text stringlengths 16 3.88k | source stringlengths 60 201 |
|---|---|
2
�
� E¯ 2 +
|
|
| −
·
|
= −
− E ¯ J ¯
·
dV = E ¯ × H ¯ · dS ¯
�
V
�
�
E ¯ × H ¯ +
� ·
E ¯ × H ¯ �
� · �
�
¯ H ¯
E × · d¯
a +
S
S
d
dt
� �
V
1
� E 2 + µ ¯
| ¯ |
2
1
2
|H|2
�
�
¯
= − E · J dV
¯
dV
V
S ¯ = E ¯ × H ¯
W = �
� 1
2 �|E¯ |2 + 1
V
�
¯
¯
·
Pd = V E J dV
2 µ|H¯ |2 �
dV
�
�
Po... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/2f455332ba1548a8db83ef1d78592088_lec8.pdf |
= −�Φ (Kirchoff’s Voltage Law
�
k vk = 0
(Kirchoff’s current law
�
k
ik = 0
� × H ¯ = J ¯ ⇒ � · J ¯ = 0,
�
S
J ¯ · dS ¯ = 0
�
Pin = − E ¯ × H ¯ dS ¯
S
¯ �
�
¯
= − � · E × H dV
�
·
�
E ¯
0
−
� · �
� × �
V
��
E ¯ × H ¯ = H ¯ ���
· � × ¯
E
� · �
= ����� 0
�
· �
� · J ¯ + J ¯ (�Φ)
�
J¯Φ
·
�
� ... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/2f455332ba1548a8db83ef1d78592088_lec8.pdf |
H¯ˆ (¯r)ejωt �
�
H¯ (¯r, t) = Re
=
=
E¯ˆ(¯r)ejωt + Eˆ¯∗(¯r)e−jωt �
1 �
2
Hˆ¯ (¯r)ejωt + Hˆ¯ ∗(¯r)e−jωt �
1 �
2
�
��
�
The real part of a complex number is
one-half of the sum of the number and its
complex conjugate
2
Maxwell’s Equations in Sinusoidal Steady State
� × Eˆ¯(¯r) = −jωµ Hˆ¯ (¯r)
� × Hˆ¯ (... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/2f455332ba1548a8db83ef1d78592088_lec8.pdf |
�
1
Eˆ¯(¯r) × Hˆ¯ ∗(¯r)
Re
2
ˆ
¯
�
�
Eˆ¯∗(¯r) × Hˆ¯ (¯r)
Re
� �
¯
S =
=
=
1
2
=
ˆ
¯
(A complex number plus its complex conjugate is twice the real part of that number.)
�
� · Sˆ = � ·
¯
Sˆ¯ =
�
1
Eˆ(¯r) × Hˆ ∗(¯r)
¯
2
=
¯
=
=
1
E¯ˆ(¯r) × H¯ˆ (¯r)∗
2
1 �
2
1 �
2
1
2
�
Hˆ ∗(¯r) · � × Eˆ(¯r) − Eˆ... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/2f455332ba1548a8db83ef1d78592088_lec8.pdf |
(ρf = 0, J ¯ = 0)
A. Wave equation
H ¯
∂
∂t
∂E ¯
∂t
� × ¯
E = −µ
¯
� × H = �
� · ¯
E = 0
� · H ¯ = 0
3
�
�
� × � × ¯
∂ �
� ×
E = −µ
∂t
�
������0
E
�
E
�
� × � × ¯ = � � · ¯ − �
2 ¯
E = −�µ
¯ �
H = −µ
∂ �
�
∂t
∂E ¯ �
∂t
∂2E ¯
∂t2
Wave equation
�2E ¯ =
1 ∂2E ¯
c ∂t2
2
�µ is the speed of... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/2f455332ba1548a8db83ef1d78592088_lec8.pdf |
c2
ˆEx
d2 ˆEx
dz2 = −
+ k2Eˆx = 0
d2Eˆx
dz2
4
Ex- = Re[Ex-(z)exp ](j t)Ex+ = Re[Ex+ (z)exp ](j t)Hy+ = Re[Hy+ (z)exp ](j t)Kx = Re[K0 exp ](j t)Hy- = Re[Hy-(z)exp ](j t)e, me, mxyzwwwww where we have
is the wavenumber, λ is the wavelength
ω2
k2 = 2 = ω2�µ
c
2π
λ
k = ±
k =
⇒
ω
c
ω = kc
ω = 2πf =
2π ... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/2f455332ba1548a8db83ef1d78592088_lec8.pdf |
> 0
2 ¯iz z < 0
(Kˆ 0 real)
Ex(z, t) = Re Ex(z)e
�
ˆ
�
jωt
=
Hˆy(z)ejωt �
�
Hy(z, t) = Re
=
Sz = ExHy =
�Sz� =
�
�
�
−
−
�
cos(ωt − kz) z > 0
cos(ωt + kz) z < 0
ηK0
2
ηK0
2
− K
0 cos(ωt − kz) z > 0
2
+ K
0 cos(ωt + kz) z < 0
2
ηK2
0 cos2(ωt − kz)
4
− ηK0
4
2
ηK0
8
2
ηK0
−
8
z > 0
cos2(ω... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/2f455332ba1548a8db83ef1d78592088_lec8.pdf |
From Electromagnetic Field Theory: A Problem Solving Approach, by Markus Zahn, 1987. Used with permission.
