volts) to which the system is connected. An ex- ample here is if you take a 100-watt light bulb and connect this light bulb to the wall power voltage of 115 volts, the resulting current will be 100/115 = 0.87 amperes.
    [Show full text]
  • Comparing the Emission Spectra of U and Th Hollow Cathode Lamps and a New U Line-List
    Astronomy & Astrophysics manuscript no. HCL_U_Th_Ull_S2018 c ESO 2018 October 1, 2018 Comparing the emission spectra of U and Th hollow cathode lamps and a new U line-list L. F. Sarmiento1,⋆, A. Reiners1, P. Huke1, F. F. Bauer1, E. W. Guenter2,3, U. Seemann1, and U. Wolter4 1 Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany 2 Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg, Germany 3 Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain 4 Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany Received , 22 February 2018; accepted , 5 June 2018 ABSTRACT Context. Thorium hollow cathode lamps (HCLs) are used as frequency calibrators for many high resolution astronomical spectro- graphs, some of which aim for Doppler precision at the 1 m/s level. Aims. We aim to determine the most suitable combination of elements (Th or U, Ar or Ne) for wavelength calibration of astronomical spectrographs, to characterize differences between similar HCLs, and to provide a new U line-list. Methods. We record high resolution spectra of different HCLs using a Fourier transform spectrograph: (i) U-Ne, U-Ar, Th-Ne, and Th-Ar lamps in the spectral range from 500 to 1000 nm and U-Ne and U-Ar from 1000 to 1700 nm; (ii) we systematically compare the number of emission lines and the line intensity ratio for a set of 12 U-Ne HCLs; and (iii) we record a master spectrum of U-Ne to create a new U line-list. Results. Uranium lamps show more lines suitable for calibration than Th lamps from 500 to 1000 nm.
    [Show full text]
  • Printer Tech Tips—Cause & Effects of Static Electricity in Paper
    Printer Tech Tips Cause & Effects of Static Electricity in Paper Problem The paper has developed a static electrical charge causing an abnormal sheet-to- sheet or sheet-to-material attraction which is difficult to separate. This condition may result in feeder trip-offs, print voids from surface contamination, ink offset, Sappi Printer Technical Service or poor sheet jog in the delivery. 877 SappiHelp (727 7443) Description Static electricity is defined as a non-moving, non-flowing electrical charge or in simple terms, electricity at rest. Static electricity becomes visible and dynamic during the brief moment it sparks a discharge and for that instant it’s no longer at rest. Lightning is the result of static discharge as is the shock you receive just before contacting a grounded object during unusually dry weather. Matter is composed of atoms, which in turn are composed of protons, neutrons, and electrons. The number of protons and neutrons, which make up the atoms nucleus, determine the type of material. Electrons orbit the nucleus and balance the electrical charge of the protons. When both negative and positive are equal, the charge of the balanced atom is neutral. If electrons are removed or added to this configuration, the overall charge becomes either negative or positive resulting in an unbalanced atom. Materials with high conductivity, such as steel, are called conductors and maintain neutrality because their electrons can move freely from atom to atom to balance any applied charges. Therefore, conductors can dissipate static when properly grounded. Non-conductive materials, or insulators such as plastic and wood, have the opposite property as their electrons can not move freely to maintain balance.
    [Show full text]
  • Mössbauer Spectroscopy 9.1 Recoil Free Resonance Absorption
    Chapter 9, page 1 9 Mössbauer Spectroscopy 9.1 Recoil free resonance absorption Robert Wood published in 1905 an article "Resonance Radiation of Sodium Vapor" (see Literature) and reported that if a bulb containing pure sodium vapor was illuminated by light from a sodium flame, the vapor emitted a yellow light which spectroscopic analysis showed to be identical with the exciting light, in other words, the two D lines. Sodium is liquid above 98 °C, boiling point 883 °C, thus a remarkable vapor pressure exists, if sodium is heated by the Fig. 9.1: Wood's apparatus for the Bunsen burner above 200 °C. Wood used the name resonance radiation of the sodium "resonance radiation" for the effect of identical D lines. absorbed radiation and fluorescence radiation. Now we use the term "resonance absorption" instead. Since 1900 γ-rays were known as a highly energetic monochromatic radiation, but the anticipated γ-ray resonance fluorescence failed to occur. Werner Kuhn succeeded in publishing such an experiment that don't work and argued in 1929: "The (third) influence, reducing the absorption, arises from the emission process of the γ-rays. The emitting atom will suffer recoil due to the projection of the γ-ray. The wavelength of the radiation is therefore shifted to the red; the emission line is displaced relative to the absorption line.... It is thus possible that by a large γ-shift, the whole emission line is brought out of the absorption region”. (see Literature, Kuhn) Intensity In the case of γ-radiation the atoms suffer recoil, which is not significant for radiation in the visible range, were the recoil energy is small compared with the linewidth of the h δν1/2 radiation (times h), see Fig.
