Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction...
-
date post
22-Dec-2015 -
Category
Documents
-
view
310 -
download
3
Transcript of Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction...
![Page 1: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/1.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 1
Chapter 1Introduction to Electronics
Microelectronic Circuit DesignRichard C. JaegerTravis N. Blalock
![Page 2: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/2.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 2
Chapter Goals
• Explore the history of electronics.• Quantify the impact of integrated circuit
technologies.• Describe classification of electronic signals.• Review circuit notation and theory.• Introduce tolerance impacts and analysis.• Describe problem solving approach
![Page 3: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/3.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 3
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.
![Page 4: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/4.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 4
Electronics Milestones
1874 Braun invents the solid-state rectifier.
1906 DeForest invents triode vacuum tube.
1907-1927First radio circuits de-veloped 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 opamp1970 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
![Page 5: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/5.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 5
Evolution of Electronic Devices
VacuumTubes
DiscreteTransistors
SSI and MSIIntegratedCircuits
VLSISurface-Mount
Circuits
![Page 6: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/6.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 6
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 109 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.
![Page 7: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/7.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 7
Device Feature Size
• Feature size reductions enabled by process innovations.
• Smaller features lead to more transistors per unit area and therefore higher density.
![Page 8: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/8.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 8
Rapid Increase in Density of Microelectronics
Memory chip density versus time.
Microprocessor complexity versus time.
![Page 9: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/9.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 9
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.
![Page 10: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/10.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 10
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.
![Page 11: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/11.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 11
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.
VLSB 2 nVFS
VO (b12 1 b2 2 2 ...bn 2 n )VFS
![Page 12: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/12.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 12
Analog-to-Digital (A/D) Conversion
• Analog input voltage vx is converted to the nearest n-bit number.• For a four bit converter, 0 -> vx 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:
V vx (b12 1 b2 2 2 ...bn 2 n )VFS
![Page 13: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/13.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 13
A/D Converter Transfer Characteristic
V vx (b12 1 b2 2 2 ...bn 2 n )VFS
![Page 14: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/14.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 14
Notational Conventions
• 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.
vT VDC VsigiT IDC isig
Gx 1
Rx and g
1
r
![Page 15: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/15.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 15
Problem-Solving Approach
• Make a clear problem statement.• List known information and given data.• Define the unknowns required to solve the problem.• List assumptions.• Develop an approach to the solution.• Perform the analysis based on the approach.• Check the results.
– Has the problem been solved? Have all the unknowns been found?– Is the math correct?
• Evaluate the solution.– Do the results satisfy reasonableness constraints?– Are the values realizable?
• Use computer-aided analysis to verify hand analysis
![Page 16: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/16.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 16
What are Reasonable Numbers?
• If the power suppy is +-10 V, a calculated DC bias value of 15 V (not within the range of the power supply voltages) is unreasonable.
• Generally, our bias current levels will be between 1 uA and a few hundred milliamps.
• A calculated bias current of 3.2 amps is probably unreasonable and should be reexamined.
• Peak-to-peak ac voltages should be within the power supply voltage range.
• A calculated component value that is unrealistic should be rechecked. For example, a resistance equal to 0.013 ohms.
• Given the inherent variations in most electronic components, three significant digits are adequate for representation of results. Three significant digits are used throughout the text.
![Page 17: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/17.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 17
Circuit Theory Review: Voltage Division
v1 isR1
v2 isR2
and
vs v1 v2 is (R1 R2)
is vs
R1 R2
v1 vsR1
R1 R2
v2 vsR2
R1 R2
Applying KVL to the loop,
Combining these yields the basic voltage division formula:
and
![Page 18: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/18.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 18
v1 10 V8 k
8 k 2 k8.00 V
Using the derived equations with the indicated values,
v2 10 V2 k
8 k 2 k2.00 V
Design Note: Voltage division only applies when both resistors are carrying the same current.
Circuit Theory Review: Voltage Division (cont.)
![Page 19: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/19.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 19
Circuit Theory Review: Current Division
is i1 i2
and
i1 isR2
R1 R2
Combining and solving for vs,
Combining these yields the basic current division formula:
where
i2 vsR2
i1 vsR1
and
vs is1
1
R1
1
R2
isR1R2
R1 R2
isR1 || R2
i2 isR1
R1 R2
![Page 20: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/20.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 20
Circuit Theory Review: Current Division (cont.)
i1 5 ma3 k
2 k 3 k3.00 mA
Using the derived equations with the indicated values,
Design Note: Current division only applies when the same voltage appears across both resistors.
i2 5 ma2 k
2 k 3 k2.00 mA
![Page 21: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/21.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 21
Circuit Theory Review: Thevenin and Norton Equivalent Circuits
![Page 22: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/22.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 22
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 vTH.
