1. Circuits and Analog Electronics 电路与模拟电子技术 Prof. Li Chen, School of Information Science and Technology, Sun Yat-sen University 中山大学信息科学与技术学院 陈立副教授 Email: chenli55@mail.sysu.edu.cn 10 级计算机科学 2 ＋ 2

2. References ： W. H. Hayt, Jr., J. E. Kemmerly and S. M. Durbin, Engineering Circuit Analysis, McGraw-Hill, 2005, ISBN 978-7-121-01667-7. R. L. Boylestad and L. Nashelsky, Electronic Devices and Circuit Theory, Pearson Education, 2007, ISBN 978-7-121-04396-3. 高玉良, 电路与模拟电子技术, 高教出版社, 2004, ISBN 7-04- 014536-7. Circuits and Analog Electronics

3. Handouts available at: sist.sysu.edu.cn/~chenli References ： W. H. Hayt, Jr., J. E. Kemmerly and S. M. Durbin, Engineering Circuit Analysis, McGraw-Hill, 2005, ISBN 978-7-121-01667-7. R. L. Boylestad and L. Nashelsky, Electronic Devices and Circuit Theory, Pearson Education, 2007, ISBN 978-7-121-04396-3. 高玉良, 电路与模拟电子技术, 高教出版社, 2004, ISBN 7-04-014536-7. Circuits and Analog Electronics

4. WeeksChaptersReferences 1, 2Basis concepts and laws of electronicsHayt: Ch 1 2 5 3, 4Basis analysis methods to circuitsHayt: Ch 3 4 5Basis RL & RC circuitsHayt: Ch 6 6, 7, 8Sinusoidal steady state analysisHayt: Ch 7 9Midterm 10Diodes and diodes circuitsBoylestad: Ch 1 2 11, 12, 13Basic BJT amplifier circuitsBoylestad: Ch 3-6 14, 15, 16Operational amplifier and Op Amp circuitsBoylestad: Ch 11 17Review Teaching Schedule

5. Ch1 Basic Concepts and Laws of Electric Circuits 1.1 Basic Concepts and Electric Circuits 1.2 Basic Quantities Circuit Elements 1.3 Circuit Elements 1.4 Kirchhoff's Current and Voltage Laws References: Hayt: Ch1, 2, 5; Gao: Ch1; Circuits and Analog Electronics

6. transmission Signal processing and transmission Amplifiers 1.1 Basic Concepts and Electric Circuits Electrical powertransmission Electrical power conversion and transmission Power SuppliesTransmissionLoads CircuitsKinescope Antenna Speaker transmitter

7. 1.1 Basic Concepts and Electric Circuits Electrical power conversion and transmission

8. 1.1 Basic Concepts and Electric Circuits Question: What is the current through the bulb? Concept of Abstraction Solution: In order to calculate the current, we can replace the bulb with a resistor. R is the only subject of interest, which serves as an abstraction of the bulb.

9. 1.1 Basic Concepts and Electric Circuits Lumped circuit abstraction! A resistor is a circuit element that transforms the electrical energy (e.g. electricity  heat); Commonly used devices that are modeled as resistors include incandescent, heaters, wires and etc; A circuit consists of sources, resistors, capacitors, inductors and conductors; Elements are lumped. Conductors are perfect. Resistance: R = V/I, 1  =1V/A, ohm; Conductance: G = 1/R = 1A/V, siemens (S); 1S = 1A/V, i(t) = G × v(t); Instantaneous current and voltage at time t;

10. 1.1 Basic Concepts and Electric Circuits Understanding the AM radio requires knowledge of several concepts Communications/signal processing (frequency domain analysis) Electromagnetics (antennas, high-frequency circuits) Power (batteries, power supplies) Solid state (miniaturization, low-power electronics) The AM Radio System TransmitterReceiver

11. Example 1: The AM audio system Example 2: The telephone system 1.1 Basic Concepts and Electric Circuits

12. The AM Radio System A signal is a quantity that may vary with time. * Voltage or current in a circuit * Sound (sinusoidal wave traveling through air) * Light or radio waves (electromagnetic energy traveling through free space) The analysis and design of AM radios (and communication systems in general) is usually conducted in the frequency domain using Fourier analysis, which allows us to represent signals as combinations of sinusoids (sines and cosines).