For Eˆi = Ei real we have:
�
Ex(z, t) = Ex,i(z, t) + Ex,r(z, t) = Re Eˆi e−jkz − e +jkz ejωt
� �
�
Hy(z, t) = Hy,i(z, t) + Hy,r(z, t) = Re
= 2Ei sin(kz) sin(ωt)
�
Eˆi �
η
e−jkz + e +jkz �
�
ejωt
=
2E... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/2f455332ba1548a8db83ef1d78592088_lec8.pdf |
|Eˆi|2
2η1
1
2η2
Re
|Eˆi|2 − | Eˆr|2 �
�
�
1
EˆrEˆ
Re
2η1
�
|Eˆi|2 − | Eˆr|2 �
�
1 − R2�
�
∗e 2jk1z − Eˆ
i
��
pure imaginary
r
∗Eˆie−2jk1z �
�
|Eˆt|2 =
ˆ 2T 2
|E
i|
η2
2
=
| ˆ |
Ei
2(1 − R2)
2η1
= �Sz,i�
V. Lossy Dielectrics - J ¯ = σE ¯
Ampere’s Law: � × H ¯ = J ¯ + � ∂ ¯ = σE ¯ + � ∂ ¯
E
∂t
... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/2f455332ba1548a8db83ef1d78592088_lec8.pdf |
Wave-particle Duality: Electrons are not just particles
• Compton, Planck, Einstein
– light (xrays) can be ‘particle-like’
• DeBroglie
– matter can act like it has a ‘wave-nature’
• Schrodinger, Born
– Unification of wave-particle duality, Schrodinger
Equation
©1999 E.A. Fitzgerald
1
Light has momentum: Compt... | https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/2f6b82d24ba7b65e1fa265e8dec88989_lecture_3.pdf |
L
Therefore, sinkz must equal zero at z=0 and z=L
sin kL = 0; kL =πn; k =
n
π
L
Also, since k=2π/λ,
n =
L
2
λ
or λ=
L
2
n
In 3-D, λ=
2L
2 + n 2
nx
2
y + nz
Note that the wavelength for E-M
waves is ‘quantized’ classically just by
applying a confining boundary
condition
ν =
c nx
2 + nz
2
2 + n ... | https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/2f6b82d24ba7b65e1fa265e8dec88989_lecture_3.pdf |
3
L3
=
2
8πν kT
c 3
The classical assumption was used, i.e. Ewave=kbT
This results in a ρ (ν ) that goes as ν 2
At higher frequencies, blackbody radiation deviates substantially from this dependence
©1999 E.A. Fitzgerald
6
800
600
)
)
m
n
/
J
k
(
400
)
l
(
u
200
y
t
i
s
n
e
t
n
I
Missing higher frequencies
T... | https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/2f6b82d24ba7b65e1fa265e8dec88989_lecture_3.pdf |
than ρ (ν ) would not have ν 2 dependence at higher ν
•P(E) will decrease at higher E if E is a function of ν
•Experimental fit to data suggests that E is a linear function in ν , therefore E=nhν where h
is some constant
E =
nhν
−
e kbT
nhν =
−
e
k T
b
∞
∑ nhν
0 k T
b
∞ 1
∑
0 kbT
hν
hν
e k T − 1
b
... | https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/2f6b82d24ba7b65e1fa265e8dec88989_lecture_3.pdf |
intensity, no e
-
©1999 E.A. Fitzgerald
11
Light is always quantized: Photoelectric
effect (Einstein)
Ein=hν
E
EF
vacuum
ΔE
Evac=Ein-ΔE
Emax=Ein-ΔE=hν-hνc
x
Ein=hν!
Strange consequence of Compton plus E=hν: light has momentum but no mass
λ=
hc
E
=
h
p
since E = cp for a photon
©1999 E.A. Fitzgerald
... | https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/2f6b82d24ba7b65e1fa265e8dec88989_lecture_3.pdf |
Example of Diffraction from Thin Film of
Different Lattice Constant
•
InGaAs on GaAs deposited by molecular beam epitaxy (MBE)
• Can determine lattice constant (In concentration) and film thickness
from interference fringes
GaAs
InxGa1-xAs
Interference fringes
from optical effect
GaAs
X-ray
intensity
In0.05G... | https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/2f6b82d24ba7b65e1fa265e8dec88989_lecture_3.pdf |
Gex Layers
(each layer about 3000A)
©1999 E.A. Fitzgerald
39
20 | https://ocw.mit.edu/courses/3-225-electronic-and-mechanical-properties-of-materials-fall-2007/2f6b82d24ba7b65e1fa265e8dec88989_lecture_3.pdf |
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(cid:10) 6.642 Continuum Electromechanics
Fall 2008
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
(cid:13)
6.642, Continuum Electromechanics, Fall 2004
Prof. Markus Zahn
Lecture 9: Plasma Stability (z-θ pinch)
Continuum E... | https://ocw.mit.edu/courses/6-642-continuum-electromechanics-fall-2008/2f958b16182841cc15aec7ee419806bc_lec09_f08.pdf |
⎞
⎟
⎠
- H + h
a
(
z
2
)
⎤
⎥
⎥
⎦
≈
1
2
⎡
μ ⎢
⎣
0
-H - 2H h -
t
θ
2
t
⎛
⎜
⎝
H
ξ
t
R
⎞
⎟
⎠
- H - 2H h
a z
2
a
⎤
⎥
⎦
'T =
rr
−μ
0
⎡
⎣
H h - H R + H h
ξ
t
θ
a
t
)
(
⎤
⎦z
T = h Hμ
0 r
rθ
t
T n = h H n
μ
t θ
rθ θ
0 r
second order
6.642, Continuum Electromechanics Lecture 9
Prof. Markus Zahn Page 3 of 5
... | https://ocw.mit.edu/courses/6-642-continuum-electromechanics-fall-2008/2f958b16182841cc15aec7ee419806bc_lec09_f08.pdf |
(cid:108)
Ψ
c
= kF
m
(
)
a, R
⎡
(cid:3)
ξ ⎢
⎣
m
R
H + kH
t
a
⎤
⎥
⎦
IV. Dispersion Relation
2
ω ρ
(cid:3)
)
F 0, R = - H F
ξ
μ
(
m
0
t m
(
a, R
)
m m
(cid:3)
ξ
R
R
⎡
⎢
⎣
+
(cid:3)
γξ ⎡
2
1 - m - kR
⎣
R
(
2
2
)
⎤
⎦
H + kH +
a
t
⎤
⎥
⎦
μ
2
H
0
t
R
(cid:3)
ξ μ
- H kF
0
a
m
(
)
a, R
(cid:3)
ξ
m
R
⎡
⎢
⎣
H + kH
t
a
⎤
⎥
⎦
2... | https://ocw.mit.edu/courses/6-642-continuum-electromechanics-fall-2008/2f958b16182841cc15aec7ee419806bc_lec09_f08.pdf |
�
2
kR + m - 1 + F
0 m
μ
2
)
⎤
⎦
(
a, R
)
m
R
⎡
⎢
⎣
H + kH
t
a
2
⎤
⎥
⎦
-
μ
2
H
0
t
R
Stabilizing
Destabilizing
6.642, Continuum Electromechanics Lecture 9
Prof. Markus Zahn Page 4 of 5
V. Stability
Surface tension: stabilizing for m≥1
destabilizing ... | https://ocw.mit.edu/courses/6-642-continuum-electromechanics-fall-2008/2f958b16182841cc15aec7ee419806bc_lec09_f08.pdf |
9v† ^_wífë¢â ô_ífA9_ío Aí 9†¢Uo _m 9v† B†à_ôA9â õ_9†í9Aëà φ f†Üí†f ^â
ï}I UI àa F
φ;
∇
MIT OpenCourseWare
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2.062J / 1.138J / 18.376J Wave Propagation
Spring 2017
For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms. | https://ocw.mit.edu/courses/2-062j-wave-propagation-spring-2017/2f9f71f7f386b36c9c42f48c03aecfe6_MIT2_062J_S17_Chap1.pdf |
6.891: Lecture 4 (September 20, 2005)
Parsing and Syntax II
Overview
• Weaknesses of PCFGs
• Heads in context-free rules
• Dependency representations of parse trees
• Two models making use of dependencies
Weaknesses of PCFGs
• Lack of sensitivity to lexical information
• Lack of sensitivity to structural frequen... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
probable.