• Approach: Voltage source vTH is defined as the output voltage with no load.
• Assumptions: None.
• Analysis: Next slide…
![Page 23: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/23.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 23
Circuit Theory Review: Find the Thevenin Equivalent Voltage
i1 vo vsR1
voRS
G1 vo vs GSvo
i1 G1 vo vs
G1 1 vs G1 1 GS vo
vo G1 1
G1 1 GSvs
R1RSR1RS
1 RS
1 RS R1
vs
Applying KCL at the output node,
Current i1 can be written as:
Combining the previous equations
![Page 24: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/24.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 24
Circuit Theory Review: Find the Thevenin Equivalent Voltage (cont.)
vo 1 RS
1 RS R1
vs 501 1 k
501 1 k 1 kvs 0.718vs
Using the given component values:
and
vTH 0.718vs
![Page 25: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/25.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 25
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 voltage vTH.
• Approach: Voltage source vTH is defined as the output voltage with no load.
• Assumptions: None.
• Analysis: Next slide…
Test voltage vx has been added to the previous circuit. Applying vx and solving for ix allows us to find the Thevenin resistance as vx/ix.
![Page 26: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/26.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 26
Circuit Theory Review: Find the Thevenin Equivalent Resistance (cont.)
ix i1 i1 GSvxG1vx G1vx GSvx G1 1 GS vx
Rth vxix
1
G1 1 GSRS
R1
1
Applying KCL,
Rth RSR1
11 k
20 k501
1 k 392 282
![Page 27: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/27.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 27
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 iN.
• 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.
![Page 28: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/28.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 28
Circuit Theory Review: Find the Thevenin Equivalent Resistance (cont.)
iN i1 i1G1vs G1vsG1 1 vs
vs 1 R1
Applying KCL,
iN 501
20 kvs
vs392
(2.55 mS)vs
Short circuit at the output causes zero current to flow through RS.Rth is equal to Rth found earlier.
![Page 29: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/29.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 29
Final Thevenin and Norton Circuits
Check of Results: Note that vTH=iNRth and this can be used to check the calculations: iNRth=(2.55 mS)vs(282 ) = 0.719vs, 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!
![Page 30: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/30.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 30
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.
![Page 31: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/31.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 31
Frequencies of Some Common Signals
• Audible sounds 20 Hz - 20 KHz• Baseband TV 0 - 4.5 MHz• FM Radio 88 - 108 MHz• Television (Channels 2-6) 54 - 88 MHz• Television (Channels 7-13) 174 - 216 MHz• Maritime and Govt. Comm. 216 - 450 MHz• Cell phones 1710 - 2690 MHz• Satellite TV 3.7 - 4.2 GHz
![Page 32: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/32.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 32
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:
v(t) VDC 2VO
sin0t 1
3sin 30t
1
5sin 50t ...
0=2/T (rad/s) is the fundamental radian frequency and f0=1/T (Hz) is the fundamental frequency of the signal. 2f0, 3f0, 4f0 and called the second, third, and fourth harmonic frequencies.
![Page 33: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/33.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 33
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.
![Page 34: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/34.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 34
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:
vs Vs sin(st )
vo Vo sin(st )
v s Vs
vo Vo( )
A vo
v s
Vo( )
VsVoVs
![Page 35: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/35.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 35
Amplifier Input/Output Response
vs = sin2000t V
Av = -5
Note: negative gain is equivalent to 180 degress of phase shift.
![Page 36: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/36.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 36
Ideal Operation Amplifier (Op Amp)
Ideal op amps are assumed to have infinite voltage gain, andinfinite input resistance.
These conditions lead to two assumptions useful in analyzing ideal op amp circuits:
1. The voltage difference across the input terminals is zero.2. The input currents are zero.
![Page 37: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/37.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 37
Ideal Op Amp Example
vs isR1 i2R2 vo 0
is i2 vs vR1
is vsR1
Av vovs
R2
R1
Writing a loop equation:
From assumption 2, we know that i- = 0.
Assumption 1 requires v- = v+ = 0.
Combining these equations yields:
Assumption 1 requiring v- = v+ = 0
creates what is known as a virtual ground.
![Page 38: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/38.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 38
Ideal Op Amp Example (Alternative Approach)
is vsR1
i2 v voR2
voR2
Av vovs
R2
R1
Writing a loop equation:
From assumption 2, we know that i- = 0.
Assumption 1 requires v- = v+ = 0.
