1. Digital Electronics Chap 1

2. The Start of the Modern Electronics Era 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.

3. Electronics Milestones 1874 Braun invents the solid-state rectifier. 1906 DeForest invents triode vacuum tube. 1907-1927 First radio circuits developed from diodes and triodes. 1925 Lilienfeld field-effect device patent filed. 1947 Bardeen and Brattain at Bell Laboratories invent bipolar transistors. 1952 Commercial bipolar transistor production at Texas Instruments. 1956 Bardeen, Brattain, and Shockley receive Nobel prize. 1958 Integrated circuit developed by Kilby and Noyce 1961 First commercial IC from Fairchild Semiconductor 1963 IEEE formed from merger or IRE and AIEE 1968 First commercial IC opamp 1970 One transistor DRAM cell invented by Dennard at IBM. 1971 4004 Intel microprocessor introduced. 1978 First commercial 1-kilobit memory. 1974 8080 microprocessor introduced. 1984 Megabit memory chip introduced. 2000 Alferov, Kilby, and Kromer share Nobel prize

4. Evolution of Electronic Devices Vacuum Tubes Discrete Transistors SSI and MSI Integrated Circuits VLSI Surface-Mount Circuits

5. 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 9 transistors were produced in a recent year. Roughly 50 transistors for every ant in the world. *Source: Gordon Moore ’ s Plenary address at the 2003 International Solid State Circuits Conference.

6. 5 Commendments Moore’s Law : The number of transistors on a chip doubles annually Rock’s Law : The cost of semiconductor tools doubles every four years Machrone’s Law: The PC you want to buy will always be $5000 Metcalfe’s Law : A network’s value grows proportionately to the number of its users squared

7. 5 Commandments(cont.) Wirth’s Law : Software is slowing faster than hardware is accelerating Further Reading: “5 Commandments”, IEEE Spectrum December 2003, pp. 31- 35.

8. Moore’s law Moore predicted that the number of transistors that can be integrated on a die would grow exponentially with time. Amazingly visionary – million transistor/chip barrier was crossed in the 1980’s. 16 M transistors (Ultra Sparc III) 140 M transistor (HP PA-8500) 1.7B transistor (Intel Montecito)

11. DEC PDP-11 CPU

12. HP PA7000 RISC

13. Motorola 68020

14. Motorola 68040

15. Toshiba MIPS

16. Intel 8088

17. Intel 80386

18. 80386 (cont.)

19. Intel 80486

20. Intel Pentium

21. Intel Pentium 4 Prescott

23. Penryn and Nehalem Penryn : 45nm Core 2 Architecture : Core 2 Extreme QX9650 Nehalem : Core i7

24. Intel CPU Evolution

25. Device Feature Size Feature size reductions enabled by process innovations. Smaller features lead to more transistors per unit area and therefore higher density.

26. Rapid Increase in Density of Microelectronics Memory chip density versus time. Microprocessor complexity versus time.

27. IC Design Step 1: RTL

28. IC Design 2 : Layout

29. IC Design 3 : Fabrication

30. IC Design 4 : Chip

31. IC Design 5 : System

32. IC design is mostly coding Hardware Description Language (Verilog, VHDL) are widely used in today’s IC design. C programs need to obey rules set by OS. HDL programs need to obey physical rules in the real world.

33. Analog versus Digital Electronics Most observables are analog But the most convenient way to represent and transmit information electronically is digital Analog/digital and digital/analog conversion is essential

37. Digital signal representation By using binary numbers we can represent any quantity. For example a binary two (10) could represent a 2 volt signal. But we generally have to agree on some sort of “code” and the dynamic range of the signal in order to know the form and the minimum number of bits. Possible digital representation for a pure sine wave of known frequency. We must choose maximum value and “resolution” or “error,” then we can encode the numbers. Suppose we want 1V accuracy of amplitude with maximum amplitude of 50V, we could use a simple pure binary code with 6 bits of information.

38. Digital representations of logical functions Digital signals also offer an effective way to execute logic. The formalism for performing logic with binary variables is called switching algebra or boolean algebra. Digital electronics combines two important properties:  The ability to represent real functions by coding the information in digital form.  The ability to control a system by a process of manipulation and evaluation of digital variables using switching algebra.

39. Digital Representations of logic functions (cont.) Digital signals can be transmitted, received, amplified, and retransmitted with no degradation. Binary numbers are a natural method of expressing logic variables. Complex logic functions are easily expressed as binary function. With digital representation, we can achieve arbitrary levels of “ dynamic range,” that is, the ratio of the largest possible signal to the smallest than can be distinguished above the background noise. Digital information is easily and inexpensively stored

40. Signal Types Analog signals take on continuous values - typically current or voltage. Digital signals appear at discrete levels. Usually we use binary signals which utilize only two levels. One level is referred to as logical 1 and logical 0 is assigned to the other level.

41. Analog and Digital Signals Analog signals are continuous in time and voltage or current. (Charge can also be used as a signal conveyor.) After digitization, the continuous analog signal becomes a set of discrete values, typically separated by fixed time intervals.