Attachment decision is completely independent of the words
A Case of Coordination Ambiguity
NP
CC
and
NP
NNS
cats
(a)
NP
NP
PP
NNS
IN
NP
dogs
in
NNS
houses
(b)
NP
NP
NNS
dogs
IN
in
PP
NP
NP
CC
NP
NNS
and NNS
houses
cats
(a)
Rules
NP � NP CC NP
NP � NP PP
NP � NNS
PP � IN... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
Vi
VP ∈ Vt NP
VP ∈ VP PP
NP ∈ DT NN
NP ∈ NP PP
IN NP
PP ∈
Vi ∈ sleeps
Vt ∈ saw
NN ∈ man
NN ∈ woman
NN ∈
DT ∈
IN ∈ with
IN ∈
telescope
the
in
Note: S=sentence, VP=verb phrase, NP=noun phrase, PP=prepositional
phrase, DT=determiner, Vi=intransitive verb, Vt=transitive verb, NN=noun,
IN=preposition
M... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
VP ∈ Vt NP
VP ∈ VP PP
Adding Headwords to Trees
S
NP
VP
DT
the
NN
lawyer
Vt
NP
questioned
DT
the
NN
witness
�
S(questioned)
NP(
lawyer
)
VP(questioned)
DT(the)
NN(lawyer)
the
lawyer
Vt(questioned)
NP(witness)
questioned
DT(the) NN(witness)
the
witness
Adding Headwords to Trees
S(question... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
grammar:
• N is a set of non-terminal symbols
• � is a set of terminal symbols
• R is a set of rules which take one of three forms:
– X(h) � Y1(h) Y2(w) for X � N , and Y1, Y2 � N , and h, w � �
– X(h) � Y1(w) Y2(h) for X � N , and Y1, Y2 � N , and h, w � �
– X(h) � h for X � N , and h � �
• S � N is a distingui... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
Logical form/Predicate-argument structure
Adding Predicate Argument Structure to our Grammar
• Identify words with lambda terms:
likes
Bill
Clinton Clinton
�y, x
Bill
like(x, y)
• Semantics for an entire constituent is formed by applying
semantics of head (predicate) to the other children (arguments)
[�y, x
=
... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
and Dependencies
S(told,V[6])
NP(yesterday,NN) NP(Hillary,NNP)
VP(told,V[6])
�
(told, V[6], yesterday, NN, S, VP, NP, LEFT)
(told, V[6], Hillary, NNP, S, VP, NP, LEFT)
A Special Case: the Top of the Tree
TOP
S(told,V[6])
�
( ,
, told, V[6], TOP, S,
, SPECIAL)
S(told,V[6])
NP(Hillary,NNP)
VP(told,V[6])
NNP ... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
,Vt)
Smoothed Estimation
P (NP( ,NN) VP | S(questioned,Vt)) =
�1 ×
Count(S(questioned,Vt)�NP( ,NN) VP)
Count(S(questioned,Vt))
+�2 ×
Count(S( ,Vt)�NP( ,NN) VP)
Count(S( ,Vt))
• Where 0 � �1, �2 � 1, and �1 + �2 = 1
Smoothed Estimation
P (lawyer | S,VP,NP,NN,questioned,Vt) =
�1 ×
Count(lawyer | S,VP,NP,NN,questio... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
(questioned,Vt)
NP( ,NN) VP(questioned,Vt)
• Relies on counts of entire rules
• These counts are sparse:
– 40,000 sentences from Penn treebank have 12,409 rules.
– 15% of all test data sentences contain a rule never seen in training
Motivation for Breaking Down Rules
Rule Count No. of Rules Percentage No. of Rul... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
ov Processes
• Step 2: generate left modifiers in a Markov chain
S(told,V[6])
??
NP(Hillary,NNP)
VP(told,V[6])
∈
S(told,V[6])
NP(yesterday,NN) NP(Hillary,NNP)
VP(told,V[6])
Ph(VP | S, told, V[6]) × Pd(NP(Hillary,NNP) | S,VP,told,V[6],LEFT)×
Pd(NP(yesterday,NN) | S,VP,told,V[6],LEFT)
Modeling Rule Productions ... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
,VP,told,V[6],LEFT) ×
Pd(STOP | S,VP,told,V[6],RIGHT)
A Refinement: Adding a Distance Variable
• � = 1 if position is adjacent to the head.
S(told,V[6])
?? VP(told,V[6])
≈
S(told,V[6])
NP(Hillary,NNP)
VP(told,V[6])
Ph(VP | S, told, V[6])×
Pd(NP(Hillary,NNP) | S,VP,told,V[6],LEFT,� = 1)
A Refinement: Adding a Di... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
illary,NNP)
VP(told,V[6])
NN
yesterday
NNP
Hillary
V[6]
. . .
told
• Hillary is the subject
• yesterday is a temporal modifier
• But nothing to distinguish them.
Adding the Complement/Adjunct Distinction
VP
V
NP
verb object
VP(told,V[6])
V[6]
told
NP(Bill,NNP)
NP(yesterday,NN) SBAR(that,COMP)
NNP
... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
-C(that,COMP)
NNP
Bill
NN
yesterday
. . .
