전자회로 I
심재윤
포항공과대학교
전자회로 I
심재윤
포항공과대학교
 KCL and KVL
 Laplace transform
 PN junction
 Impedance 늪
컴퓨터
돈을 모음
컴퓨터의 필수요소
If 천원 초과?
Yes
콜라와 거스름돈
출력
No
If
반도체
conduit.ir/insulator.o.
C
If C = 1?
.
ha11
I
I
,
In suit
I
,
,
!
!
i
:
:
I
i
i
세g이 세g
Yes
(
i
or
No
conduit.ir
도체
of
부도체
What
ifeo.ci?O
0.25
0.5
,
075
1
c
,
C
=
지난 60년간 반도체는 계속 작아짐
=> 작아짐에 따라 성능 (속도, 전력) 향상됨
0.25 ?
~
current
⇒
flow T
spedtreducespowerconsurpt.com
완벽한 CMOS
1
P
N
:
P < N
:
)
Out
V
Put
T
atputv osactuahy.to/l.finte.Chargingcuwent.:consumes
PMOS
두 저항이 각각
최대 on & 최대 off
Boolean
expression
NMOS
P
0 t
1
0
CMOS (Complementary MOS) : NMOS + PMOS
t
1
0
Power
.
컴퓨터의 역사 = CMOS의 역사
[Eoin Malins, OPIG 19]
fxe.cl ( GHz )
.
CMOS 컴퓨터 vs. 양자컴퓨터
자연현상 ( 중첩 얽힘 )
,
.
문제 : 백만 페이지의 책에서 특정단어 찾기
CMOS 컴퓨터
0.1초당 1페이지씩 속독이 가능한 한사람
양자컴퓨터
분당 1페이지씩 읽기가 가능한 백만명의 쌍둥이
(단, 쌍둥이들은 서로의 상태가 공유됨)
양자컴퓨터는 경우의 수가 너무 많아 풀지못하는 문제를 풀어내는데 특화됨
Quantum
Computing
.
길찾기 시작
오른쪽
갈림길
직진
왼쪽
직진
상태공유
중첩
얽힘
확률
Super position
10
et
Et
Entangle.me
int
T
O
O
o
1
1
1
I
of
Representation of a Point on Arbitrary Line in XY Plane
Y
(g⋅cosθ, g⋅sinθ)
g
θ
X
g⋅(cos2θ + sin2θ)
Note : g 크기는 θ와 무관
Mapping to a Complex Number
Im
g⋅{cos(θ) + j⋅sin(θ)}
g
θ
Re
g⋅(cos2θ + sin2θ)
Time-Dependent Movement on the Given Line
Im
g(t)⋅{cos(θ) + j⋅sin(θ)}
g(t)
θ
Re
Specific f Component Can be Extracted by Rotating Axes with the Same f
Im
g(t)⋅{cos(-2πft)+j⋅sin(-2πft)}
=g(t)⋅{cos(2πft) - j⋅sin(2πft)} = g(t)⋅e-j2πft
⇒ g(t)의 f 성분 크기에
비례하는 DC가 나옴
g(t)
2πft씩
감소
Re
Fourier Transform
( St
Z
.
) (
St
전)
+∞
(St Pi ) ( St 1조 ) ( St P3 )
−∞
Im
X
X
O
XO
𝑔𝑔 𝑡𝑡 𝑒𝑒 −𝑗𝑗2𝜋𝜋𝑓𝑓𝑓𝑓 𝑑𝑑𝑡𝑡
𝐺𝐺 𝑓𝑓 = �
Re
Laplace Transform : 미분방정식을 쉽게 풀기 위한 변환
+∞
𝐿𝐿{𝑓𝑓 𝑡𝑡 } = �
𝑔𝑔 𝑡𝑡 𝑒𝑒 −𝑠𝑠𝑓𝑓 𝑑𝑑𝑡𝑡
−∞
Laplace transform 변환된 식의 s를 jω로 생각하면 Fourier 변환과 같아져 주파수 정보를 알 수 있음.
۞ Dimension of s in Laplace Transform
e jα = cos α + j sin α
Definition of e jα by Euler's formula :
α : an angular quantity (degree or radian)
But, e jα is dimensionless.
