Chapter 1
Introduction to Electronics
Microelectronic Circuit Design
Richard C. Jaeger
Travis N. Blalock
Modified by Ming Ouhyoung
Microelectronic Circuit Design, 4E
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Chap 1 - 1

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
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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.
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Chap 1 - 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 circuits developed by
Kilby and Noyce
1961 First commercial IC from Fairchild
Semiconductor
1963 IEEE formed from merger of 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
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Chap 1 - 4

• The Nobel Prize in Physics 2000 was awarded
"for basic work on information and communication technology" with one half jointly to Zhores I. Alferov and Herbert Kroemer "for developing semiconductor heterostructures used in high-speed- and opto-electronics" and the other half to Jack S. Kilby "for his part in the invention of the integrated circuit“.
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Chap 1 - 5

Evolution of Electronic Devices
Vacuum
Tubes
Discrete
Transistors
SSI and MSI
Integrated
Circuits
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VLSI
Surface-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 10 18 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.
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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.
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Chap 1 - 8

Rapid Increase in Density of
Microelectronics
Memory chip density versus time.
Microprocessor complexity
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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.
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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.
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Chap 1 - 11

Digital-to-Analog (D/A) Conversion
V
FS
= Full -Scale Voltage
• For an n-bit D/A converter, the output voltage is expressed as:
V
O
 ( b
1
2
 1  b
2
2
 2  ...
 b n
2
 n ) V
FS

• The smallest possible voltage change is known as the least significant bit or LSB.
V
LSB
 2  n V
FS
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Chap 1 - 12


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 output.
input yields a 0000 → 1111 digital
• Output is approximation of input due to the limited resolution of the nbit output. Error is expressed as:
V

 v x
 ( b
1
2
 1  b
2
2
 2  ...
 b n
2
 n
) V
FS
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Chap 1 - 13

A/D Converter Transfer Characteristic

V

 v x
 ( b
1
2
 1  b
2
2
 2  ...
 b n
2
 n ) V
FS
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Chap 1 - 14

Notational Conventions
• Total signal = DC bias + time varying signal i v
T
T


V
DC
I
DC
 v
 i sig sig
• Resistance and conductance - R and G with same subscripts will denote reciprocal quantities. Most convenient form will be used within expressions.
G x

1
R x and g


1 r

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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 and the assumptions.
– Has the problem been solved? Have all the unknowns been found?
– Is the math correct? Have the assumptions been satisfied?
• Evaluate the solution .
– Do the results satisfy reasonableness constraints?
– Are the values realizable?
• Use computer-aided analysis to verify hand analysis
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Chap 1 - 16

What are Reasonable Numbers?
• If the power supply 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 μ A 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.
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Chap 1 - 17



Circuit Theory: Voltage Division (9/19) v
1
 i i
R
1 and v
2
 i i
R
2
Applying KVL (Kirchhoff’s voltage law) to the loop, v i
 v
1
 v and i i
2

 i i

R
1
( R v
1 i

 R
2
R
2
)
Combining these yields the basic voltage division formula:
 v
1
 v i R
1
R
1
 R
2 v
2
 v i R
1
R
2
 R
2
Chap 1 - 18

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



Circuit Theory: Voltage Division (cont.)
Using the derived equations with the indicated values, v
1
 10 V
8 k 
8 k   2 k 
 8.00 V v
2
 10 V
2 k 
8 k   2 k 
 2.00 V
Design Note: Voltage division only applies when both resistors are carrying the same current.
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Chap 1 - 19

Kirchhoff's voltage law (KVL)
• The principle of conservation of energy implies that
– The directed sum of the electrical potential differences
(voltage) around any closed circuit is zero.
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Chap 1 - 20



Circuit Theory: Current Division i i
 i
1
 i
2 where i
1
 v i
R
1 and
Combining and solving for v s
, i
2
 v i
R
2 v i
 i i
1

R
1

1
 i i  R
1
R
1
R
2
 R
2
 i i
R
1
|| R
2
R
2
Combining these yields the basic current division formula: i
1
 i i R
1
R
2
 R
2 i
2
 i i R
1
R
1
 R
2

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Chap 1 - 21



Circuit Theory: Current
Division (cont.)
Using the derived equations with the indicated values, i
1
 5 ma
3 k 
2 k   3 k 
 3.00 mA i
2
 5 ma
2 k 
2 k   3 k 
 2.00 mA
Design Note: Current division only applies when the same voltage appears across both resistors.
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Chap 1 - 22

Kirchhoff's current law (KCL)
• The principle of conservation of electric charge implies that:
– At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node.
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Chap 1 - 23

Circuit Theory: Thévenin and Norton
Equivalent Circuits
Thévenin
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Norton
Chap 1 - 24

Thévenin Equivalent Circuits
( 戴維寧等效電路 )
• The Thévenin-equivalent voltage is the voltage at the output terminals of the original circuit.
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Chap 1 - 25