Adding Subcategorization Probabilities
• Step 1: generate category of head child
S(told,V[6])
≈
S(told,V[6])
VP(told,V[6])
Ph(VP | S, told, V[6])
Adding Subcategorization Probabilities
• Step 2: choose left subcategorization frame
S(told,V[6])
VP(told,V[6])
≈
S(... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
(told,V[6])
{}
�
S(told,V[6])
STOP
NP(yesterday,NN) NP-C(Hillary,NNP)
VP(told,V[6])
{}
Ph(VP | S, told, V[6]) × Plc ({NP-C} | S, VP, told, V[6])
Pd(NP-C(Hillary,NNP) | S,VP,told,V[6],LEFT,{NP-C})×
Pd(NP(yesterday,NN) | S,VP,told,V[6],LEFT,{})×
Pd(STOP | S,VP,told,V[6],LEFT,{})
The Final Probabilities
S(told,... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
P) | VP,V[6],told,V[6],RIGHT,� = 1,{NP-C, SBAR-C})×
Pd(NP(yesterday,NN) | VP,V[6],told,V[6],RIGHT,� = 0,{SBAR-C})×
Pd(SBAR-C(that,COMP) | VP,V[6],told,V[6],RIGHT,� = 0,{SBAR-C})×
Pd(STOP | VP,V[6],told,V[6],RIGHT,� = 0,{})
Summary
• Identify heads of rules ∈ dependency representations
• Presented
two variants of PCF... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
– Decision Trees (Magerman 95) 84.0%
85.3%
Lexical Dependencies (Collins 96)
86.3%
Conditional Models – Logistic (Ratnaparkhi 97)
86.7%
Generative Lexicalized Model (Charniak 97)
87.5%
Model 1 (no subcategorization)
88.1%
Model 2 (subcategorization)
74.8%
84.3%
85.7%
87.5%
86.6%
87.7%
88.3%
Effect of... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
VP attachment:
(S (NP The men) (VP dumped (NP sacks) (PP of (NP the substance))))
S(told,V[6])
NP-C(Hillary,NNP)
VP(told,V[6])
NNP
Hillary
V[6](told,V[6])
NP-C(Clinton,NNP)
SBAR-C(that,COMP)
V[6]
told
NNP
Clinton
COMP
that
S-C
NP-C(she,PRP)
VP(was,Vt)
PRP
she
Vt
NP-C(president,NN)
was
NN
presid... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
40.55
48.72
54.03
59.30
64.18
68.71
73.13
74.53
75.83
77.08
78.28
79.48
80.40
81.30
82.18
82.97
P
29.65
10.90
8.17
5.31
5.27
4.88
4.53
4.42
1.40
1.30
1.25
1.20
1.20
0.92
0.90
0.88
0.79
Count Relation
11786 NPB TAG TAG L
PP TAG NP-C R
4335
S VP NP-C L
3248
NP NPB PP R
2112
VP TA... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
Count
Recall
Precision
Complement to a verb
6495 = 16.3% of all cases
Other complements
7473 = 18.8% of all cases
Subject
Object
S VP NP-C L
VP TAG NP-C R
VP TAG SBAR-C R
VP TAG SG-C R
VP TAG S-C R
S VP S-C L
S VP SG-C L
...
TOTAL
PP TAG NP-C R
VP TAG VP-C R
SBAR TAG S-C R
SBAR WHNP SG-C R
PP TAG ... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
R
ADVP TAG PP R
NP NP PP R
PP PP PP L
NAC TAG PP R
...
TOTAL
NP NP NP R
VP VP VP R
S S S R
ADJP TAG TAG R
VP TAG TAG R
NX NX NX R
SBAR SBAR SBAR R
PP PP PP R
...
TOTAL
2112
1801
287
90
35
23
19
12
4473
289
174
129
28
25
25
19
14
84.99
83.62
90.24
75.56
68.57
0.00
21.05
50.00
82... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
91
51.72
14.81
66.67
93.20
74.34
79.20
77.56
88.89
45.28
35.42
62.50
93.46
92.82
75.68
71.24
81.65
71.43
66.67
76.92
92.59
75.72
79.54
72.60
81.16
60.00
54.84
69.77
1418
73.20
75.49
Type
Sentential head
1917 = 4.8% of all cases
Adjunct to a verb
2242 = 5.6% of all cases
Sub-type
De... | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
.00
2242
75.11
78.44
Some Conclusions about Errors in Parsing
• “Core” sentential structure (complements, NP chunks)
recovered with over 90% accuracy.
• Attachment ambiguities involving adjuncts are resolved with
much lower accuracy (� 80% for PP attachment, � 50 − 60%
for coordination). | https://ocw.mit.edu/courses/6-864-advanced-natural-language-processing-fall-2005/2fcb90c84d2859c5292fdebfad49b464_lec4.pdf |
6.045: Automata, Computability, and
Complexity
Or, Great Ideas in Theoretical
Computer Science
Spring, 2010
Class 10
Nancy Lynch
Today
• Final topic in computability theory: Self-Reference
and the Recursion Theorem
• Consider adding to TMs (or programs) a new,
powerful capability to “know” and use their own
desc... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
3 >
– Run P3 on w
– If P3 on w outputs a number n then output n+1.
• A valid self-referencing program.
• What does P3 compute?
• Seems contradictory: if P3 on w outputs n then P3
on w outputs n+1.
• But according to the usual semantics of recursive
calls, it never halts, so there’s no contradiction.
• P3 computes a pa... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
r(w) = t(<R>, w).
<M>
w
• Example: P2, revisited
– Computes length of input.
– What are T and R?
– Here is a version of P2 with an extra
input <M>:
– T2: On inputs <M> and w:
• If w = ε then output 0
• Else run M on tail(w); if it outputs n then
output n+1.
T
R
t(<M>, w)
w
t(<R>, w)
The Recursion Theorem
• Example:... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
computes the function r: Σ* → Σ*,
where for any w, r(w) = t(<R>, w).
w
R
t(<R>, w)
Applications of the Recursion
Theorem
Applications of Recursion Theorem
• The Recursion Theorem can be used to show various
negative results, e.g., undecidability results.
• Application 1: AccTM is undecidable
– We already know this... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
:
– If R accepts w, then
• D accepts <R, w> since D is a decider for AccTM, so
• R rejects w by definition of R.
– If R does not accept w, then
• D rejects <R, w> since D is a decider for AccTM, so
• R accepts w by definition of R.