=> jα at exponent can be thought to be dimensionless for convenience.
𝑒𝑒 −𝑠𝑠𝑓𝑓
: Dimension of s => Hz
( 11t
)
.
radian
dimensionless
j 2π f t
Ex) LPF
Vi
1
R
Vo
C
Vo(s ) /Vi (s ) =
sC
R +
1
sC
1
=
1+
s
1/ RC
ω p = 1 / RC ~ Hz
f p = 1 /(2 πRC )
Dimension of 1/sC
V=Q/C=It/C => 1/sC ~ t/C ~ V/I ~ Ω
5¥
RLC Basics & Filters
frequency 4
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t
11
R
No frequency dependence
t
VR
Frequency
0
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Peak appeasce.ge
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appeavsb.ae
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NO
Ve
Frequency
=
f
t
U
.
(
I
sl.oppositedirect.io
Push
current
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존재
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in
o
n
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이
j.tl
되는
.
✗
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۞ dB & dBm
dB : 10log(ratio of two power quantities)
=> Gain (배)을 나타낼 때 사용
2x power gain : 10log(2) = 3dB
PI
>
X2
TellThe
To
/
☆
"메에다
얘쐐'
V/V, V/I, I/V, I/I 경우 : 전력량으로 환산
2x gain : 10log{(2)2/(1)2} = 6dB
P NI
=
√2x gain : 10log{(√2)2/(1)2} = 3dB
10x gain :
10log{(10)2/(1)2}
as
same
= 20dB
E
\^
=
R
is
I2 R
same
dBm : 10log(power/mW) : absolute power quantity
ex) 1mW=0dBm, 10mW=10dBm,
[ ]dBm - [ ]dBm = [ ]dB
[ ]dBm - [ ]dB = [ ]dBm
100mW=20dBm,
1W=30dBm
10dBm
PI
7dB
3
y
dB
"
attena.to
.
P
.
.
Bo de
Hot
|v/i| (dB)
f
고자
|v/i| = |1/jωC|
capacitive
-20dB/dec
.
10x
=>주파수에 반비례
oxw.EU
10x
ω (log)
|v/i| (dB)
|v/i| = |jωL|
10x
inducitive
+20dB/dec
10x
ω (log)
=>주파수에 비례
✗
ㅥ
1st Order System
E
=
0 et
1Ω
1
1v
0
At
Don’t be confused with
0.lv
Vo
RC
to.zvunt.IN
$
1 A
Vs
t=0
At
o
O
.
1Ω
1F
8 A
V9
Vo
1A
1F
Is
t=0
7 €
1F
Vo
1v
1Ω
Vs
t=0
e −1 = 0.37
一一
€1 ☐
tscdjfactor.l.TO
-
☐ e
-
e
대지
+ o
a
0.37a
b
τ
0.37b
τ
현재 시간과 그 때의 값을 기준점으로 시정수 이후엔 최종 값까지의 63%에 도달
t
1st Order System
Von
1H
1v
t=0
Vs
燾召
N
Vo
1Ω
txL.xle.tk/R
1Ω
Vo
1v
t=0
Vs
ㅡㅡ.ee#@
1H
t.us "∴
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Leo Load
Its V0
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RN
P
load
.
di
;
HI
國王
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N
.
猷戱
Game
幽
line
> v
言凰
Rz
工鬪
PN Junction Diode
ID
ID
|
아주
고정
작은
kaka.ge
t re
𝐼𝐼𝐷𝐷 = 𝐼𝐼𝑠𝑠 �
If
Up
If
Up CO
)
0
,
.
↳
.
Score: 저항과
IS
+
𝑉𝑉𝐷𝐷
(𝑒𝑒 𝑛𝑛�𝑉𝑉𝑇𝑇
if n=1
𝑉𝑉𝐷𝐷
𝑑𝑑𝐼𝐼𝐷𝐷
1
𝐼𝐼𝐷𝐷
𝑛𝑛�𝑉𝑉
≅
� 𝐼𝐼𝑠𝑠 � 𝑒𝑒 𝑇𝑇 =
𝑑𝑑𝑉𝑉𝐷𝐷 𝑉𝑉𝑇𝑇
𝑉𝑉𝑇𝑇
ㅎ
VD
𝐼𝐼𝐷𝐷 ≅ 𝐼𝐼𝑠𝑠
𝑉𝑉𝐷𝐷
� 𝑒𝑒 𝑉𝑉𝑇𝑇
.