    [Show full text]
  • Electromagnetism What Is the Effect of the Number of Windings of Wire on the Strength of an Electromagnet?
    TEACHER’S GUIDE Electromagnetism What is the effect of the number of windings of wire on the strength of an electromagnet? GRADES 6–8 Physical Science INQUIRY-BASED Science Electromagnetism Physical Grade Level/ 6–8/Physical Science Content Lesson Summary In this lesson students learn how to make an electromagnet out of a battery, nail, and wire. The students explore and then explain how the number of turns of wire affects the strength of an electromagnet. Estimated Time 2, 45-minute class periods Materials D cell batteries, common nails (20D), speaker wire (18 gauge), compass, package of wire brad nails (1.0 mm x 12.7 mm or similar size), Investigation Plan, journal Secondary How Stuff Works: How Electromagnets Work Resources Jefferson Lab: What is an electromagnet? YouTube: Electromagnet - Explained YouTube: Electromagnets - How can electricity create a magnet? NGSS Connection MS-PS2-3 Ask questions about data to determine the factors that affect the strength of electric and magnetic forces. Learning Objectives • Students will frame a hypothesis to predict the strength of an electromagnet due to changes in the number of windings. • Students will collect and analyze data to determine how the number of windings affects the strength of an electromagnet. What is the effect of the number of windings of wire on the strength of an electromagnet? Electromagnetism is one of the four fundamental forces of the universe that we rely on in many ways throughout our day. Most home appliances contain electromagnets that power motors. Particle accelerators, like CERN’s Large Hadron Collider, use electromagnets to control the speed and direction of these speedy particles.
    [Show full text]
  • Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function
    Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function Shuming Wen ( [email protected] ) Faculty of Land and Resources Engineering, Kunming University of Science and Technology. Research Article Keywords: probability origin, wave-function collapse, uncertainty principle, quantum tunnelling, double-slit and single-slit experiments Posted Date: November 16th, 2020 DOI: https://doi.org/10.21203/rs.3.rs-95171/v2 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function Shuming Wen Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093 Abstract The theoretical calculation of quantum mechanics has been accurately verified by experiments, but Copenhagen interpretation with probability is still controversial. To find the source of the probability, we revised the definition of the energy quantum and reconstructed the wave function of the physical particle. Here, we found that the energy quantum ê is 6.62606896 ×10-34J instead of hν as proposed by Planck. Additionally, the value of the quality quantum ô is 7.372496 × 10-51 kg. This discontinuity of energy leads to a periodic non-uniform spatial distribution of the particles that transmit energy. A quantum objective system (QOS) consists of many physical particles whose wave function is the superposition of the wave functions of all physical particles. The probability of quantum mechanics originates from the distribution rate of the particles in the QOS per unit volume at time t and near position r. Based on the revision of the energy quantum assumption and the origin of the probability, we proposed new certainty and uncertainty relationships, explained the physical mechanism of wave-function collapse and the quantum tunnelling effect, derived the quantum theoretical expression of double-slit and single-slit experiments.
    [Show full text]
  • Notes for Lab 1 (Bipolar (Junction) Transistor Lab)
    ECE 327: Electronic Devices and Circuits Laboratory I Notes for Lab 1 (Bipolar (Junction) Transistor Lab) 1. Introduce bipolar junction transistors • “Transistor man” (from The Art of Electronics (2nd edition) by Horowitz and Hill) – Transistors are not “switches” – Base–emitter diode current sets collector–emitter resistance – Transistors are “dynamic resistors” (i.e., “transfer resistor”) – Act like closed switch in “saturation” mode – Act like open switch in “cutoff” mode – Act like current amplifier in “active” mode • Active-mode BJT model – Collector resistance is dynamically set so that collector current is β times base current – β is assumed to be very high (β ≈ 100–200 in this laboratory) – Under most conditions, base current is negligible, so collector and emitter current are equal – β ≈ hfe ≈ hFE – Good designs only depend on β being large – The active-mode model: ∗ Assumptions: · Must have vEC > 0.2 V (otherwise, in saturation) · Must have very low input impedance compared to βRE ∗ Consequences: · iB ≈ 0 · vE = vB ± 0.7 V · iC ≈ iE – Typically, use base and emitter voltages to find emitter current. Finish analysis by setting collector current equal to emitter current. • Symbols – Arrow represents base–emitter diode (i.e., emitter always has arrow) – npn transistor: Base–emitter diode is “not pointing in” – pnp transistor: Emitter–base diode “points in proudly” – See part pin-outs for easy wiring key • “Common” configurations: hold one terminal constant, vary a second, and use the third as output – common-collector ties collector