• Contradiction. So D can’t exist, so AccTM is undecidable.
Applications of Recursion... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
recognizable languages. Let MP = { < M > | L(M)
∈ P }. Then MP is undecidable.
– Nontriviality: There is some M1 with L(M1) ∈ P, and
some M2 with L(M2) ∉ P.
– Implies lots of things are undecidable.
– We already proved this; now, a new proof using the
Recursion Theorem.
– Suppose for contradiction that D is a TM tha... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
L(R) ∈ P, then
• D accepts <R>, since D decides MP, so
• L(R) = L(M2) by definition of R, so
• L(R) ∉ P.
Application 3: Using Recursion
Theorem to prove Rice’s Theorem
• Rice’s Theorem: Let P be a nontrivial property of Turing-
recognizable languages. Let MP = { < M > | L(M) ∈ P }.
Then MP is undecidable.
• L(M1) ∈... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
recognizable.
– Then it’s enumerable, say by enumerator TM E.
– R: On input w:
• Obtain <R>.
• Run E, producing list < M1 >, < M2 >, … of all minimal TMs, until
you find some < Mi > with |< Mi >| strictly greater than |< R >|.
– That is, until you find a TM with a rep bigger than yours.
• Run Mi(w) and do the same thi... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
izer).
– If not, we don’t care what B does.
• B outputs the encoding of the combination of two
machines, P<M> and M.
• The first machine is P<M>, which simply outputs <M>.
• The second is the input machine M.
• P<M> ° M:
<M>
P<M>
M
Some output
Construction of B
< P<M> ° M >
<M>
B
• How can B generate < P<M> ° M >?
– ... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
is not the general RT.
• RT says not just that:
– There is a TM that outputs its own description.
• But that:
– There are TMs that can use their own descriptions, in
“arbitrary ways”.
• The “arbitrary ways” are captured by the
machine T in the RT statement.
<M>
w
T
t(<M>, w)
The Recursion Theorem
• Recursion Theorem... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
-input TM, which uses output of
P<M> as first input of M.
P<M>
M
Combining the Pieces
• R = (A ° B) °1 T
A
B
w
T
• Claim R outputs t(<R>, w):
• A is P<B °1 T>, so the output from A to B is <B °1 T >:
<B °1 T >
< P<B °
1
T > °1 (B °1 T) >
A = P<B °1 T>
B
<M>
< P<M> °1 M >
B
• Now recall definition of B:
• Plug in B ° ... | https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/2fe1aea3ab4dd67aff81f2a04fc010ef_MIT6_045JS11_lec10.pdf |
Examples of Transient RC and RL Circuits.
The Series RLC Circuit
Impulse response of RC Circuit.
Let’s examine the response of the circuit shown on Figure 1. The form of the source
voltage Vs is shown on Figure 2.
R
Vs
C
+
vc
-
Figure 1. RC circuit
Vs
Vp
0
tp
Figure 2.
t
We will investigate the response
vc t
( ... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
⎝
−
+
=
1
2
⎛
⎜
⎜
⎝
+
⎤
…⎥
⎥
⎦
⎞
⎟
⎟
⎠
0
t
≤ ≤
tp
(1.3)
When
RC t(cid:21)
the higher order terms may be neglected resulting in
vc t
( )
(cid:17)
Vp
t
RC
0
t
≤ ≤
tp
At the end of the pulse (at
t
tp=
) the voltage becomes
vc t
(
=
tp
)
(cid:17)
Vptp
RC
6.071/22.071 Spring 2006, Chaniotakis and Cory
(1.4)
(1.5)
2... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
The spark plug in your car (a simplified model)
Consider the circuit shown on Figure 5. The battery Vb corresponds to the 12 Volt car
battery. The spark plug is connected actors the inductor and current may flow though it
only if the voltage across the gap of the plug exceeds a very large value (about 20 kV).
+
Vb
... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
t
−
0.002
The voltage across the coil when the switch is opened is
v L
=
i
∆
t
∆
=
0.01
2.4
1 10
×
−
6
=
24
kV
6.071/22.071 Spring 2006, Chaniotakis and Cory
5
Response of RC circuit driven by a square wave.
Let’s now consider the RC circuit shown on Figure 6(a) driven by a square wave signal o... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
T
−
RC
⎤
⎥
⎦
+
t
−
RC
⎤
Vp e
⎥
⎥
⎦
(1.13)
(1.14)
Similarly the response during the first part of the second cycle starts with the value of vc
at t=T and evolves towards the value Vp.
If the time constant is small compared to the period of the square wave, the response will
reach the maximum and minimum values of... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
circuit. We will analyze this
circuit in order to determine its transient characteristics once the switch S is closed.
Vs
S
+ vR -
+ vL -
R
L
C
+
vc
-
Figure 10
The equation that describes the response of the system is obtained by applying KVL
around the mesh
vR vL vc Vs
+
=
+
The current flowing in the circuit is... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
2s
= − +
2
α α ω
ο
−
2
= − −
2
α α ω
ο
−
2
And the homogeneous solution becomes
hvc
=
A e
1
1
s t
2
s t
+
A e
2
The total solution now becomes
vc Vs A e
1
=
+
s t
1
+
A e
2
s t
2
6.071/22.071 Spring 2006, Chaniotakis and Cory
(1.22)
(1.23)
(1.24)
(1.25)
(1.26)
(1.27)
(1.28)
(1.29)
11
... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
As the resistance increases the value of α increases and the system is driven
towards an over damped response.
• The frequency
1
LC
or the resonant frequency.
οω =
(rad/sec) is called the natural frequency of the system
• The quantity
L
C
has units of resistance
Figure 11 shows the response of the series RLC c... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
)ο
t
(1.30)
(1.31)
(1.32)
(1.33)
(1.34)
(1.35)
The constants A1, A2 or B1, B2 are determined from the initial conditions of the system.