Combining these equations yields:
Design Note: The virtual ground is not an actual ground. Do not short the inverting input to ground to simplify analysis.
vsR1
voR2
![Page 39: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/39.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 39
Amplifier Frequency Response
Low-Pass High-Pass BandPass Band-Reject All-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:
![Page 40: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/40.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 40
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.
![Page 41: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/41.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 41
Tolerance Modeling
• For symmetrical parameter variations
PNOM(1 - ) P PNOM(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
![Page 42: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/42.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 42
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 overdesign 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.
![Page 43: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/43.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 43
Worst Case Analysis Example
Problem: Find the nominal and worst-case values for output voltage and source current.
Solution:• Known Information and Given
Data: Circuit topology and values in figure.
• Unknowns: Vonom, Vo
min , Vomax,
ISnom, IS
min, ISmax .
• Approach: Find nominal values and then select R1, R2, and Vs values to generate extreme cases of the unknowns.
• Assumptions: None.• Analysis: Next slides…
Nominal voltage solution:
Vonom VS
nom R1nom
R1nom R2
nom
15V18k
18k 36k5V
![Page 44: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/44.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 44
Worst-Case Analysis Example (cont.)
Nominal Source current:
ISnom
VSnom
R1nom R2
nom
15V
18k 36k278A
Rewrite Vo to help us determine how to find the worst-case values.
Vo VSR1
R1 R2
VS
1R2
R1
Vo is maximized for max Vs, R1 and min R2.
Vo is minimized for min Vs, R1, and max R2.
Vomax
15V (1.1)
136K (0.95)
18K (1.05)
5.87V
Vomin
15V (0.95)
136K (1.05)
18K (0.95)
4.20V
![Page 45: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/45.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 45
Worst-Case Analysis Example (cont.)
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:
ISmax
VSmax
R1min R2
min
15V (1.1)
18k(0.95) 36k(0.95)322A
ISmin
VSmin
R1max R2
max
15V (0.9)
18k(1.05) 36k(1.05)238A
![Page 46: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/46.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 46
Monte Carlo Analysis
• Parameters are varied randomly and output statistics are gathered.
• We use programs like MATLAB, Mathcad, or a spreadsheet to complete a statistically significant set of calculations.
• For example, with Excel, a resistor with 5% tolerance can be expressed as:
The RAND() functions returns random numbers uniformly distributed between 0 and 1.
R Rnom (1 2 (RAND() 0.5))
![Page 47: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/47.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 47
Monte Carlo Analysis Example
Problem: Perform a Monte Carlo analysis and find the mean, standard deviation, min, and max for Vo, Is, and power delivered from the source.
Solution:• Known Information and Given
Data: Circuit topology and values in figure.
• Unknowns: The mean, standard deviation, min, and max for Vo, Is, and Ps.
• Approach: Use a spreadsheet to evaluate the circuit equations with random parameters.
• Assumptions: None.• Analysis: Next slides…
Monte Carlo parameter definitions:
Vs 15(1 0.2(RAND() 0.5))
R1 18,000(1 0.1(RAND() 0.5))
R2 36,000(1 0.1(RAND() 0.5))
![Page 48: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/48.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 48
Monte Carlo Analysis Example (cont.)
Nominal Source current:
ISnom
VSnom
R1nom R2
nom
15V
18k 36k278A
Rewrite Vo to help us determine how to find the worst-case values.
Vo VSR1
R1 R2
VS
1R2
R1
Vo is maximized for max Vs, R1 and min R2.
Vo is minimized for min Vs, R1, and max R2.
Vomax
15V (1.1)
136K (0.95)
18K (1.05)
5.87V
Vomin
15V (0.95)
136K (1.05)
18K (0.95)
4.20V
![Page 49: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/49.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 49
Monte Carlo Analysis Example (cont.)
Histogram of output voltage from 1000 case Monte Carlo simulation.
See table 5.1 for complete results.
![Page 50: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/50.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 50
Temperature Coefficients
• Most circuit parameters are temperature sensitive.
P=Pnom(1+1∆T+ 2∆T2) where ∆T=T-Tnom
Pnom is defined at Tnom
• 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.
![Page 51: Jaeger/Blalock 7/1/03 Microelectronic Circuit Design McGraw-Hill Chap 1 - 1 Chapter 1 Introduction to Electronics Microelectronic Circuit Design Richard.](https://reader033.fdocuments.us/reader033/viewer/2022061418/56649d7a5503460f94a5e940/html5/thumbnails/51.jpg)
Jaeger/Blalock7/1/03
Microelectronic Circuit DesignMcGraw-Hill
Chap 1 - 51
End of Chapter 1