42. Digital-to-Analog (D/A) Conversion For an n-bit D/A converter, the output voltage is expressed as: The smallest possible voltage change is known as the least significant bit or LSB.

43. DAC TI’s 20-bit sigma delta DAC

44. Analog-to-Digital (A/D) Conversion Analog input voltage v x is converted to the nearest n-bit number. For a four bit converter, 0 -> v x input yields a 0000 -> 1111 digital output. Output is approximation of input due to the limited resolution of the n-bit output. Error is expressed as:

45. ADC Die Photo Rockwell Scientific 4Gsps ADC

46. A/D Converter Transfer Characteristic

47. Introduction to Circuit Theory Circuit theory is based on the concept of modeling. To analyze any complex physical system, we must be able to describe the system in terms of an idealized model that is an interconnection of idealized elements. By analyzing the circuit model, we can predict the behavior of the physical circuit and design better circuits.

48. Lumped Circuits Lumped circuits are obtained by connecting lumped elements. Typical lumped elements are resistors, capacitors, inductors, and transformers. The size of lumped circuit is small compared to the wavelength of their normal frequency of operation.

49. Operating Frequency vs. Size Audio Circuit operate @ 25Khz, the wavelength λ~=12Km, which is much larger than the size of any elements Computer Circuit @ 500 Mhz, λ=0.6m, the lumped approx. is not so good. Microwave circuit, where λis between 10cm to 1mm, Kirchhoff’s laws do not apply for the cavity resonators.

50. Lumped Circuit definition A lumped circuit is by definition an interconnecting lumped element. The two terminal elements are called branches, the terminals of the elements are called nodes. The branch voltage and branch current are the basic variables of interest in circuit theory.

51. Lumped circuit figure

52. Reference Directions A two terminal lumped elements (branch) with nodes A and B. The reference directions for the branch voltage v and branch current i are shown in the graph. The reference direction is chosen arbitrarily.

53. Notational conventions Total quantities will be represented by lowercase letters with capital subscripts, such as v T anf i T. The dc components are represented by capital letters with capital subscripts as V DC and I DC ; changes or variations from the dc value are represented by v ac and i ac. v T = V DC + v ac i T = I DC + i ac

55. Kirchhoff’s Current Law (KCL) For any lumped electric circuit, for any of its nodes, and at any time, the algebraic sum of all branch currents leaving the node is zero.

56. KCL Example When applying KCL to circuit, first assign reference direction for each branch. For node 2, i 4 -i 3 -i 6 =0 For node 1, -i 1 +i 2 +i 3 =0

57. Kirchhoff’s Voltage Law (KVL) For any lumped electric circuit, for any of its loops, and at any time, the algebraic sum of the branch voltages around the loop is zero.

58. KVL Example For loop I, v 4 +v 5 -v 6 =0 Loop II, v 4 +v 5 -v 2 -v 1 =0

59. Properties of KCL and KVL KCL imposes a linear constraint on the branch currents. KCL applies to any lumped electric circuit; it is independent of the nature of the elements. KCL expresses the conservation of charge at any time.

60. Properties of KVL and KCL (cont.) An example where KCL doesn’t apply is the whip antenna. The antenna is about ¼ wavelength so it is not a lumped circuit. KVL imposes a linear constraint between branch voltages of a loop. KVL is independent of the natural of the elements.

61. Circuit Elements Resistors Independent sources Capacitors Inductors

62. 被動元件

63. Resistors v(t) = Ri(t) or i(t)=Gv(t) R is the resistance G is called the conductance For linear time-invariant resistors, R and G are constants.

64. Independent Sources Independent sources maintains a prescribed voltage or current across the terminals of the arbitrary circuit to which it is connected.

65. Capacitors Capacitors store electrical charges. i(t) = dq/dt q(t) = Cv(t) i(t) = Cdv(t)/dt

66. Parallel Plate Capacitance K = relative permittivity of the dielectric material in between two plates. K= 1 for free space, K=3.9 for SiO2 High K (K > 3.9)dielectric (e.g. (BaSr)TiO3, barium strontium titanate for K=160-600 for storage capacitance; zirconium silicate, ZrSiO4 with K=15 for next generation gate oxide) Low K (K < 3.9)dielectric for ILD (interlayer dielectrics ) to insulate between metal lines (e.g. Porous SiO2 for K=1.3)

67. Inductors Inductors store energy in their magnetic fields. V(t) = dΦ/dt Φ(t)=Li(t) V(t) = L di/dt

68. RLC Effects in Real Circuit Power (Thermal) Time Delay

69. Physical Componenets vs. Circuit Elements Range of Operation Temperature Effect Parasitic effect Typical Element Size  Resistor : 1ohm to Mohms  Capacitor : femto Farad to micro Farad

70. Circuit Theory Review: Voltage Division and Applying KVL to the loop, Combining these yields the basic voltage division formula: and

71. Using the derived equations with the indicated values, Design Note: Voltage division only applies when both resistors are carrying the same current. Circuit Theory Review: Voltage Division (cont.)

72. Circuit Theory Review: Current Division and Combining and solving for v s, Combining these yields the basic current division formula: whereand

73. Circuit Theory Review: Current Division (cont.) Using the derived equations with the indicated values, Design Note: Current division only applies when the same voltage appears across both resistors.

