jaeger/blalock 7/1/03 microelectronic circuit design mcgraw-hill chap 1 - 1 chapter 1 introduction...

Jaeger/Blalock7/1/03

Microelectronic Circuit DesignMcGraw-Hill

Chap 1 - 1

Chapter 1Introduction to Electronics

Microelectronic Circuit DesignRichard C. JaegerTravis N. Blalock



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



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.



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



Chap 1 - 5

Evolution of Electronic Devices

VacuumTubes

DiscreteTransistors

SSI and MSIIntegratedCircuits

VLSISurface-Mount

Circuits



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.



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.



Chap 1 - 8

Rapid Increase in Density of Microelectronics

Memory chip density versus time.

Microprocessor complexity versus time.



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.



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.



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



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



Chap 1 - 13

A/D Converter Transfer Characteristic

V vx (b12 1 b2 2 2 ...bn 2 n )VFS



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



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



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.



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



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.)



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



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



Chap 1 - 21

Circuit Theory Review: Thevenin and Norton Equivalent Circuits



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…



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



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



Chap 1 - 25

Circuit Theory Review: Find the Thevenin Equivalent Resistance

Problem: Find the Thevenin equivalent resistance.

Solution:


• Unknowns: Thevenin equivalent voltage vTH.

• Approach: Voltage source vTH is defined as the output voltage with no load.



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.



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



Chap 1 - 27

Circuit Theory Review: Find the Norton Equivalent Circuit

Problem: Find the Norton equivalent circuit.

Solution:


• Unknowns: Norton equivalent short circuit current iN.

• Approach: Evaluate current through output short circuit.



A short circuit has been applied across the output. The Norton current is the current flowing through the short circuit at the output.



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.



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!



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.



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



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.



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.



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



Chap 1 - 35

Amplifier Input/Output Response

vs = sin2000t V

Av = -5

Note: negative gain is equivalent to 180 degress of phase shift.



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.



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.



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



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:



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.



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



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.



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



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



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



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))



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))



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



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.



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.



Chap 1 - 51

End of Chapter 1

jaeger/blalock 7/1/03 microelectronic circuit design mcgraw-hill chap 1 - 1 chapter 1 introduction...

Documents

review circuit notation

bipolar transistors

blalock slide

approach slide

germanium bipolar transistor

world transistor production

electronics milestones

history of electronics