Thévenin Equivalent Circuits
• The Thévenin-equivalent resistance is the resistance measured across points A and B
"looking back" into the circuit.
• It is important to first replace all voltage- and current-sources with their internal resistances.
• For an ideal voltage source, this means replace the voltage source with a short circuit.
• For an ideal current source, this means replace the current source with an open circuit.
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Circuit Theory: Find the Thévenin
Equivalent Voltage
Problem: Find the Thévenin equivalent voltage at the output.
Solution:
• Known Information and
Given Data: Circuit topology and values in figure.
• Unknowns: Thévenin equivalent voltage v th
.
• Approach: Voltage source v th is defined as the output voltage with no load.
• Assumptions: None.
• Analysis: Next slide…
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Chap 1 - 27



Circuit Theory: Find the Thévenin
Equivalent Voltage
Applying KCL at the output node,
 i
1
 v o

R
1 v i
 v o
R
S

G
1
 v o
 v i

Current i
1 can be written as: i
1


G
S v o
G
1
 v i
 v o

Combining the previous equations
G
1
   1
 v i


G
1
   1
  G
S
 v o v o

G
1

G
1
 
  1

 1


G
S v i

R
1
R
S
R
1
R
S

   1

R
S
   1

R
S
 R
1 v i
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Chap 1 - 28


Circuit Theory: Find the Thévenin
Equivalent Voltage (cont.)
Using the given component values: v o

   1

R
   1

R
S
S
 R
1 v i


50  1

1 k 

50  1

1 k   1 k  v i
 0.718
v i and v th
 0.718
v i

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Chap 1 - 29

Circuit Theory: Find the Thévenin
Equivalent Resistance
Problem: Find the Thévenin equivalent resistance.
Solution:
• Known Information and
Given Data : Circuit topology and values in figure.
• Unknowns : Thévenin equivalent Resistance R th
.
• Approach : Find R th as the output equivalent resistance with independent sources set to zero.
• Assumptions : None.
• Analysis : Next slide…
Test voltage v x previous circuit. Applying v x solving for i x has been added to the
Thévenin resistance as v x
/i x
.
and allows us to find the
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Chap 1 - 30



Circuit Theory: Find the Thévenin
Equivalent Resistance (cont.)
Applying KCL, i x
  i
1
  i
1
 G
S v x
 G
1 v


G
1 x
  G
1 v x
   1
  G
 G
S
 v x
S v x
R th
 v x i x

G
1

1
  1
  G
S
 R
S
R
1
  1
R th
 R
S
R
1
  1
 1 k 
20 k 
50  1
 1 k  392   282 
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Chap 1 - 31

Norton Equivalent Circuits
• Calculate the output current, I
AB circuit as the load.
, with a short
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Chap 1 - 32

Circuit Theory: 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.
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Chap 1 - 33



Circuit Theory: Find the Norton
Equivalent Circuit (cont.)
Applying KCL, i n i n
 i
1
 v i


 i
1
 G
1 v
 G
1 s
  G
1 v
   1
 v i
  1
R
1
 i
Short circuit at the output causes zero current to flow through R
S
R th is equal to R th found earlier.
.

50  1
20 k  v i
 v i
392 
 (2.55 mS) v i
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Chap 1 - 34

Final Thévenin and Norton Circuits
Check of Results: calculations: i n round-off error.
R
Note that v th
=(2.55 mS) v th i
= i n
R th and this can be used to check the
(282  ) = 0.719
v i
, accurate within
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!
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Chap 1 - 35

Ω ℧
• The SI unit of electrical conductance is the siemens , also known as the mho (ohm spelled backwards, symbol is ℧); it is the reciprocal of resistance in ohms.
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Chap 1 - 36

Frequency Spectrum of Electronic
Signals
• Non repetitive 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.
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Chap 1 - 37

Frequencies of Some Common Signals
• Audible sounds
• Baseband TV
• FM Radio
• Television (Channels 2-6)
• Television (Channels 7-13)
• Maritime and Govt. Comm.
• Cell phones and other wireless
• Satellite TV
• Wireless Devices
20 Hz - 20 KHz
0 - 4.5 MHz
88 - 108 MHz
54 - 88 MHz
174 - 216 MHz
216 - 450 MHz
1710 - 2690 MHz
3.7 - 4.2 GHz
5.0 - 5.5 GHz
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Chap 1 - 38

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 )  V
DC

2 V
O


 sin 
0 t 
1
3 sin 3 
0 t 
1
5 sin 5 
0 t  ...



0
=2  /T (rad/s) is the fundamental radian frequency and f the fundamental frequency of the signal. 2f
0
, 3f
0
, 4f
0 second, third, and fourth harmonic frequencies.
0
=1/T (Hz) is and called the
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Chap 1 - 39

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Chap 1 - 40

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Chap 1 - 41

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.
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Chap 1 - 42

Amplifier Linearity
Given an input sinusoid: v i
 V i sin(  i t   )
For a linear amplifier, the output is at the same frequency, but different amplitude and phase.