    [Show full text]
  • I. Common Base / Common Gate Amplifiers
    I. Common Base / Common Gate Amplifiers - Current Buffer A. Introduction • A current buffer takes the input current which may have a relatively small Norton resistance and replicates it at the output port, which has a high output resistance • Input signal is applied to the emitter, output is taken from the collector • Current gain is about unity • Input resistance is low • Output resistance is high. V+ V+ i SUP ISUP iOUT IOUT RL R is S IBIAS IBIAS V− V− (a) (b) B. Biasing = /α ≈ • IBIAS ISUP ISUP EECS 6.012 Spring 1998 Lecture 19 II. Small Signal Two Port Parameters A. Common Base Current Gain Ai • Small-signal circuit; apply test current and measure the short circuit output current ib iout + = β v r gmv oib r − o ve roc it • Analysis -- see Chapter 8, pp. 507-509. • Result: –β ---------------o ≅ Ai = β – 1 1 + o • Intuition: iout = ic = (- ie- ib ) = -it - ib and ib is small EECS 6.012 Spring 1998 Lecture 19 B. Common Base Input Resistance Ri • Apply test current, with load resistor RL present at the output + v r gmv r − o roc RL + vt i − t • See pages 509-510 and note that the transconductance generator dominates which yields 1 Ri = ------ gm µ • A typical transconductance is around 4 mS, with IC = 100 A • Typical input resistance is 250 Ω -- very small, as desired for a current amplifier • Ri can be designed arbitrarily small, at the price of current (power dissipation) EECS 6.012 Spring 1998 Lecture 19 C. Common-Base Output Resistance Ro • Apply test current with source resistance of input current source in place • Note roc as is in parallel with rest of circuit g v m ro + vt it r − oc − v r RS + • Analysis is on pp.
    [Show full text]
  • ECE 255, MOSFET Basic Configurations
    ECE 255, MOSFET Basic Configurations 8 March 2018 In this lecture, we will go back to Section 7.3, and the basic configurations of MOSFET amplifiers will be studied similar to that of BJT. Previously, it has been shown that with the transistor DC biased at the appropriate point (Q point or operating point), linear relations can be derived between the small voltage signal and current signal. We will continue this analysis with MOSFETs, starting with the common-source amplifier. 1 Common-Source (CS) Amplifier The common-source (CS) amplifier for MOSFET is the analogue of the common- emitter amplifier for BJT. Its popularity arises from its high gain, and that by cascading a number of them, larger amplification of the signal can be achieved. 1.1 Chararacteristic Parameters of the CS Amplifier Figure 1(a) shows the small-signal model for the common-source amplifier. Here, RD is considered part of the amplifier and is the resistance that one measures between the drain and the ground. The small-signal model can be replaced by its hybrid-π model as shown in Figure 1(b). Then the current induced in the output port is i = −gmvgs as indicated by the current source. Thus vo = −gmvgsRD (1.1) By inspection, one sees that Rin = 1; vi = vsig; vgs = vi (1.2) Thus the open-circuit voltage gain is vo Avo = = −gmRD (1.3) vi Printed on March 14, 2018 at 10 : 48: W.C. Chew and S.K. Gupta. 1 One can replace a linear circuit driven by a source by its Th´evenin equivalence.
    [Show full text]
  • Is EE Right for You?
    Erik Jonsson School of Engggineering and The Un ivers ity o f Texas a t Da llas Computer Science Is EE Right for You? • “Toto, I have a feeling we’re not in Kansas anymore.” • Now that you are here, diii?id you make the right choice? • Electrical engineering is a challenging and satisfying profession. That does not mean it is easy. In fact, with the possible exceptions of medicine or law, it is the MOST difficult. • There are some things you need to consider if you really, really want to be an engineer. • We will consider a few today. EE 1202 Lecture #1 – Why Electrical Engineering? 1 © N. B. Dodge 01/12 Erik Jonsson School of Engggineering and The Un ivers ity o f Texas a t Da llas Computer Science Is EE Right for You (2)? • Why did you decide to be an electrical engineer? – Parents will pay for engineering education (it’s what they want). – You like math and science. – A relative is an engineer and you like him/her. – You want to challenge yourself, and engineering seems challenging. – You think you are creative and love technology. – You want to make a difference in society . EE 1202 Lecture #1 – Why Electrical Engineering? 2 © N. B. Dodge 01/12 Erik Jonsson School of Engggineering and The Un ivers ity o f Texas a t Da llas Computer Science The High School “Science Student” Problem • In high school, you were FAR above the average. – And you probably didn’t study too hard, right? • You liked science and math, and they weren’t terribly hard.
    [Show full text]