VD
− 1)
neglec.tt
only-l~vollogedimens.com
관련된 값
IS : Reverse saturation current
n : Nonideality factor (1~2)
.
VT : Thermal voltage (kT/q), 25mV at room temperature
25mU
.
Bipolar Junction Transistor (BJT)
Emitter
Base
Collector
N
P
N
# of
s at C = β⋅(# of s at B)
: amplification
β⋅IB
IE
IC
C
E
※ Bipolar vs. Unipolar
and
or
VBE
IB
B
Bipolar Junction Transistor (BJT)
ro = 1/slope
β⋅IB
IE
ro
IC
IE
C
E
β⋅IB
VBE
C
E
VBE
IC
re
IB
rπ
B
IB
B
VBE = IB⋅rπ = (IB+β⋅IB)⋅re = IB⋅(1+β) re
IC (mA)
β=100
slope
IB=0.4mA
IB=0.3mA
IB=0.2mA
IB=0.1mA
IB=0
40
30
20
10
0
VCE(V)
5
rπ = (1+β) re
Small Signal Parameters from Bias Current
Considering VBE is a diode voltage,
𝐼𝐼𝐵𝐵 ≅ 𝐼𝐼𝑠𝑠 �
𝑉𝑉𝐵𝐵𝐵𝐵
𝑒𝑒 𝑉𝑉𝑇𝑇
𝑉𝑉𝐵𝐵𝐵𝐵
𝑑𝑑𝐼𝐼𝐶𝐶
𝑑𝑑𝐼𝐼𝐵𝐵
𝛽𝛽
𝐼𝐼𝐵𝐵
𝐼𝐼𝐶𝐶
𝑛𝑛�𝑉𝑉
𝑇𝑇
𝑔𝑔𝑔𝑔 =
= 𝛽𝛽
=
� 𝐼𝐼 � 𝑒𝑒
= 𝛽𝛽
=
𝑑𝑑𝑉𝑉𝐵𝐵𝐵𝐵
𝑑𝑑𝑉𝑉𝐵𝐵𝐵𝐵
𝑉𝑉𝑇𝑇 𝑠𝑠
𝑉𝑉𝑇𝑇 𝑉𝑉𝑇𝑇
gm = IC/VT
From
𝑑𝑑𝐼𝐼𝐶𝐶 𝑑𝑑𝑉𝑉𝐵𝐵𝐵𝐵 𝑑𝑑𝐼𝐼𝐶𝐶
�
=
𝑑𝑑𝑉𝑉𝐵𝐵𝐵𝐵 𝑑𝑑𝐼𝐼𝐵𝐵
𝑑𝑑𝐼𝐼𝐵𝐵
gm ⋅ rπ = β
From
rπ = (1+β) re
gm ⋅ re = α
where α = β/(β+1)
re = α/gm = 1/gm
if α ≅ 1
ro
VB
VB
rπ
re=α/gm
R
VB
VB
R
R
Rb
VB
Rb
Rb
Rb
Rb
VB
R
Rb
VB
VB
R
R
Noise
Without noise
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
With noise
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
Noise : The number of charge carriers passing
through a cross section changes in time.
Noise sources
1. Temperature (thermal, ~white)
2. Defect in conductor (flicker, ~1/f)
3. Natural quantum noise (shot, ~white)
Transistor Noise
Real
Ideal
I(t)
I(t)
I(t)
I(t)
thermal
noise
I(VG,VD,VS)
I(t)
t
t
t
t
flicker
noise
t
Long t
Transistor Noise
Power/Hz
1/f noise
Thermal noise
∆f
Corner freq.
Open-circuit time constant vs. Short-circuit time constant
𝑠𝑠
𝑠𝑠
𝑠𝑠
)(1 +
) ��� (1 +
)
𝜔𝜔𝑧𝑧1
𝜔𝜔𝑧𝑧2
𝜔𝜔𝑧𝑧𝑘𝑘
𝐴𝐴0
𝑠𝑠
𝑠𝑠
𝑠𝑠
)(1 +
) ��� (1 +
)
(1 +
𝜔𝜔𝑝𝑝1
𝜔𝜔𝑝𝑝2
𝜔𝜔𝑝𝑝𝑛𝑛
(1 +
=
𝐴𝐴0
☐
1
≡
s.is?..s3.. shnaaTEcEtee.first2termsaredomlnant.