In phasor notation:
Amplifier gain is:
 v i
A 
 V i
  v o v i 
 v o
 V o
 (    )
V o
 (    )
V i
 

V o
V i
 
 v o
 V o sin(  i t     )

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Chap 1 - 43

Amplifier Input/Output Response v i
= sin2000  t V
A v
= -5
Note: negative gain is equivalent to 180 degrees of phase shift.
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Chap 1 - 44

Ideal Operational Amplifier (Op Amp)
Ideal op amps are assumed to have infinite voltage gain, and infinite 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.
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Chap 1 - 45

Ideal Op Amp Example
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 .

 v i
 i i i i
R
1
 i
2
 i
2

R v
2 i
A v
 i i v o v i

 v
 v v i
R
1
R
1
 
R
2
R
1 o

 0
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Chap 1 - 46

Ideal Op Amp Example
(Alternative Approach)
From Assumption 2, i
2
= i i
:
Yielding:

Design Note: The virtual ground is not an  actual ground. Do not short the inverting input to ground to simplify analysis.
 i i
 v i
R
1
 i
2
A v v i
R
1


 v

 v o
R
2
 v o
R
2 v o v i
 
R
2
R
1

 v o
R
2
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Chap 1 - 47

Amplifier Frequency Response
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:
Low Pass High Pass Band Pass Band Reject All Pass
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Chap 1 - 48

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.
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Chap 1 - 49

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 
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Chap 1 - 50

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 worstcase approach.
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Chap 1 - 51

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 : V
I
I nom , I
I min , I
I max
O nom
.
, V
O min , V
O max
• Approach : Find nominal values and then select R of the unknowns.
1
, R
2
, and V
I values to generate extreme cases
,
• Assumptions : None.
• Analysis : Next slides…
Nominal voltage solution:
V
O nom  V
I nom
 15 V
R
1 nom
R
1 nom
 R
2 nom
18 k 
18 k   36 k 
 5 V
Chap 1 - 52 Microelectronic Circuit Design, 4E
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




Worst-Case Analysis Example (cont.)
Nominal Source current:
I
I nom 
R
1
V
I nom nom  R
2 nom

18 k
15
 
V
36 k 
 278  A
Rewrite V
O to help us determine how to find the worst-case values.
V
O
 V
I R
1
R
1
 R
2

1
V
I

R
2
R
1
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
.
V
O max 
1 
15 V (1.1)
36 K (0.95)
18 K (1.05)
 5.87
V V
O min 
1
15 V (0.95)

36 K (1.05)
18 K (0.95)
 4.20
V
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
Chap 1 - 53

Worst-Case Analysis Example (cont.)

Worst-case source currents:
I
I max 
R
1 min
V
I max
 R
2 min

15 V (1.1)
18 k  (0.95)  36 k  (0.95)
 322  A
I
I min 
R
1 max
V
I min
 R
2 max

15 V (0.9)
18 k  (1.05)  36 k  (1.05)
 238  A

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.
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Monte Carlo Analysis
• Parameters are varied randomly and output statistics are gathered.
• We use programs like MATLAB, Mathcad, SPICE, or a spreadsheet to complete a statistically significant set of calculations.
• For example, a resistor with Epsilon ε% tolerance can be expressed as:
R

R nom
( 1

2

( RAND ()

0 .
5 ))
The RAND() function returns random numbers uniformly distributed between 0 and 1.
Microelectronic Circuit Design, 4E
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Monte Carlo Analysis Result
WC WC
Histogram of output voltage from 1000 case Monte Carlo simulation.
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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:
• Known Information and Given
Data : Circuit topology and values in figure.
• Unknowns : The mean, standard deviation, min, and max for V and P
I
.
O
, I
I
,
• Approach : Use a spreadsheet to evaluate the circuit equations with random parameters.
• Assumptions : None.
• Analysis : Next slides…
Monte Carlo parameter definitions:
V
I
R
1
R
2

 18,000(1  0.1( RAND ()  0.5))

15(1  0.2(
36,000(1 
RAND
0.1(
() 
RAND
0.5))
()  0.5))

Microelectronic Circuit Design, 4E
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Chap 1 - 57


Monte Carlo Analysis Example (cont.)
Monte Carlo parameter definitions:
V
S
 15(1  0.2( RAND ()  0.5))
R
1
 18,000(1  0.1( RAND ()  0.5))
R
2
 36,000(1  0.1( RAND ()  0.5))
Circuit equations based on Monte Carlo parameters:
V
O
 V
I

R
1
R
1
 R
2
I
I

R
1
V
I
 R
2
Results:
I
V o
I
(V)
(mA)
P (mW)
P
I
 V
I
I
I
Avg Nom.
Stdev


5.00
0.30
5.70
0.278 0.0173 0.310
5.87
0.322
4.37
0.242
4.20
0.238
4.12
4.17
0.490
5.04
-3.29
--
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Chap 1 - 58

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.
Microelectronic Circuit Design, 4E
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Chap 1 - 59

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.
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Homework
• Problems 1.24, 1.25
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End of Chapter 1
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