1. Topic 1 Introduction to Electronics ECE 271 Electronic Circuits I NJIT ECE-271 Dr. S. Levkov Chap 1 - 1

2. Topic Goals Explore the history of electronics. Describe classification of electronic signals. Introduce tolerance impacts and analysis. NJIT ECE-271 Dr. S. Levkov Chap 1 - 2

3. 1. The Subject of the Course The subject of the course is modern electronics, or microelectronics. Microelectronics refers to the integrated-circuit (IC) technology IC – can contains hundreds of millions of components on a IC chip with the area of the order 100 sq. mm. Subject of study: - electronic components/devices that can be used singly (discrete circuits) - electronic components/devices that can be used as components of the IC NJIT ECE-271 Dr. S. Levkov Chap 1 - 3

4. 2. Brief History NJIT ECE-271 Dr. S. Levkov Chap 1 - 4 Bardeen, Shockley, and Brattain at Bell Labs - Brattain and Bardeen invented the bipolar transistor in 1947. The first germanium bipolar transistor. Roughly 50 years later, electronics account for 10% (4 trillion dollars) of the world GDP. It can be said that the invention of the transistor and the subsequent development of the microelectronics have done more to shape the modern era than any other invention. The Start of the Modern Electronics Era

5. Electronics Milestones 1874Braun invents the solid-state rectifier ( using point contact based on lead sulphide ) 1906DeForest invents triode vacuum tube. 1907-1927 First radio circuits developed from diodes and triodes. 1925Lilienfeld field-effect device patent filed. 1947Bardeen and Brattain at Bell Laboratories invent bipolar transistors. 1952Commercial bipolar transistor production at Texas Instruments. 1956Bardeen, Brattain, and Shockley receive Nobel prize. 1958Integrated circuits developed by Kilby (TI) and Noyce and Moore (Fairchild Semiconductor) 1961First commercial IC from Fairchild Semiconductor 1963IEEE formed from merger of IRE and AIEE 1968First commercial IC opamp 1970One transistor DRAM cell invented by Dennard at IBM. 19714004 Intel microprocessor introduced. 1978First commercial 1-kilobit memory. 19748080 microprocessor introduced. 1984Megabit memory chip introduced. 1995 Gigabite memory chip presented. NJIT ECE-271 Dr. S. Levkov Chap 1 - 5

6. Evolution of Electronic Devices NJIT ECE-271 Dr. S. Levkov Chap 1 - 6 Vacuum Tubes Discrete Transistors SSI and MSI Integrated Circuits VLSI Surface-Mount Circuits

7. Evolution of Electronic Devices NJIT ECE-271 Dr. S. Levkov Chap 1 - 7 A work of art from the Museum of Modern Art, Paris

8. Microelectronics Proliferation The integrated circuit was invented in 1958. World transistor production has more than doubled every year for the past twenty years. NJIT ECE-271 Dr. S. Levkov Chap 1 - 8

9. Microelectronics Proliferation The integrated circuit was invented in 1958. World transistor production has more than doubled every year for the past twenty years. Every year, more transistors are produced than in all previous years combined. Approximately 10 18 transistors were produced in a recent year. NJIT ECE-271 Dr. S. Levkov Chap 1 - 9

10. Microelectronics Proliferation The integrated circuit was invented in 1958. World transistor production has more than doubled every year for the past twenty years. Every year, more transistors are produced than in all previous years combined. Approximately 10 18 transistors were produced in a recent year. To compare: –Number of cells in a human body - NJIT ECE-271 Dr. S. Levkov Chap 1 - 10

11. Microelectronics Proliferation The integrated circuit was invented in 1958. World transistor production has more than doubled every year for the past twenty years. Every year, more transistors are produced than in all previous years combined. Approximately 10 18 transistors were produced in a recent year. To compare: –Number of cells in a human body - 10 14 NJIT ECE-271 Dr. S. Levkov Chap 1 - 11

12. Microelectronics Proliferation The integrated circuit was invented in 1958. World transistor production has more than doubled every year for the past twenty years. Every year, more transistors are produced than in all previous years combined. Approximately 10 18 transistors were produced in a recent year. To compare: –Number of cells in a human body - 10 14 –Number of seconds elapsed since Big Bang – NJIT ECE-271 Dr. S. Levkov Chap 1 - 12