13. 1.1 Basic Concepts and Electric Circuits The AM Radio System Frequency is the rate at which a signal oscillates. Duration of the signal T, frequency of the signal f = 1/T. High FrequencyLow Frequency

14. 1.1 Basic Concepts and Electric Circuits The AM Radio System Visible light is the electromagnetic energy with frequency between 380THz (Terahertz) and 860THz. Our visual system perceives the frequency of the electromagnetic energy as color: is 460THz, is 570THz, and is 630THz. An AM radio signal has a frequency of between 500kHz and 1.8MHz. FM radio and TV uses different frequencies. Mathematical analysis of signals in terms of frequency Most commonly encountered signals can be represented as a Fourier series or a Fourier transform. A Fourier series is a weighted sum of cosines and sines. redgreen blue

15. 1.1 Basic Concepts and Electric Circuits The AM Radio System Fourier Series: A Fourier series decomposes a periodic function (or signal) into the sum of a set of sines and cosines. Given function f(t) with angular frequency ω and period T, its Fourier series can be written as: f(t) = A 0 + A 1m sin(ωt + ψ 1 ) + A 2m sin(2ωt + ψ 2 ) + ··· =

16. 1.1 Basic Concepts and Electric Circuits Example: Given function during a period: t For the example :, k is even., k is odd.

17. 1.1 Basic Concepts and Electric Circuits The AM Radio System Example-Fourier Series Signals can be represented in terms of their frequency components. The AM transmitter and receiver are analyzed in terms of their effects on the frequency components signals. 1 st series + 3 rd series 1 st series (k = 1) 3 rd series (k = 3)

18. 1.1 Basic Concepts and Electric Circuits The AM Radio System The modulator converts the frequency of the input signal from the audio range (0-5kHz) to the carrier frequency of the station (i.e. 605kHz-615kHz) freq 5kHz Frequency domain representation of input Frequency domain representation of output freq 610kHz Modulator Signal Source Modulator Power Amplifier Antenna Transmitter Block Diagram

19. 1.1 Basic Concepts and Electric Circuits The AM Radio System Input Signal Output Signal Modulator: Time Domain

20. 1.1 Basic Concepts and Electric Circuits The AM Radio System A typical AM station broadcasts several kW –Up to 50kW-Class I or Class II stations –Up to 5kW-Class III station –Up to 1kW-Class IV station Typical modulator circuit can provide at most a few mW Power amplifier takes modulator output and increases its magnitude Power Amplifier The antenna converts a current or a voltage signal to an electromagnetic signal which is radiated through the space. Antenna

21. 1.1 Basic Concepts and Electric Circuits The AM Radio System RF Amplifier IF Mixer IF Amplifier Envelope Detector Audio Amplifier Antenna Speaker Receiver Block Diagram

22. 1.1 Basic Concepts and Electric Circuits The AM Radio System The antenna captures electromagnetic energy and converts it to a small voltage or current. In the frequency domain, the antenna output is 0 frequency Undesired Signals Desired Signal Carrier Frequency of desired station Antenna interferences

23. 1.1 Basic Concepts and Electric Circuits The AM Radio System RF Amplifier amplifies small signals from the antenna to voltage levels appropriate for transistor circuits. RF Amplifier also performs as a Bandpass filter for the signal –Bandpass filter attenuates the other components outside the frequency range that contains the desired station RF (Radio Frequency) Amplifier 0 frequency Undesired Signals Desired Signal Carrier Frequency of desired station

