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Digital Electronics
Chap 1
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.
Electronics Milestones
1874
1906
Braun invents the solid-state
rectifier.
DeForest invents triode vacuum
tube.
1907-1927
1925
1947
1952
1956
First radio circuits developed from
diodes and triodes.
Lilienfeld field-effect device patent
filed.
Bardeen and Brattain at Bell
Laboratories invent bipolar
transistors.
Commercial bipolar transistor
production at Texas Instruments.
Bardeen, Brattain, and Shockley
receive Nobel prize.
1958
1961
1963
1968
1970
1971
1978
1974
1984
2000
Integrated circuit developed by
Kilby and Noyce
First commercial IC from Fairchild
Semiconductor
IEEE formed from merger or IRE
and AIEE
First commercial IC opamp
One transistor DRAM cell invented
by Dennard at IBM.
4004 Intel microprocessor
introduced.
First commercial 1-kilobit memory.
8080 microprocessor introduced.
Megabit memory chip introduced.
Alferov, Kilby, and Kromer share
Nobel prize
Evolution of Electronic Devices
Vacuum
Tubes
Discrete
Transistors
SSI and MSI
Integrated
Circuits
VLSI
Surface-Mount
Circuits
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.
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
5 Commandments(cont.)
Wirth’s Law : Software is slowing faster
than hardware is accelerating
 Further Reading: “5 Commandments”,
IEEE Spectrum December 2003, pp. 3135.

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)
DEC PDP-11 CPU
HP PA7000 RISC
Motorola 68020
Motorola 68040
Toshiba MIPS
Intel 8088
Intel 80386
80386 (cont.)
Intel 80486
Intel Pentium
Intel Pentium 4 Prescott
Penryn and Nehalem


Penryn : 45nm Core 2
Architecture : Core 2
Extreme QX9650
Nehalem : Core i7
Intel CPU Evolution
Device Feature Size


Feature size
reductions enabled by
process innovations.
Smaller features lead
to more transistors
per unit area and
therefore higher
density.
Rapid Increase in Density of
Microelectronics
Memory chip density
versus time.
Microprocessor complexity
versus time.
IC Design Step 1: RTL
IC Design 2 : Layout
IC Design 3 : Fabrication
IC Design 4 : Chip
IC Design 5 : System
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.

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

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.
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.
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
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.
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.
Digital-to-Analog (D/A)
Conversion

For an n-bit D/A converter, the output voltage is
expressed as:
1
2
n
VO  (b1 2  b2 2  ...  bn 2 )VFS

The smallest possible voltage change is known as the
least significant bit or LSB.

VLSB  2n VFS
DAC
TI’s 20-bit sigma delta DAC
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  v x  (b1 21  b2 22  ...  bn 2n )VFS
ADC Die Photo

Rockwell Scientific 4Gsps ADC
A/D Converter Transfer
Characteristic
V  v x  (b1 21  b2 22  ...  bn 2n )VFS
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.
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.

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.

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.

Lumped circuit figure
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.
A
i
+
v
B
Notational conventions
Total quantities will be represented by
lowercase letters with capital subscripts,
such as vT anf iT.
 The dc components are represented by
capital letters with capital subscripts as
VDC and IDC; changes or variations from
the dc value are represented by vac and iac.
 vT = VDC + vac
 iT = IDC + iac

+
v1
g m v1
i 1
i 1
(a) VC C S
(b) CC C S
+
v1
A v1
i1
(c) VC VS
(d) CC VS
F igu r e 1 . 1 0 - C o n t r o lled S o u r ces
(a ) Vo lt a ge- co n t r o lled cu r r en t s o u r ce - (VC C S )
(b )C u r r en t - co n t r o lled cu r r en t s o u r ce - (C C C S )
(c) Vo lt a ge- co n t r o lled vo lt a ge s o u r ce - (VC VS )
(d ) C u r r en t - co n t r o lled vo lt a ge s o u r ce - (C C VS ).
i 1
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.
KCL Example



When applying KCL to circuit, first assign reference
direction for each branch.
For node 2, i4-i3-i6=0
For node 1, -i1+i2+i3=0
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.
KVL Example
For loop I, v4+v5-v6=0
 Loop II, v4+v5-v2-v1=0

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.

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.