13. Microelectronics Proliferation The integrated circuit was invented in 1958. World transistor production has more than doubled every year for the past twenty years. Every year, more transistors are produced than in all previous years combined. Approximately 10 18 transistors were produced in a recent year. To compare: –Number of cells in a human body - 10 14 –Number of seconds elapsed since Big Bang – 10 17 NJIT ECE-271 Dr. S. Levkov Chap 1 - 13

14. Microelectronics Proliferation The integrated circuit was invented in 1958. World transistor production has more than doubled every year for the past twenty years. Every year, more transistors are produced than in all previous years combined. Approximately 10 18 transistors were produced in a recent year. To compare: –Number of cells in a human body - 10 14 –Number of seconds elapsed since Big Bang – 10 17 –Number of ants in the world - NJIT ECE-271 Dr. S. Levkov Chap 1 - 14

15. Microelectronics Proliferation The integrated circuit was invented in 1958. World transistor production has more than doubled every year for the past twenty years. Every year, more transistors are produced than in all previous years combined. Approximately 10 18 transistors were produced in a recent year. To compare: –Number of cells in a human body - 10 14 –Number of seconds elapsed since Big Bang – 10 17 –Number of ants in the world - roughly 50 transistors for every ant in the world. * Source: Gordon Moore’s Plenary address at the 2003 International Solid State Circuits Conference. NJIT ECE-271 Dr. S. Levkov Chap 1 - 15

16. Rapid Increase in Density of Microelectronics NJIT ECE-271 Dr. S. Levkov Chap 1 - 16 Memory chip density versus time. Microprocessor complexity versus time.

17. Device Feature Size Feature size reductions enabled by process innovations. Smaller features lead to more transistors per unit area and therefore higher density. SSI – small scale integration (< 10 2 ) MSI – medium SI (10 2- 10 3 ) LSI – large SI (10 3- 10 4 ) VLSI – very large SI (10 4- 10 9 ) ULSI & GSI– ultra large SI & giga- scale integration (> 10 9 ) NJIT ECE-271 Dr. S. Levkov Chap 1 - 17

18. 3. Types of Signals Analog signals take on continuous values - typically current or voltage. NJIT ECE-271 Dr. S. Levkov Chap 1 - 18

19. 3. Types of Signals Analog signals take on continuous values - typically current or voltage. Digital signals appear at discrete levels (do not confuse with discrete times). NJIT ECE-271 Dr. S. Levkov Chap 1 - 19

20. 3. Types of Signals Analog signals take on continuous values - typically current or voltage. Digital signals appear at discrete levels (do not confuse with discrete times). Usually we use binary signals with only two levels - One level is referred to as logical 1 and logical 0 is assigned to the other level. Typically: - was standard for many years - used now. Bipolar levels also exist NJIT ECE-271 Dr. S. Levkov Chap 1 - 20

21. Analog and Digital Signals Analog signals usually are continuous in time and in values. NJIT ECE-271 Dr. S. Levkov Chap 1 - 21 Analog signal

22. Analog and Digital Signals Analog signals usually are continuous in time and in values. Sampled, discrete time signals are discrete in time (values are typically separated by fixed time intervals). The values are continuous. Needs digitization. NJIT ECE-271 Dr. S. Levkov Chap 1 - 22 Analog signalDiscrete time signal

23. Analog and Digital Signals Sampled discrete time signal NJIT ECE-271 Dr. S. Levkov Chap 1 - 23

24. Analog and Digital Signals Sampled discrete time signalDigitized discrete time signal - discrete time and digitized discrete values. The values are not continuous – belong to a finite set. NJIT ECE-271 Dr. S. Levkov Chap 1 - 24

25. Analog and Digital Signals Sampled discrete time signalDigitized discrete time signal - discrete time and digitized discrete values. The values are not continuous – belong to a finite set. NJIT ECE-271 Dr. S. Levkov Chap 1 - 25

26. Analog and Digital Signals Sampled discrete time signalDigitized discrete time signal - discrete time and digitized discrete values. The values are not continuous – belong to a finite set. NJIT ECE-271 Dr. S. Levkov Chap 1 - 26

27. Digital-to-Analog (D/A) Conversion NJIT ECE-271 Dr. S. Levkov Chap 1 - 27 The input is a binary number Let’s introduce and then define

28. Digital-to-Analog (D/A) Conversion The least significant bit (LSB) - the smallest possible binary number (smallest voltage change) is known as resolution of the converter. NJIT ECE-271 Dr. S. Levkov Chap 1 - 28 The input is a binary number Let’s introduce and then define

29. Digital-to-Analog (D/A) Conversion The least significant bit (LSB) - the smallest possible binary number (smallest voltage change) is known as resolution of the converter. The most significant bit (MSB) - NJIT ECE-271 Dr. S. Levkov Chap 1 - 29 The input is a binary number Let’s introduce and then define ?