24. The AM Radio System 0 frequency Undesired Signals Desired Signal 455 kHz IF (Intermediate Frequency) Mixer The IF Mixer shifts its input in the frequency domain from the carrier frequency to an intermediate frequency of 455kHz The IF amplifier bandpass filters the output of the IF mixer, eliminating all of the undesired signals. IF Amplifier 0 frequency Desired Signal 455 kHz

25. 1.1 Basic Concepts and Electric Circuits The AM Radio System Computes the envelope of its input signal Envelope Detector Output Signal Input Signal

26. 1.1 Basic Concepts and Electric Circuits The AM Radio System Audio Amplifier Amplifies signal from envelope detector Provides power to drive the speaker Hierarchical System Models Modelling at different levels of abstraction Higher levels of the model describe overall function of the system Lower levels of the model describe necessary details to implement the system In the AM receiver, the input is the antenna voltage and the output is the sound energy produced by the speaker. In EE, a system is an electrical and/or mechanical device, a process, or a mathematical model that relates one or more inputs to one or more outputs. System InputsOutputs

27. 1.1 Basic Concepts and Electric Circuits The AM Radio System Top Level Model AM ReceiverInput SignalSound Second Level Model RF Amplifier IF Mixer IF Amplifier Envelope Detector Audio Amplifier Antenna Speaker Power Supply

28. 1.1 Basic Concepts and Electric Circuits The AM Radio System Half-wave Rectifier Low-pass Filter Low Level Model Envelope Detector. Circuit Level Model Envelope Detector + - RC + - V out V in

29. 1.1 Basic Concepts and Electric Circuits The Telephone System The modern telephone system is developed from the following Electrical Engineering sub-disciplines: Signal processing: Speech compression, noise reduction, A/D and D/A conversion. E.g. channel coding + equalisation. Communications and networking: transmission technologies, network architectures and protocols. Digital and computer: configurable switching hardware. Electromagnetics: microwave transmission hardware. Solid state: miniaturization, integration of complex systems onto a single chip. E.g. building a signal processing chips, called very- large-scale integration(VLSI) Power Electronics: extremely reliable power supplies.

30. 1.1 Basic Concepts and Electric Circuits The Telephone System An Early Phone System Telephone Speaker Mic. Telephone Speaker Mic. Central Office Switchboard Speaker Mic. Power Supply

31. 1.1 Basic Concepts and Electric Circuits The Telephone System The major components include a carbon microphone and a speaker made from an electromagnet and a paramagnetic diaphragm. Telephones were connected to the central office by twisted-pair wires. At the central office, calls were completed by a human operator at a switchboard-a physical connection between two telephones was made. An Early Phone System An Early Phone Circuit Telephone Handset Carbon Microphone Earphone Central Office Battery Telephone Handset Carbon Microphone Earphone

32. 1.1 Basic Concepts and Electric Circuits The Telephone System The Modern Telephone System PCM Encoder PCM Decoder Switching Network PCM Decoder PCM Encoder Analog Digital A similar network structure... There are very significant differences: –Data, video, and other signals are transmitted along with speech. –Calls are routed automatically under software control. –Most transmission is digital.

33. 1.1 Basic Concepts and Electric Circuits The Telephone System Analog Vs. Digital An analog signal is a continuous signal represented over time domain: A digital signal is a sequence of 1’s and 0’s: 1101001010011100100110001001110 time BPSK Input 1, ψ=0° Input 0, ψ=180°

34. 1.1 Basic Concepts and Electric Circuits The Telephone System Why Digital? Analogue signal is prone to interference and degradation. Digital signal easily be retreated and repeat without any signal distortion -- long distance transmission. Can carry many types of information (phone, video, data, etc.) Digital hardware is less expensive. Digital data can be encrypted. PCM-Pulse Code Modulation A PCM encoder converts an analog signal into a digital signal with a particular format. A PCM decoder converts a digital signal into an analog signal. PCM is a form of quantization. PCM is a form of analog-to-digital (A/D) conversion.