1
1
1
1 + 𝑠𝑠
+
+��� +
+���
𝜔𝜔𝑝𝑝1 𝜔𝜔𝑝𝑝2
𝜔𝜔𝑝𝑝𝑛𝑛
'
(𝑠𝑠 + 𝜔𝜔𝑧𝑧1 )(𝑠𝑠 + 𝜔𝜔𝑧𝑧2 ) ��� (𝑠𝑠 + 𝜔𝜔𝑧𝑧𝑘𝑘 )
𝐵𝐵0
(𝑠𝑠 + 𝜔𝜔𝑝𝑝1 )(𝑠𝑠 + 𝜔𝜔𝑝𝑝2 ) ��� (𝑠𝑠 + 𝜔𝜔𝑝𝑝𝑛𝑛 )
=
挺恬
1
以幽
𝐵𝐵0
☐
𝑠𝑠 𝑛𝑛 + 𝑠𝑠 𝑛𝑛−1 𝜔𝜔𝑝𝑝1 + 𝜔𝜔𝑝𝑝2 +��� +𝜔𝜔𝑝𝑝𝑛𝑛 +���
2
'
s.IS#
,
2
속
1
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,
sh
3
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HP F
l
GIRL
T
7
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FE
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脈弟
b
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Y
☒
ㅋ
effect of
Making
(
Guns for function
⇒
( as
,
GS
owinglgbk.CC
작이서 )
utgedwpl.PE
Night요에서
.
den ve
Whole
ga
Int
⇒
비효율적
.
polefeuencj.org
Open-circuit time constant vs. Short-circuit time constant
𝑠𝑠
𝑠𝑠
𝑠𝑠
)(1 +
) ��� (1 +
)
𝜔𝜔𝑧𝑧1
𝜔𝜔𝑧𝑧2
𝜔𝜔𝑧𝑧𝑘𝑘
𝐴𝐴0
𝑠𝑠
𝑠𝑠
𝑠𝑠
)(1 +
) ��� (1 +
)
(1 +
𝜔𝜔𝑝𝑝1
𝜔𝜔𝑝𝑝2
𝜔𝜔𝑝𝑝𝑛𝑛
(1 +
=
⇒한 놈
𝐴𝐴0
말고 다른
Ra
CEO을
≡
만듦C9화
=
Ta Ta
1
1
1
1 + 𝑠𝑠
+
+��� +
+���
𝜔𝜔𝑝𝑝1 𝜔𝜔𝑝𝑝2
𝜔𝜔𝑝𝑝𝑛𝑛
/
1
(𝑠𝑠 + 𝜔𝜔𝑧𝑧1 )(𝑠𝑠 + 𝜔𝜔𝑧𝑧2 ) ��� (𝑠𝑠 + 𝜔𝜔𝑧𝑧𝑘𝑘 )
𝐵𝐵0
(𝑠𝑠 + 𝜔𝜔𝑝𝑝1 )(𝑠𝑠 + 𝜔𝜔𝑝𝑝2 ) ��� (𝑠𝑠 + 𝜔𝜔𝑝𝑝𝑛𝑛 )
G.cz G
⑤ @@
𝑠𝑠 𝑛𝑛 + 𝑠𝑠 𝑛𝑛−1 𝜔𝜔𝑝𝑝1 + 𝜔𝜔𝑝𝑝2 +��� +𝜔𝜔𝑝𝑝𝑛𝑛 +���
宖宖2
jwen
,
𝐵𝐵0
⇒ 또
.
긂
이를 만듦
o
P이다
.
wpi.LT
긂o
1
,
UP
Zero
o
2
乏晄
(Shot)
.
녹R
斷
.
.
Copa its
HP F
i
Vol
1
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級
3
독RD
f
"
R문구인
추모
y
孟謎一
Rst
凡追
47
b
V0
ㅋ
ㅋ
effect of
Making
(
Guns for function
⇒
( as
,
GS
owinglgbk.CC
작이서 )
utgedwpl.PE
Night요에서
.