Circuit Elements
Resistors
 Independent sources
 Capacitors
 Inductors

被動元件
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.
Independent Sources

Independent sources
maintains a prescribed
voltage or current across
the terminals of the
arbitrary circuit to which
it is connected.
Capacitors
Capacitors store electrical
charges.
 i(t) = dq/dt
 q(t) = Cv(t)
 i(t) = Cdv(t)/dt

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)
Inductors
Inductors store energy in
their magnetic fields.
 V(t) = dΦ/dt
 Φ(t)=Li(t)
 V(t) = L di/dt

RLC Effects in Real Circuit
Power (Thermal)
 Time Delay

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
Circuit Theory Review: Voltage Division
v1  i s R1
and
v 2  i s R2
Applying KVL to the loop,
v s  v1  v 2  i s (R1  R2 )
and

is 
vs
R1  R2
Combining these yields the basic voltage division formula:
R1
R2
v1  v s
v2  vs

R1  R2
R1  R2
Circuit Theory Review: Voltage Division
(cont.)
Using the derived equations
with the indicated values,
v1  10 V
8 k
 8.00 V
8 k  2 k
2 k
v 2  10 V
 2.00 V
8 k  2 k
Design Note: Voltage division only applies when both
resistors are carrying the same current.
Circuit Theory Review: Current Division
i s  i1  i 2
where i1 
vs
vs
i

and 2
R2
R1
Combining and solving for vs,
1
RR
v s  i s 
 i s  1 2  i sR1 || R2
1
1
R1  R2

R1 R2
Combining these yields the basic current division formula:
R2
i1  i s
R1  R2
i2  is
R1
R1  R2
and
Circuit Theory Review: Current
Division (cont.)
Using the derived equations
with the indicated values,
i1  5 ma
3 k
 3.00 mA
2 k  3 k
i 2  5 ma
2 k
 2.00 mA
2 k  3 k
Design Note: Current division only applies when the same
voltage appears across both resistors.
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.

Circuit Theory Review: Thevenin
and Norton Equivalent Circuits
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…
Circuit Theory Review: Find the
Thevenin Equivalent Voltage
Applying KCL at the output node,
vo  vs v o
i1 

 G1v o  v s   G S v o
R1
RS
Current i1 can be written as: i1  G1v o  v s 
Combining the previous equations
G1 1vs G1 1 GS v o
G1 1
 1RS
R1RS

vo 
vs 

vs
G1 1  G S
R1RS  1RS  R1
Circuit Theory Review: Find the
Thevenin Equivalent Voltage (cont.)
Using the given component values:
 1RS
50 11 k


vo 
vs 
v s  0.718 v s
 1RS  R1
50 11 k 1 k
and
v TH  0.718 v s
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 RTH.
 Approach: RTH 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 vx has been added to the
previous circuit. Applying vx and
solving for ix allows us to find the
Thevenin resistance as vx/ix.
Circuit Theory Review: Find the
Thevenin Equivalent Resistance (cont.)
Applying KCL,
i x  i1  i1  G S v x
 G1v x  G1v x  G S v x
 G1   1  G S v x
vx
1
R1
Rth 

 RS
i x G1   1  G S
 1
R1
20 k
Rth  RS
 1 k
 1 k 392   282 
 1
50 1
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.
Circuit Theory Review: Find the
Thevenin Equivalent Resistance (cont.)
Applying KCL,
i N  i1  i1
 G1v s  G1v s
 G1  1v s
v s   1

R1
iN 
Short circuit at the output causes
zero current to flow through RS.
Rth is equal to Rth found earlier.
50 1
vs
vs 
 (2.55 mS)v s
20 k
392 
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!
Example : Circuit with a controlled
source






Applying KVL around the loop containing vs
yields
vs = isR1 + i2R2 = isR1 + (is + gmv1)R2 (1.33)
v1 = isR1
(1.34)
vs = is(R1 + R2 + gmR1R2)
(1.35)
Req = vs / is = R1 + R2 (1+ gmR1)
(1.36)
Req = 3KΩ+2KΩ[1+0.1S*3KΩ] = 605 kΩ. This
value is far larger than either R1 or R2.
iS
+
R
1
gmv1
v
1
3 k
0.1 v
-
v
1
i2
S
R
2
2 k
Figure 1.17 - Circuit containing a voltage-controlled current source
iS
KVL
+
R
1
gmv1
v
1
3 k
0.1 v
-
v
1
i2
S
R
2
2 k
Figure 1.17 - Circuit containing a voltage-controlled current source
Circuitry Snacks
from : www.evilmadscientist.com
Joule Thief
555 LED Blink
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.
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
Satellite TV
20 Hz - 20
0 - 4.5
88 - 108
54 - 88
174 - 216
216 - 450
1710 - 2690
3.7 - 4.2
KHz
MHz
MHz
MHz
MHz
MHz
MHz
GHz
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.
Antenna
RF
Amplifier
and Filter
Mixer
(88 - 108 MHz)
IF
Amplifier
and Filter
FM
Detector
10.7 MHz
Audio
Amplifier
50 Hz - 15 kHz
Local
Oscillator
(77.3 - 97.3 MHz)
Figure 1.21 - Block diagram for an FM radio Receiver
Speaker
Amplifier Input/Output
Response
vs = sin2000t V
Av = -5
Note: negative
gain is equivalent
to 180 degress of
phase shift.
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
BandPass
Band-Reject
All-Pass
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.
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 

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.
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.

HW 1
1.2
 1.11
 1.20
 1.22
 1.48