35. 1.1 Basic Concepts and Electric Circuits The Telephone System PCM-Pulse Code Modulation PCM Encoder A continuous signal is converted into a bit stream: 0 1 1 Involves three operations: Sampling, Quantization and Encoding time

36. The Telephone System PCM-Pulse Code Modulation Sampling: Value of the signal is obtained at equally spaced points in time: time Quantization: each sample is quantized to one of a finite number of values. 1.1 Basic Concepts and Electric Circuits time T s –– sampling time. F s =1/T s ––sampling frequency.

37. The Telephone System PCM-Pulse Code Modulation Encoding: a pattern of bits is used to represent different output level of the quantizer; n bits can represent 2 n quantizer output levels. PCM decoder is one type of digital-to-analog (D/A) converter. 0000010100000000111111 1.1 Basic Concepts and Electric Circuits We have 5 output levels, we need at least 3 bits to represent them.. 000 001 100 001 011 000........ 010

38. Telephone Network A house or business is called a subscriber. Typically, phone lines to houses or small businesses are analog twisted- pair wire connections. Subscribers’ analog lines are connected to a Regional Terminal (RT) or to a Central Office (CO). At the RT or CO, the analog signal is converted to a digital signal. The Telephone System RT Subscriber CO Long-distance Network 1.1 Basic Concepts and Electric Circuits

39. 1.2 Basic Quantities Units Standard SI Prefixes –10 -12 pico (p) –10 -9 nano (n) –10 -6 micro (  ) –10 -3 milli (m) –10 3 kilo (k) –10 6 mega (M) –10 9 giga (G) –10 12 tera (T) Electric charge (q) –in Coulombs (C) Current (I) –in Amperes (A) Voltage (V) –in Volts (V) Energy (W) –in Joules (J) Power (P) –in Watts (W)

40. Current Time rate of change of charge Constant current Time varying current Unit (1 A = 1 C/s) 1.2 Basic Quantities Notation: Current flow represents the flow of positive charge Alternating versus direct current (AC vs DC) i(t) t t DC AC Time – varying current Steady current A mount of electric charges flowing through the surface per unit time.

41. Current Positive versus negative current 2 A -2 A P1.1, In the wire electrons moving left to right to create a current of 1 mA. Determine I 1 and I 2. Ans: I 1 = -1 mA; I 2 = +1 mA. 1.2 Basic Quantities Current is always associated with arrows (directions) Negative charge of -2C/s moving Positive charge of 2C/s moving or Negative charge of -2C/s moving Positive charge of 2C/s moving or

42. Voltage(Potential) Voltage Units: 1 V = 1 J/C Positive versus negative voltage + – – + 2 V -2 V 1.2 Basic Quantities Energy per unit charge. It is an electrical force drives an electric current. +/- of voltage (V) tell the actual polarity of a certain point. DN Two “Do Not (DN)” +/- of current (I) tell the actual direction of particle’s movement. DN

43. Voltage (Potential)   a b a 、 b, which point’s potential is higher ？  b  a V ab = ? ab  Positive? or negative +Q from point b to point a get energy ， Point a is Positive? or negative ? 1.2 Basic Quantities Example

44. Voltage (Potential) a b c´c´ cd d´d´ 1.2 Basic Quantities Example I

45. Voltage (Potential) K Open K C lose V a =? 1.2 Basic Quantities Example II

46. I 1.2 Basic Quantities Example I

47. Power One joules of energy is expanded per second. Rate of change of energy P = W/t Used to determine the electrical power is being absorbed or supplied –if P is positive (+), power is absorbed –if P is negative (–), power is supplied + – v(t) i(t) p(t) = v(t) i(t) v(t) is defined as the voltage with positive reference at the same terminal that the current i(t) is entering. 1.2 Basic Quantities

48. Power Example 1.2 Basic Quantities 2A + – -5V Power is supplied. delivered power to external element. + – 5V 2A Power is absorbed. Power delivered to Note : + – +5V + – -5V 2A -2A Power absorbed.