74. Equivalent Circuit Thevenin and Norton Equivalent circuit represents real-world battery models. Complex circuits can be simplified to these representation to help us understand the circuits.

75. Circuit Theory Review: Thevenin and Norton Equivalent Circuits

76. Circuit Theory Review: Find the Thevenin Equivalent Voltage Problem: Find the Thevenin equivalent voltage at the output. Solution: Known Information and Given Data: Circuit topology and values in figure. Unknowns: Thevenin equivalent voltage v TH. Approach: Voltage source v TH is defined as the output voltage with no load. Assumptions: None. Analysis: Next slide …

77. Circuit Theory Review: Find the Thevenin Equivalent Voltage Applying KCL at the output node, Current i 1 can be written as: Combining the previous equations

78. Circuit Theory Review: Find the Thevenin Equivalent Voltage (cont.) Using the given component values: and

79. Circuit Theory Review: Find the Thevenin Equivalent Resistance Problem: Find the Thevenin equivalent resistance. Solution: Known Information and Given Data: Circuit topology and values in figure. Unknowns: Thevenin equivalent resistance R TH. Approach: R TH is defined as the equivalent resistance at the output terminals with all independent sources in the network set to zero. Assumptions: None. Analysis: Next slide … Test voltage v x has been added to the previous circuit. Applying v x and solving for i x allows us to find the Thevenin resistance as v x /i x.

80. Circuit Theory Review: Find the Thevenin Equivalent Resistance (cont.) Applying KCL,

81. Circuit Theory Review: Find the Norton Equivalent Circuit Problem: Find the Norton equivalent circuit. Solution: Known Information and Given Data: Circuit topology and values in figure. Unknowns: Norton equivalent short circuit current i N. Approach: Evaluate current through output short circuit. Assumptions: None. Analysis: Next slide … A short circuit has been applied across the output. The Norton current is the current flowing through the short circuit at the output.

82. Circuit Theory Review: Find the Thevenin Equivalent Resistance (cont.) Applying KCL, Short circuit at the output causes zero current to flow through R S. R th is equal to R th found earlier.

83. Final Thevenin and Norton Circuits 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 s (282  ) = 0.719v s, accurate within round-off error. While the two circuits are identical in terms of voltages and currents at the output terminals, there is one difference between the two circuits. With no load connected, the Norton circuit still dissipates power!

84. Example : Circuit with a controlled source Applying KVL around the loop containing v s yields v s = i s R 1 + i 2 R 2 = i s R 1 + (i s + g m v 1 )R 2 (1.33) v 1 = i s R 1 (1.34) v s = i s (R 1 + R 2 + g m R 1 R 2 ) (1.35) R eq = v s / i s = R 1 + R 2 (1+ g m R 1 ) (1.36) R eq = 3KΩ+2KΩ[1+0.1S*3KΩ] = 605 kΩ. This value is far larger than either R1 or R2.

86. KVL

87. Circuitry Snacks from : www.evilmadscientist.com

88. Joule Thief

89. 555 LED Blink

90. Frequency Spectrum of Electronic Signals Nonrepetitive signals have continuous spectra often occupying a broad range of frequencies Fourier theory tells us that repetitive signals are composed of a set of sinusoidal signals with distinct amplitude, frequency, and phase. The set of sinusoidal signals is known as a Fourier series. The frequency spectrum of a signal is the amplitude and phase components of the signal versus frequency.

91. 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 phones1710 - 2690MHz Satellite TV3.7 - 4.2GHz

92. Fourier Series Any periodic signal contains spectral components only at discrete frequencies related to the period of the original signal. A square wave is represented by the following Fourier series:  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 and called the second, third, and fourth harmonic frequencies.

93. Amplifier Basics Analog signals are typically manipulated with linear amplifiers. Although signals may be comprised of several different components, linearity permits us to use the superposition principle. Superposition allows us to calculate the effect of each of the different components of a signal individually and then add the individual contributions to the output.

95. Amplifier Linearity Given an input sinusoid: For a linear amplifier, the output is at the same frequency, but different amplitude and phase. In phasor notation: Amplifier gain is:

96. Amplifier Input/Output Response v s = sin2000  t V A v = -5 Note: negative gain is equivalent to 180 degress of phase shift.

97. Amplifier Frequency Response Low-PassHigh-PassBandPassBand-RejectAll-Pass Amplifiers can be designed to selectively amplify specific ranges of frequencies. Such an amplifier is known as a filter. Several filter types are shown below:

98. 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.

99. Tolerance Modeling For symmetrical parameter variations P NOM (1 -  )  P  P NOM (1 +  ) For example, a 10K resistor with  5% percent tolerance could take on the following range of values: 10k(1 - 0.05)  R  10k(1 + 0.05) 9,500   R  10,500 

100. 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.  The design can be optimized 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.

101. Amplifiers in a familiar electronic system The local oscillator, which tunes the radio receiver to select the desired station. The mixer circuit actually changes the frequency of the incoming signal and is thus a nonlinear circuit.

102. HW 1 1.2 1.11 1.20 1.22 1.48