鹹綎
Dshat
爾
suit
.
"
혻璣숯겚 絅忍
쁘꽌!먁
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=
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비
.
.
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TR c
( 반도체로 흐르는 전류
.
매우 작을
지함 매우 커서 )
frqciftllttiic.tw
bond )
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ii) Open
羅驪癎첖
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Cgs (
1341잤뫼nmnm
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makepole.IR
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전류 감소
.
폭
rest for G에
RD
騙爽
군자만
TTvher_pteo.tt
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vj.HR
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s
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ftwh-A.it
龍慟刻
可
.it
①
I
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ㅋ
Casede
3dB
더
David
gs.RS
도
장점
£9
Miller
Cg이
H13
'
( 12st
얎)
B
G인
다
위에
,
.
'
R
,
R
Open-circuit time constant vs. Short-circuit time constant
ㅋ
안에
-
들어있음
𝑠𝑠
𝑠𝑠
PC go.in 𝑠𝑠
(1 +
)(1 +
) ��� (1 +
)
𝜔𝜔𝑧𝑧1
𝜔𝜔𝑧𝑧2
𝜔𝜔𝑧𝑧𝑘𝑘
𝐴𝐴0
○
𝑠𝑠
𝑠𝑠
𝑠𝑠
)(1 +
) ��� (1 +
)
(1 +
𝜔𝜔𝑝𝑝1
𝜔𝜔𝑝𝑝2
𝜔𝜔𝑝𝑝𝑛𝑛
.
=
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.
≡
=
1
1
1
1 + 𝑠𝑠
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+��� +
+���
𝜔𝜔𝑝𝑝1 𝜔𝜔𝑝𝑝2
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1
B
(𝑠𝑠 + 𝜔𝜔𝑧𝑧1 )(𝑠𝑠 + 𝜔𝜔𝑧𝑧2 ) ��� (𝑠𝑠 + 𝜔𝜔𝑧𝑧𝑘𝑘 )
𝐵𝐵0
(𝑠𝑠 + 𝜔𝜔𝑝𝑝1 )(𝑠𝑠 + 𝜔𝜔𝑝𝑝2 ) ��� (𝑠𝑠 + 𝜔𝜔𝑝𝑝𝑛𝑛 )
萩
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2
V
p
Tr
E-g.RO
rm
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Vo
Vs
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2
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poles = (−ζ ± ζ 2 − 1 )ωn
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ζ : damping ratio
ωn : natural frequency
ζ > 1 : real poles
overdamped
ζ = 1 : duplicated poles
critically damped
ζ < 1 : complex poles
under damped
higher ζ : more stable
ωn : natural undamped frequency
=> oscillation frequency when ζ = 0
2nd Order Filters
H (s ) =
H (s ) =
H (s ) =
H (s ) =
H (s ) =
ωn
2
s + 2ζωns + ωn
2
2
LP
2
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2
BP
2
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s 2 + 2ζωns
s + 2ζωns + ωn
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2
s + 2ζωns + ωn
2
2nd Order Filters
Band-pass
X
H (s ) =
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2
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Low-pass
H (s ) =
2ζωns + ωn
X
2
s 2 + 2ζωns + ωn
X
X
2
X
Notch
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H (s ) =
X
2
s + 2ζωns + ωn
2
2
X
X
ωn
s 2 + 2ζωns + ωn
X
X
X
H (s ) =
s 2 + 2ζωns
2
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X
H (s ) =
s2
s 2 + 2ζωns + ωn
2
X
X
X
X
X
X
Butterworth Filter (Maximally Flat Passband Response)
X
X
45°
90°
X
X
30°
60°
45°
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X
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30°
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X
22.5°
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onjugate)
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.
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o
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effect of
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apsiassumedtobeze.ro
.
Want
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Ref
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L씨-0
Ceff
t이
ratio
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Q
rate
.
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OU
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=
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s
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s
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Ref
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.
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.
CH
LD
left
∴
것
Ceff = C
open
Ceff
Miller effect
ㅨ
C
△U
@
⇒
boostapacito.ee
to
2x
f
一一 C
Ceff = -C
Ref
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=
-
R
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amplif.edu
Ref
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f
7
C
t
10 C
.