30. Digital-to-Analog (D/A) Conversion The least significant bit (LSB) - the smallest possible binary number (smallest voltage change) is known as resolution of the converter. The most significant bit (MSB) - NJIT ECE-271 Dr. S. Levkov Chap 1 - 30 The input is a binary number Let’s introduce and then define

31. Digital-to-Analog (D/A) Conversion The least significant bit (LSB) - the smallest possible binary number (smallest voltage change) is known as resolution of the converter. The most significant bit (MSB) - Then for an n-bit D/A converter, the output voltage is expressed as: NJIT ECE-271 Dr. S. Levkov Chap 1 - 31 The input is a binary number Let’s introduce and then define

32. Digital-to-Analog (D/A) Conversion The least significant bit (LSB) - the smallest possible binary number (smallest voltage change) is known as resolution of the converter. The most significant bit (MSB) - Then for an n-bit D/A converter, the output voltage is expressed as: NJIT ECE-271 Dr. S. Levkov Chap 1 - 32 The input is a binary number Let’s introduce and then define

33. Digital-to-Analog (D/A) Conversion The least significant bit (LSB) - the smallest possible binary number (smallest voltage change) is known as resolution of the converter. The most significant bit (MSB) - Then for an n-bit D/A converter, the output voltage is expressed as: NJIT ECE-271 Dr. S. Levkov Chap 1 - 33 The input is a binary number Let’s introduce and then define

34. Analog-to-Digital (A/D) Conversion Analog input voltage V x is converted to the nearest n-bit number that represent V O - the closest (WRT to the accuracy = V LSB /2) value to the V x Output is approximation of input due to the limited resolution of the n-bit output. Error is expressed as: NJIT ECE-271 Dr. S. Levkov Chap 1 - 34

35. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 35

36. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 36

37. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 37

38. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 38

39. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 39

40. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 40

41. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 41

42. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 42

43. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 43

44. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 44

45. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 45

46. A/D Converter Transfer Characteristic (input-output) NJIT ECE-271 Dr. S. Levkov Chap 1 - 46

47. 4. Notational Conventions In many circuits the signal will be a combination of the dc and time varying values. Total signal = DC bias + time varying signal Resistance and conductance - R and G with same subscripts will denote reciprocal quantities. Most convenient form will be used within expressions. NJIT ECE-271 Dr. S. Levkov Chap 1 - 47

48. 5. Circuit Theory Review: Thévenin and Norton Equivalent Circuits NJIT ECE-271 Dr. S. Levkov Chap 1 - 48 Thévenin Norton

49. 5. Circuit Theory Review: Thévenin and Norton Equivalent Circuits NJIT ECE-271 Dr. S. Levkov Chap 1 - 49 Thévenin Norton

50. 5. Circuit Theory Review: Thévenin and Norton Equivalent Circuits NJIT ECE-271 Dr. S. Levkov Chap 1 - 50 Thévenin Norton

51. Circuit Theory Review: Find the Thévenin Equivalent Voltage Problem: Find the Thévenin equivalent voltage at the output. Solution Approach: Voltage source v th is defined as the output voltage with no load. NJIT ECE-271 Dr. S. Levkov Chap 1 - 51

52. Circuit Theory Review: Find the Thévenin Equivalent Voltage NJIT ECE-271 Dr. S. Levkov Chap 1 - 52

53. Circuit Theory Review: Find the Thévenin Equivalent Voltage NJIT ECE-271 Dr. S. Levkov Chap 1 - 53 Applying KCL at the output node, Current i 1 can be written as: Substituting into previous expression:

54. Circuit Theory Review: Find the Thévenin Equivalent Voltage (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 54 Using the given component values: and

55. Circuit Theory Review: Find the Thévenin Equivalent Resistance NJIT ECE-271 Dr. S. Levkov Chap 1 - 55

56. Circuit Theory Review: Find the Thévenin Equivalent Resistance Problem: Find the Thévenin equivalent resistance. Solution Approach: Find R th as the output equivalent resistance with independent sources set to zero. NJIT ECE-271 Dr. S. Levkov Chap 1 - 56 Test voltage v x has been added to the previous circuit. Applying v x and solving for i x allows us to find the Thévenin resistance as v x /i x.