6.071/22.071 Spring 2006, Chaniotakis and Cory
14
For
vc t
(
=
0)
=
Vo
and for
have from Equation (1.34)
0... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
less system
6.071/22.071 Spring 2006, Chaniotakis and Cory
15
(a) Voltage across the capacitor
(b) Voltage across the inductor
(c)Current flowing in the ciruit
Figure 13
6.071/22.071 Spring 2006, Chaniotakis and Cory
16
(a) Energy stored in the capaci... | https://ocw.mit.edu/courses/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/3021be47ce51060507c5fa54373f2d78_trns1_rc_lc_rlc1.pdf |
Image Quality Metrics
• Image quality metrics
• Mutual information (cross-entropy) metric
• Intuitive definition
• Rigorous definition using entropy
• Example: two-point resolution problem
• Example: confocal microscopy
• Square error metric
• Receiver Operator Characteristic (ROC)
• Heterodyne detection
MIT 2.71... | https://ocw.mit.edu/courses/2-717j-optical-engineering-spring-2002/302f8fb4454a52e44502785c2e046203_imgq.pdf |
2
k 1=
ln
+
1
2
ln +
1
µ
2
−
2
t
2σ
µ
k
=
2σ
ln
+
+
1
≈precision
of (t-2)th measurement
E.g. 0.5470839348
these digits worthless
if σ ≈10-5
MIT 2.717
Image quality metrics p-5
2
<
<
−µ
σ
µ
2
2
t
t 1
noise floor
−µ
σ
2
t 1
2 +
+
ln
1
... | https://ocw.mit.edu/courses/2-717j-optical-engineering-spring-2002/302f8fb4454a52e44502785c2e046203_imgq.pdf |
1
1
2
• Unfair coin: p(H)=1/4; p(T)=3/4
1
Entropy = −
4
log2
log
2
1
4
3
4
−
3
=
4
81.0
bits
Maximum entropy ⇔⇔⇔⇔⇔⇔⇔⇔ Maximum uncertainty
Maximum uncertainty
Maximum entropy
MIT 2.717
Image quality metrics p-7
Formal definition of cross-entropy (3)
Joint Entropy
Joint Entropy
log2[how many are the possible ... | https://ocw.mit.edu/courses/2-717j-optical-engineering-spring-2002/302f8fb4454a52e44502785c2e046203_imgq.pdf |
eliminates information
adds uncertainty to the measurement wrt the object
eliminates information from the measurement wrt object
MIT 2.717
Image quality metrics p-10
Formal definition of cross-entropy (6)
uncertainty added due to noise
representation by
Seth Lloyd, 2.100
Entropy(
)F
information
contained
in th... | https://ocw.mit.edu/courses/2-717j-optical-engineering-spring-2002/302f8fb4454a52e44502785c2e046203_imgq.pdf |
from among a continuum)
– definition of differential entropy
Diff.
Entropy
= −
Ω(
( )ln
∫
x p
)X
( ) dx
x p
– unit: 1 nat (=diff. entropy value of a significant digit in the
representation of a random number, divided by ln10)
MIT 2.717
Image quality metrics p-14
Image Mutual Information (IMI)
object
hardw... | https://ocw.mit.edu/courses/2-717j-optical-engineering-spring-2002/302f8fb4454a52e44502785c2e046203_imgq.pdf |
f B B
Two point-detectors
(measurement)
~
A g A
~
B
g B
Classical view
intensities
measured
intensities
emitted
MIT 2.717
Image quality metrics p-17
noiseless
intensity
@detector
plane
Ag
Bg
x
Cross-leaking power
g
g
A
B
=
=
f
A
sf
A
+
sf
+
f
B
B
=
sinc
2
s
( )x
ss
~
A
~
B
MIT 2.717
Image qu... | https://ocw.mit.edu/courses/2-717j-optical-engineering-spring-2002/302f8fb4454a52e44502785c2e046203_imgq.pdf |
matrices (1)
H
=
=
H
underdetermined
underdetermined
(more unknowns than
measurements)
overdetermined
overdetermined
(more measurements
than unknowns)
eigenvalues cannot be computed, but instead
we compute the singular values
singular values of the
rectangular matrix
MIT 2.717
Image quality metrics p-21
IM... | https://ocw.mit.edu/courses/2-717j-optical-engineering-spring-2002/302f8fb4454a52e44502785c2e046203_imgq.pdf |
the
imaging system can successfully discern; this includes
–
the rank of the system, i.e. the number of object dimensions that
the system can map
the precision available at each rank, i.e. how many significant
digits can be reliably measured at each available dimension
• An alternative interpretation of IMI is t... | https://ocw.mit.edu/courses/2-717j-optical-engineering-spring-2002/302f8fb4454a52e44502785c2e046203_imgq.pdf |
6.231: DYNAMIC PROGRAMMING
LECTURE 1
LECTURE OUTLINE
Problem Formulation
Examples
The Basic Problem
Significance of Feedback
•
•
•
•
1 DP AS AN OPTIMIZATION METHODOLOGY
Generic optimization problem:
•
min g(u)
u∈U
where u is the optimization/decision variable, g(u)
is the cost function, and U is the constraint set
•
Cat... | https://ocw.mit.edu/courses/6-231-dynamic-programming-and-stochastic-control-fall-2015/304cf17d604e774625dae63810777264_MIT6_231F15_Lec1.pdf |
1 = xk + uk - wk
Cost of Period k
r(xk) + cuk
Stock ordered at
Period k
uk
Discrete-time system
xk+1 = fk(xk, uk, wk) = xk + uk
wk
−
Cost function that is additive over time
•
•
N −1
E
gN (xN ) +
(
k=0
X
N −1
gk(xk, uk, wk)
)
= E
cuk + r(xk + uk
(
k=0
X (cid:0)
(cid:1)
ns uk =
Optimization over policies: Rules/functio
... | https://ocw.mit.edu/courses/6-231-dynamic-programming-and-stochastic-control-fall-2015/304cf17d604e774625dae63810777264_MIT6_231F15_Lec1.pdf |
AB
CAD
CDA
CDA
CAB
6 STOCHASTIC FINITE-STATE PROBLEMS
•
Example: Find two-game chess match strategy
Timid play draws with prob. pd > 0 and loses
pd. Bold play wins with prob. pw <
•
with prob. 1
−
1/2 and loses with prob. 1
pw
−
0.5-0.5
pd
0 - 0
1 - pd
pw
1 - 0
0 - 0
1 - pw
0 - 1
0 - 1
1st Game / Timid Play
1st Game / ... | https://ocw.mit.edu/courses/6-231-dynamic-programming-and-stochastic-control-fall-2015/304cf17d604e774625dae63810777264_MIT6_231F15_Lec1.pdf |
J ∗(x0) = min Jπ(x0)
π
Optimal policy π∗ satisfies
•
•
Jπ∗ (x0) = J ∗(x0)
When produced by DP, π∗ is independent of x0.