=
fvt
Miller Capacitance
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.it
Ceff
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Ceff
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C
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Z
f
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Y
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.
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는 Y (
Z
.
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=
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-
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.
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Ceff
Ceff = 0
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2x
C
10x
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Ceff = 11C
Miller Multiplication of C (Revisited)
fboundavyfreq.WS?as+i-)c,f
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訃川
莊憑遼
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어쩔수 없음
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ref
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.
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on
gmt.ro
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,
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thresholdvoltage.to?
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1
𝑊𝑊
𝐼𝐼𝐷𝐷 = 𝜇𝜇𝐶𝐶𝑂𝑂𝑂𝑂
𝑉𝑉 − 𝑉𝑉𝑇𝑇𝑇𝑇
2
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2
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𝑉𝑉𝐷𝐷𝐺𝐺 ≥ 𝑉𝑉𝐺𝐺𝐺𝐺 −𝑉𝑉𝑇𝑇𝑇𝑇
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flat
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.
ibss.at
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"
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.
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ID(mA)
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.
Layer uol.tgeiDr.in
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5
,
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.
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.
4
3
2
1
o
0
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f
deukegainsplk.SC
D
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UDP
5
VDS(V)
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VGS=3V
VGS=2V
VGS=1V
VGS=0V
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✗
.
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G
,
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T
.
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.
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Good
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LET
flat
S
.
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St
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3
2
1
0
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.
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R
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e
i1
G
lix
t
:
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i=0이 됨
ro
( HR) .ro
−
.
IX, V71
D
Ratio
'
D Root
f
x
←
+
VGS
Large Signal analysis
.
gnti.RS
Signal analysis
s
ix.
R
(D
모두
.
봄
.
Small Signal AC Model
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suit
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Can
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G
gmVGS
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S
S
ro
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.
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嚴函叱
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CGD becomes a miller cap in common source amplifier configuration.
⑤
Small Signal AC Model
3개
다른
GNP (
negative P이
a
p들
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e
.
CGD
D
G
gmVGS
CGS
S
燕鄙芎
t.MG
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ro
.
ㅋ
娜
ㅋ
cnet.ir
CGD becomes a miller cap in common source amplifier configuration.
Das 전류
결정위해
쓰고싶음
.
⇒ cap 사용
.
Gm & Resistance
ID(mA)
Gm
V
I
5
4
3
2
1
VGS
5V
D
trok.lk
4V
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3V
2V
Fr
.
1V
S
0 1 2 3 4 5
ix
VDS(V)
Vds,sat
ID
G
晧
→
ii.TV
Ug
.
i
↳
-
Vs
1/
V5
as
_
gm.FR
F
other
node
are
fl
幷鳶
R
VB
? :
VB
1/gm
1/gm
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)
vgfc.ro
.
다
같은데
나만
⇒ 전류 거의
같음
좀
다들
.
.
R only changes VD.
Change of VD does not affect ID.
Vgs
Rout
ix
vx
☒
VB
gmf)
⋅ix⋅R
2
∆Vgs = -ix⋅R
R
ro
ri
(ix+gm⋅ix⋅R)⋅ro
ix⋅R
R
n
ro
,
vx= (ix+gm⋅ix⋅R)⋅ro + ix⋅R
vx/ix = gm⋅ro⋅R + ro + R
ra
오스란드
gmrozroitroztro.ir
tgnz.ro
=
.
,
( 1
e)
t
V02
2
추
Common Source Amplifier
箋朮烋旭
VDD
÷
←
폯
一匯
VO
VI
=
-9mV
:
( R방 )
퓱
R
"
.
V.
Ampeo
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宦
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9m
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,
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ro
)
Common Source Amplifier
13
1%K
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R
Io
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A
VDD
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in =
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Common Source Amplifier with Source Degeneration
9m
"
8$
HFRsgnCRHR.at
1
CAR
Rs
VDD
is
bit
Route
Vo에서
보는
저항
.
Resisee.ae
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ltgmRs.us
.
VI
VO
V0
V9
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tgmp.sc
RKRJ
Common Source Amplifier with Source Degeneration
VDD
R
11
VO
11
VI
Et
.cz
RS
!