49. Power Power absorbed by a resistor: 1.2 Basic Quantities

50. Power 1 2 34 5 I1I1 I2I2 I3I3 + - - - - - + + + + - + + - + - P1.5 Find the power absorbed by each element in the circuit. 1.2 Basic Quantities Supply energy : element 1 、 3 、 4. Absorb energy : element 2 、 5

51. Open Circuit R=R= I=0, V=E, P=0 E R0R0 Short Circuit R=0 E R0R0 R＝0R＝0 1.2 Basic Quantities

52. Loaded Circuit E R0R0 R I 1.2 Basic Quantities

53. Circuit Elements 1.3 Circuit Elements Key Words: Resistors, Capacitors, Inductors, Resistors, Capacitors, Inductors, voltage source, current source

54. Passive elements (cannot generate energy) –e.g., resistors, capacitors, inductors, etc. Active elements (capable of generating energy) –batteries, generators, etc. Important active elements –Independent voltage source –Independent current source –Dependent voltage source voltage dependent and current dependent –Dependent current source voltage dependent and current dependent Circuit Elements 1.3 Circuit Elements

55. Resistors Elements Dissipation Elements v=iR P=vi=Ri 2 =v 2 /R >0 ， v-i relationship v i Circuit Elements 1.3 Circuit Elements Resistors connected in series: –Equivalent Resistance is found by R eq = R 1 + R 2 + R 3 + … R1R1 R2R2 R3R3 Resistors connected in parallel 1/R eq =1/R 1 + 1/R 2 + 1/R 3 + … R1R1 R2R2 R3R3

56. Capacitors Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator). Charge on the two conductors creates an electric field that stores energy. The voltage difference between the two conductors is proportional to the charge: q = C v The proportionality constant C is called capacitance. Units of Farads (F) - C/V 1F= one coulomb of charge of each conductor causes a voltage of one volt across the device. 1F=10 6  F, 1  F=10 6 PF Circuit Elements 1.3 Circuit Elements

57. Capacitors store energy in an electric field v-i relationship i(t)i(t) + - v(t)v(t) The rest of the circuit Energy stored Circuit Elements 1.3 Circuit Elements Capacitors connected in series: –Equivalent capacitance is found by 1/C eq =1/C 1 + 1/C 2 + 1/C 3 + … series parallel Capacitors connected in parallel C eq = C 1 + C 2 + C 3 + … v C (t+) = v C (t-)

58. Capacitors t i(t)i(t) 1A - 1A 1s 2s i(t)i(t) + - v(t)v(t) circuit 0.2F P1.7 Circuit Elements 1.3 Circuit Elements t v(t)v(t) 5V 1s 2s (1)(1) For (1) :

59. Capacitors t i(t)i(t) 1A - 1A 1s 2s i(t)i(t) + - v(t)v(t) circuit 0.2F P1.7 Circuit Elements 1.3 Circuit Elements t w (t) 2.5J 1s 2s (2) For (2) : For (1) 、 (2) :

60. Inductors store energy in a magnetic field that is created by electric passing through it. v-i relationship i(t)i(t) + - v(t)v(t) circuit L Inductors connected in series: L eq = L 1 + L 2 + L 3 + … Inductors connected in parallel: 1/L eq =1/L 1 + 1/L 2 + 1/L 3 + … Circuit Elements 1.3 Circuit Elements Energy stored : i L (t+) = i L (t-)

61. Independent voltage source + VSVS RS＝0RS＝0 v i VSVS Ideal practical Circuit Elements 1.3 Circuit Elements

62. Independent current source I v i ISIS R S ＝ ∞ Ideal practical Circuit Elements 1.3 Circuit Elements

63. Voltage source connected in series: Voltage source connected in parallel: Circuit Elements 1.3 Circuit Elements

64. Voltage controlled (dependent) voltage source (VCVS) + _ _ + Current controlled (dependent) voltage source (CCVS) + _ Q: What are the units for  and r? Circuit Elements 1.3 Circuit Elements