57. Circuit Theory Review: Find the Thévenin Equivalent Resistance (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 57 Applying KCL, where we get, or

58. Circuit Theory Review: Find the Norton Equivalent Circuit Problem: Find the Norton equivalent circuit. Solution approach: Evaluate current through output short circuit. NJIT ECE-271 Dr. S. Levkov Chap 1 - 58

59. Circuit Theory Review: Find the Norton Equivalent Circuit NJIT ECE-271 Dr. S. Levkov Chap 1 - 59

60. Circuit Theory Review: Find the Norton Equivalent Circuit Problem: Find the Norton equivalent circuit. Solution approach: Evaluate current through output short circuit. NJIT ECE-271 Dr. S. Levkov Chap 1 - 60 A short circuit has been applied across the output. The Norton current is the current flowing through the short circuit at the output.

61. Circuit Theory Review: Find the Norton Equivalent Circuit (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 61 Applying KCL, Where Thus Short circuit at the output causes zero current to flow through R S. R th is equal to R th found earlier.

62. Final Thévenin and Norton Circuits NJIT ECE-271 Dr. S. Levkov Chap 1 - 62 Check of Results: Note that v th = i n R th and this can be used to check the calculations: i n R th =(2.55 mS)v i (282  ) = 0.719v i, accurate within round-off error. v th = 0.718v i i n = (2.55x10 -3 )v i

63. 6. Signal spectrum Any periodic signal can be represented in the form of Fourier series: NJIT ECE-271 Dr. S. Levkov Chap 1 - 63  0 =2  /T (rad/s) is the fundamental radian frequency and f 0 =1/T (Hz) is the fundamental frequency of the signal. 2f 0, 3f 0, 4f 0, ….. are called the harmonic frequencies. Alternative representation:

64. Fourier Series example For example, a square wave is represented by the following Fourier series: NJIT ECE-271 Dr. S. Levkov Chap 1 - 64 Signal Spectrum The spectrum of the periodic signal is the graph of the Fourier coefficients vs the harmonic frequencies. Periodic signals have discrete spectra. Non periodic signals have continuous spectra often occupying a broad range of frequencies.

65. Frequencies of Some Common Signals Audible sounds20 Hz - 20KHz Baseband TV0 - 4.5MHz FM Radio88 - 108MHz Television (Channels 2-6)54 - 88MHz Television (Channels 7-13)174 - 216MHz Maritime and Govt. Comm.216 - 450MHz Cell phones and other wireless1710 - 2690MHz Satellite TV3.7 - 4.2GHz Wireless Devices5.0 - 5.5GHz NJIT ECE-271 Dr. S. Levkov Chap 1 - 65 Show the Fourier applet here

66. 7. Circuit Element Variations All electronic components have manufacturing tolerances. –Resistors can be purchased with  10%,  5%, and  1% tolerance. (IC resistors are often  10%.) –Capacitors can have asymmetrical tolerances such as +20%/-50%. –Power supply voltages typically vary from 1% to 10%. Device parameters will also vary with temperature and age. Circuits must be designed to accommodate these variations. We will use worst-case and Monte Carlo (statistical) analysis to examine the effects of component parameter variations. NJIT ECE-271 Dr. S. Levkov Chap 1 - 66

67. Tolerance Modeling For symmetrical parameter variations P nom (1 -  )  P  P nom (1 +  ) P nom - is the parameter specification  - is the tolerance For example, a 10K resistor with  5% percent tolerance could exhibit the resistance in the following range of values: 10k(1 - 0.05)  R  10k(1 + 0.05) 9,500   R  10,500  NJIT ECE-271 Dr. S. Levkov Chap 1 - 67

68. Circuit Analysis with Tolerances Worst-case analysis –Parameters are manipulated to produce the worst-case min and max values of desired quantities. –This can lead to over design since the worst-case combination of parameters is rare. –It may be less expensive to discard a rare failure than to design for 100% yield. NJIT ECE-271 Dr. S. Levkov Chap 1 - 68

69. Circuit Analysis with Tolerances Worst-case analysis –Parameters are manipulated to produce the worst-case min and max values of desired quantities. –This can lead to over design since the worst-case combination of parameters is rare. –It may be less expensive to discard a rare failure than to design for 100% yield. Monte-Carlo analysis –Parameters are randomly varied to generate a set of statistics for desired outputs. –Based on that we calculate the average values and optimize the design so that failures due to parameter variation are less frequent than failures due to other mechanisms. –In this way, the design difficulty is better managed than a worst- case approach. NJIT ECE-271 Dr. S. Levkov Chap 1 - 69

70. Worst Case Analysis Example Problem: Find the nominal and worst-case values for output voltage and source current. Solution: Unknowns: V O nom, V O min, V O max, I I nom, I I min, I I max. Approach: Find nominal values and then select R 1, R 2, and V I values to generate extreme cases of the unknowns. NJIT ECE-271 Dr. S. Levkov Chap 1 - 70 Nominal voltage solution:Nominal Source current:

71. Worst-Case Analysis Example (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 71 Now we need to figure out how to find the min and max possible of the voltage and current in question.