8 SIGNIFICANCE OF FEEDBACK
•
Open-loop versus closed-loop policies
wk
u = m (x )
uk = µk(xk)
k
k
k
System
x
k + 1
= f (x ,u ,w )
k
k
k
k
xk
mk
) µk
In deterministic problems open loop is as good
•
as... | https://ocw.mit.edu/courses/6-231-dynamic-programming-and-stochastic-control-fall-2015/304cf17d604e774625dae63810777264_MIT6_231F15_Lec1.pdf |
lectures)
Chs. 6, 7: Approximate DP (6 lectures)
−
−
11 COURSE ADMINISTRATION
Homework ... once a week or two weeks (30%
•
of grade)
In class midterm, near end of October ... will
•
cover finite horizon and simple infinite horizon ma-
terial (30% of grade)
Project (40% of grade)
•
Collaboration in homework allowed but in... | https://ocw.mit.edu/courses/6-231-dynamic-programming-and-stochastic-control-fall-2015/304cf17d604e774625dae63810777264_MIT6_231F15_Lec1.pdf |
6.776
High Speed Communication Circuits
Lecture 2
Transceiver Architectures
Massachusetts Institute of Technology
February 3, 2005
Copyright © 2005 by H.-S. Lee and M. H. Perrott
Transceivers for Amplitude Modulation
H.-S. Lee & M.H. Perrott
MIT OCW
Amplitude Modulation Review
Transmitter Output
0
x(t)
y(t)
2cos(2πfo... | https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/30624026937064d06c6438a7a2b5197a_lec2.pdf |
.H. Perrott
MIT OCW
SSB Transmitter I
(cid:131) Phase-shift SSB Modulator
Balanced
modulator
-90o phase
shifter
-90o phase
shifter
Balanced
modulator
Power
Amp
+
RF
Filter
SSB
(cid:131) Sideband removal depends on phase
and amplitude matching
H.-S. Lee & M.H. Perrott
MIT OCW
Frequency Domain View of Phase-Shift SSB ... | https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/30624026937064d06c6438a7a2b5197a_lec2.pdf |
ystal earpiece
H.-S. Lee & M.H. Perrott
MIT OCW
Envelope Detector Example
vin
v1
C2
vin
R1
R2 vout
v1
C1
vout
H.-S. Lee & M.H. Perrott
MIT OCW
AM Receiver: Amplified Receiver
RF Filter
(Tunable LC)
RF Amplifier
Envelope
Detector
Audio Freq.
(AF) Amplifier
(cid:131) Better sensitivity (RF Amp)
(cid:131) Can drive lo... | https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/30624026937064d06c6438a7a2b5197a_lec2.pdf |
Filter
(Tunable LC)
RF Amplifier
Frequency
Converter
IF
Filter
IF
Amplifier
Envelope
Detector
Audio Freq.
(AF) Amplifier
(cid:131) Frequency converter mixes RF down to lower IF
frequency – better selectivity is obtained at the lower
frequency IF filter
(cid:131) Excellent selectivity due to the additional IF filteri... | https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/30624026937064d06c6438a7a2b5197a_lec2.pdf |
:131) The alternative is to employ image reject mixer
H.-S. Lee & M.H. Perrott
MIT OCW
Image Reject Mixer
RF
r(t)
y(t)
Balanced
modulator
Local Oscillator
+
LPF or
BPF
-90o phase
shifter
IF Output
Balanced
modulator
-90o phase
shifter
z(t)
z(t)^
(cid:131) Image rejected by similar method to SSB generation
(cid:131) I... | https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/30624026937064d06c6438a7a2b5197a_lec2.pdf |
Conversion (Zero-IF) Receiver
RF Filter
(Fixed
frequency)
RF Amplifier
(LNA)
Quadrature
Mixer
Frequency
Synthesizer
I/Q
I
Q
Baseband
Filter
Baseband
Amplifier
A/D converter
Baseband
Filter
Baseband
Amplifier
A/D converter
Q
DSP
(cid:131) Type of a homodyne receiver
(cid:131) Uses coherent detection: a precise local os... | https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/30624026937064d06c6438a7a2b5197a_lec2.pdf |
is not
an issue
H.-S. Lee & M.H. Perrott
MIT OCW
Image Rejection in Double Conversion Receiver
1&3
2&4
LNA Output Spectrum
1
2
3 4
I
-fIF
fIF
-fLO1
fLO1
LO1I
I-I
LO2I
I-Q
j
1,2,3&4
4&2
1&3
4&3
+
-fIF
3
LO2Q
4
Q-I
j
1&2
1
Q
j
2
fIF
LO2I
LO1Q
Q-Q
LO2Q
2&3
4&1
Q-Phase
4
1
j
+
-
4&1
I-Phase
(cid:131) Similar to Weaver SS... | https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/30624026937064d06c6438a7a2b5197a_lec2.pdf |
by
nX
H.-S. Lee & M.H. Perrott
MIT OCW
Direct FM: VCO
VCO
(cid:131) fo: ‘free running’ frequency of VCO
(cid:131) Typically, a varactor (voltage-variable capacitor) is
used to change oscillation frequency in an oscillator
(cid:131) Difficult to maintain precise output frequency due to
drift in the VCO frequency
(ci... | https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/30624026937064d06c6438a7a2b5197a_lec2.pdf |
AM Conversion
Limiter
Differentiator
Envelope
Detector
DC block
(cid:131) Differentiator converts FM signal to AM
(cid:131) Spurious AM must be suppressed by the limiter
H.-S. Lee & M.H. Perrott
MIT OCW
FM Demodulator Example: Delay-Line
+
-
delay τ
(cid:131) Differentiator is implemented by a transmission line
delay... | https://ocw.mit.edu/courses/6-776-high-speed-communication-circuits-spring-2005/30624026937064d06c6438a7a2b5197a_lec2.pdf |
Lecture 7
PN Junction and MOS Electrostatics(IV)
MetalOxideSemiconductor Structure (contd.)
Outline
1. Overview of MOS electrostatics under bias
2. Depletion regime
3. Flatband
4. Accumulation regime
5. Threshold
6.