65. Voltage controlled (dependent) current source (VCCS) Current controlled (dependent) current source (CCCS) _ + Q: What are the units for  and g? Circuit Elements 1.3 Circuit Elements

66. Independent source dependent source Can provide power to the circuit; Excitation to circuit ; Output is not controlled by external. Can provide power to the circuit; No excitation to circuit; Output is controlled by external. Circuit Elements 1.3 Circuit Elements

67. So far, we have talked about two kinds of circuit elements: –Sources (independent and dependent) active, can provide power to the circuit. –Resistors passive, can only dissipate power. Review The energy supplied by the active elements is equivalent to the energy absorbed by the passive elements! Circuit Elements 1.3 Circuit Elements

68. 1.4 Kirchhoff's Current and Voltage Laws Key Words: Nodes, Branches, Loops, KCL, KVL

69. Nodes, Branches, Loops, mesh Node: point where two or more elements are joined (e.g., big node 1) Loop: A closed path that never goes twice over a node (e.g., the blue line) Branch: Component connected between two nodes (e.g., component R4) The red path is NOT a loop Mesh: A loop that does not contain any other loops in it. 1.4 Kirchhoff's Current and Voltage Laws

70. Nodes, Branches, Loops, mesh A circuit containing three nodes and five branches. Node 1 is redrawn to look like two nodes; it is still one nodes. P1.8 1.4 Kirchhoff's Current and Voltage Laws

71. sum of all currents entering a node is zero sum of currents entering node is equal to sum of currents leaving node KCL KCL Mathematically i1(t)i1(t) i2(t)i2(t) i 4 (t) i5(t)i5(t) i3(t)i3(t) 1.4 Kirchhoff's Current and Voltage Laws

72. sum of all currents entering a node is zero sum of currents entering node is equal to sum of currents leaving node KCL P1.9 1.4 Kirchhoff's Current and Voltage Laws

73. KCL + - 120V 50* 1W Bulbs IsIs P1.10 Find currents through each light bulb: I B = 1W/120V = 8.3mA Apply KCL to the top node: I S - 50I B = 0 Solve for I S : I S = 50 I B = 417mA KCL-Christmas Lights 1.4 Kirchhoff's Current and Voltage Laws

74. KCL P1.11We can make supernodes by aggregting node. 1.4 Kirchhoff's Current and Voltage Laws

75. KCL P1.12Find i x 1.4 Kirchhoff's Current and Voltage Laws i x = 12mA

76. KCL Current divider   N V G1G1 G2G2 I + - I1I1 I2I2 1.4 Kirchhoff's Current and Voltage Laws In case of parallel :

77. sum of voltages around any loop in a circuit is zero. KVL A voltage encountered + to - is positive. A voltage encountered - to + is negative. KVL Mathematically 1.4 Kirchhoff's Current and Voltage Laws

78. KVL is a conservation of energy principle KVL A positive charge gains electrical energy as it moves to a point with higher voltage and releases electrical energy if it moves to a point with lower voltage If the charge comes back to the same Initial point the net energy gain Must be zero. 1.4 Kirchhoff's Current and Voltage Laws

79. KVL P1.13 Determine the voltages V ae and V ec. 1.4 Kirchhoff's Current and Voltage Laws 4 + 6 + V ec = 0

80. KVL Voltage divider R1R1 R2R2 - V1V1 + + - V2V2 + - V Important voltage Divider equations N 1.4 Kirchhoff's Current and Voltage Laws

81. KVL Voltage divider Volume control? P1.14 Example: V s = 9V, R 1 = 90kΩ, R 2 = 30kΩ 1.4 Kirchhoff's Current and Voltage Laws