72. Worst-Case Analysis Example (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 72 Rewrite V O to help us determine how to find the worst-case values. Now we need to figure out how to find the min and max possible of the voltage and current in question.

73. Worst-Case Analysis Example (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 73 Rewrite V O to help us determine how to find the worst-case values. V O is maximized for max V I, R 1 and min R 2. V O is minimized for min V I, R 1, and max R 2. Now we need to figure out how to find the min and max possible of the voltage and current in question.

74. Worst-Case Analysis Example (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 74 Rewrite V O to help us determine how to find the worst-case values. V O is maximized for max V I, R 1 and min R 2. V O is minimized for min V I, R 1, and max R 2. Now we need to figure out how to find the min and max possible of the voltage and current in question.

75. Worst-Case Analysis Example (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 75 Rewrite V O to help us determine how to find the worst-case values. V O is maximized for max V I, R 1 and min R 2. V O is minimized for min V I, R 1, and max R 2. Now we need to figure out how to find the min and max possible of the voltage and current in question.

76. Worst-Case Analysis Example (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 76 Worst-case source currents:

77. Worst-Case Analysis Example (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 77 Worst-case source currents:

78. Worst-Case Analysis Example (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 78 Check of Results: The worst-case values range from 14-17 percent above and below the nominal values. The sum of the three element tolerances is 20 percent, so our calculated values appear to be reasonable. Worst-case source currents:

79. Monte Carlo Analysis All parameters are selected randomly from the possible distributions Circuit is analysis is performed and solution is found Many such solutions are performed and statistics are gathered. The analysis can be done using programs like MATLAB, Mathcad, SPICE, or a spreadsheet to complete a statistically significant set of calculations. For example, with Excel , a resistor with 5% tolerance can be expressed as: NJIT ECE-271 Dr. S. Levkov Chap 1 - 79 The RAND() function returns random numbers uniformly distributed between 0 and 1.

80. Monte Carlo Analysis Result NJIT ECE-271 Dr. S. Levkov Chap 1 - 80 Histogram of output voltage from 1000 case Monte Carlo simulation. WC

81. Monte Carlo Analysis Example Problem: Perform a Monte Carlo analysis and find the mean, standard deviation, min, and max for V O, I S, and power delivered from the source. Solution: Unknowns: The mean, standard deviation, min, and max for V O, I S, and P S. Approach: Use a spreadsheet to evaluate the circuit equations with random parameters. NJIT ECE-271 Dr. S. Levkov Chap 1 - 81

82. Monte Carlo Analysis Example (cont.) NJIT ECE-271 Dr. S. Levkov Chap 1 - 82 Circuit equations based on Monte Carlo parameters: AvgNom.StdevMaxWC-maxMinWC-Min V o (V)4.965.000.305.705.874.374.20 I I (mA)0.2760.2780.01730.310 0.3220.2420.238 P (mW)4.124.170.4905.04--3.29-- Monte Carlo parameter definitions: Results:

83. Temperature Coefficients Most circuit parameters are temperature sensitive. P = P nom (1+  1 ∆T+  2 ∆T 2 ) where ∆T = T-T nom P nom is defined at T nom Most versions of SPICE allow for the specification of TNOM, T, TC1(  1 ), TC2(  2 ). SPICE temperature model for resistor: R(T) = R(TNOM)*[1+TC1*(T-TNOM)+TC2*(T-TNOM) 2 ] Many other components have similar models. NJIT ECE-271 Dr. S. Levkov Chap 1 - 83

84. Numeric Precision Most circuit parameters vary from less than +- 1 % to greater than +- 50%. As a consequence, more than three significant digits is meaningless. Results in the text will be represented with three significant digits: 2.03 mA, 5.72 V, 0.0436 µA, and so on. NJIT ECE-271 Dr. S. Levkov Chap 1 - 84