Inversion regime
Reading Assignment:
Howe and Sodini, Chapter 3, Sections 3.8-3.9
6.012 Sprin... | https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-spring-2009/30d115908b75764ef7ebe79517ac5e8a_MIT6_012S09_lec07.pdf |
1+
Cox
2C 2 (φφφφB + VGB)
εεεεsqNa
ox
− 1
Potential drop across semiconductor SCR:
VB (VGB ) =
qN x 2
d
a
2ε s
Surface potential
φφφφ(0) = φφφφp + VB(VGB)
Potential drop across oxide:
Vox (VGB ) =
qN a x d t ox
ε ox
6.012 Spring 2009
Lecture 7
5
3. Flatband
At a certain negative VGB,... | https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-spring-2009/30d115908b75764ef7ebe79517ac5e8a_MIT6_012S09_lec07.pdf |
= − φφφφp
ni
Hence:
VB (VT ) = −2φφφφp
6.012 Spring 2009
Lecture 7
9
Computation of threshold voltage (contd.)
Second, compute potential drop in oxide at threshold.
Obtain xd(VT) using relationship between VB and xd in
depletion:
VB (VGB = VT ) =
2 VT(
qNaxd
2εεεεs
)
= −2φφφφp
Solve for xd at VGB = VT: ... | https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-spring-2009/30d115908b75764ef7ebe79517ac5e8a_MIT6_012S09_lec07.pdf |
version
What happens for VGB > VT?
More electrons at Si/SiO2 interface than acceptors
⇒⇒⇒⇒ inversion.
Electron concentration at Si/SiO2 interface modulated
by VGB ⇒ VGB ↑ → n(0) ↑ → |QN| ↑ :
Fieldeffect control of mobile charge density!
[essence of MOSFET]
Want to compute QN vs. VGB [chargecontrol relation]
... | https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-spring-2009/30d115908b75764ef7ebe79517ac5e8a_MIT6_012S09_lec07.pdf |
Existence of QN and control over QN by VGB
⇒ key to MOS electronics
6.012 Spring 2009
Lecture 7
15
What did we learn today?
Summary of Key Concepts
In inversion:
QN
= Cox (VGB − VT )
for VGB > VT
6.012 Spring 2009
Lecture 7
16
MIT OpenCourseWare
http://ocw.mit.edu
6.012 Microelectronic Devices and Circuits ... | https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-spring-2009/30d115908b75764ef7ebe79517ac5e8a_MIT6_012S09_lec07.pdf |
s
1
10
25
2
20
4
15
40
35
3
35
5
t
6
30
20
s
1
10
25
2
20
4
15
40
35
3
35
5
t
6
30
20
s
1
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25
2
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35
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t
6
30
20
s
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25
2
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4
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35
3
35
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t
6
30
20
s
1
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25
2
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4
15
40
35
3
35
5
t
6
30
20
s
1
10
25
2
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4
15
40
35
3
35
5
t
6
30
20
10
1
5
3
2
4
3
2
3
6
5
-15
4
1
5
6
-5
2
4
6
7
10
The s... | https://ocw.mit.edu/courses/15-093j-optimization-methods-fall-2009/313d12c426c44380ccd838dff3151690_MIT15_093J_F09_lec10.pdf |
T+1
s
1
10
25
2
20
4
15
40
35
3
35
5
t
6
30
20
10
s
1
20
2
3
10
4
15
40
35
10
t
6
20
20
5
10
s
1
20
2
3
10
4
15
40
35
10
t
6
20
20
5
8
1
-9
2
5
-10
7
3
0
4
1
3
8
7
s
-9
2
0
4
5
-10
1
3
8
7
s
t
10
9
5
2
4
(cid:102)
(cid:102)
(cid:102)
1
3
2
4
t
10
9
(cid:102)
(cid:102)
5
8
7
s
1
4
8
12
2
5
3
10
11
9
7
6
... | https://ocw.mit.edu/courses/15-093j-optimization-methods-fall-2009/313d12c426c44380ccd838dff3151690_MIT15_093J_F09_lec10.pdf |
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. | https://ocw.mit.edu/courses/15-093j-optimization-methods-fall-2009/313d12c426c44380ccd838dff3151690_MIT15_093J_F09_lec10.pdf |
Advanced System Architecture
ESD.342/EECS 6.883
2006
• Goals of this course:
• Gain an understanding of system architecture
• Learn existing theoretical and analytical methods
• Compare systems in different domains and
understand what influences their architectures
• Apply/extend existing theory in case studies
Adv Sy... | https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/31440ed9b876651c3287b430ba75f77e_lec1.pdf |
Arch intro
8/24/2006
© Daniel E Whitney
5
Grading Formula
• 15% in-class participation (especially reading
connections)
• 25% assignments
– 5% Each for assignments 1 and 2
– 15% for assignment 3
• 60% Project
– 20% Final Written Report
– 15% Final Presentation
– 15% Modeling Status Presentation
– 10% 1st Status Prese... | https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/31440ed9b876651c3287b430ba75f77e_lec1.pdf |
Whitney
10
A Definition of Architecture
from a Practice Perspective
“An architecture is the conceptualization,
description, and design of a system, its
components, their interfaces and relationships with
internal and external entities, as they evolve over
time.”
John W. Evans
Source: “Design and Inventive Enginee... | https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/31440ed9b876651c3287b430ba75f77e_lec1.pdf |
• Deterministic
methods used
• Real things
– T
he ones we
are interested
in
• New methods
or adaptations
of existing
methods needed
• Less regular
-“Hub and spokes”
-“Small Worlds”
-“Grown” including
growth models
• No internal
structure
– Perfect gases
– Crowds of people
– Classical
economics with
invisible h... | https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/31440ed9b876651c3287b430ba75f77e_lec1.pdf |
exploitatively
– Cells, organisms, food
webs, ecological
systems
In all cases, there is legacy, possibly a dominant influence
Adv Sys Arch intro
8/24/2006
© Daniel E Whitney
18
Systems Typology III: Complex Systems Functional
Classification Matrix from Magee and de Weck
Process/Operand
Transform or
Process (1)
Tr... | https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/31440ed9b876651c3287b430ba75f77e_lec1.pdf |
These systems are similar in many ways, perhaps more
than we think
• Since we want to influence structure (not just accept it
as we are interested in design), we will also explore
how structure is determined by looking at system
typologies and constraints that influence or determine
the structure
• We will use net... | https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/31440ed9b876651c3287b430ba75f77e_lec1.pdf |
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