Chip에서
DC
go.in
전압에
변화를
의한
없앨
Common Drain Amplifier (Source Follower)
OutPut을
가져가는가
어디서
NHK에
E
回
VDD
t
Ni
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"
S
固
"
load
fdbwthepdauitgoftheg.to
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R
j
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t.it
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.
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VO
아滋
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艸幷
RL
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ftp.LVi
Common Drain Amplifier (Source Follower)
{ 스4
ft
G이가
통해
잘 맞춤
.
VDD
VDD
,
ET 巒
L
VI
VO
R
VI
0
VO
:
Common Gate Amplifier
일반적으로
Common
VDD
결
Vs
Ni
R
E
f
V
V0
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source
ap 사용
.
Common Gate Amplifier
남
VDD
金津岾
EU
弗絅
"
R
VO
陣一FR.lk
•
3k
라다
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l V
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Common Gate Amplifier
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A
S
Poker
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0
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Very
Big)
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5V
VDD
⇒
R
VO
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徘手
t
T_E.at
VI
奸縡
.
Common Gate Amplifier
VDD
R
VO
T1gm
Ygn
VI
✗
△
i
△
Ui
( 크지
않음)
.
폼
벼
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int
outptwkge.lu
current
,
Exercise ) Set Vdc and A for Largest Swing on V1
7남S
3V
4K
ABS
V1
취해 그림
Vac = Asinωt
Vdc
V2
1K
0V
↳
ioneeqaiualentde.ve
VGS’
VS
VGS
I(mA)
VDSsat
VDS’sat
1
2
3
D
VGS=3V
D
|
G
匕臣
t
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S
N
VGS=2V
○
VGS=1.5V
VGS=1V
T-T
一一
一一
=
一一
=
一一
=
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=
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-
0.125
€
1K
S’
0.25
1-7
K
속
,
0.5
(gas)
105mA
:
0.25mA
0.125mA
VGS’
VS
VGS
I(mA)
VDSsat
VDS’sat
1
0.13
0.87
0.13
0.1
0.23
2
0.45
1.55
0.45
0.2
0.65
3
0.85
2.15
0.85
0.25
1.1
D
G
S
VGS’=3
⇒
VGS’=2.5
VGS’=2
VGS’=1.5
VGS’=1
VGS’=0.5
1K
S’
1
VGS’
VS
VGS
I(mA)
VDSsat
VDS’sat
1
0.13
0.87
0.13
0.1
0.23
0.45
1.55
0.45
0.2
0.65
0.85
2.15
0.85
0.25
1.1
2
3
懊
3V
4K
D
G
.ie/
曲乘箚
R 추가
S
1K
VGS’=3
S’
VGS’=2.5
VGS’=2
VGS’=1.5
VGS’=1
VGS’=0.5
gm
작얨
더 큰
.
kbs에서
Stadion 됨
.
VGS’
VS
VGS
I(mA)
VDSsat
VDS’sat
1
0.13
0.87
0.13
0.1
0.23
2
0.45
1.55
0.45
0.2
0.65
3
0.85
2.15
0.85
0.25
1.1
3V
4K
D
G
Vac = Asinωt
S
Vdc
1K
VGS’=3
VGS’=2.5
VGS’=2
•
d.
VGS’=1.5
•
9
一一
v
VGS’=1
VGS’=0.5
대략
Vdc=1.5
A=0.8
S’
Cascode
Good current
source
outputresisenceiuergbig.to#onsistasinseies.3Vb0
Rout
If
-4mA .tt 0.45nA
△
an
△
0.05nA
VB2
.
1.5V - 25V
t
1.5V
8.li
.TT
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VB1
EEFE.at
.
:
1.5V
2.5U
a~x~veybig.LI#fixed
0.4mA
.
Cascode
5U
IN
n
HI
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to 45mA
.
Lenff
4mA
Rout
S
芎了
에
VB2
VB1
t
뻬
대사의 t source
동작 가깝게
Cascode
Rout
飜
VB2
VB1
Current Source (by Current Mirroring)
RE
"
一片
(
IREF
0.25m
Rout
te
)
RREF
f)
""
.
1.3V
F
.
6
.
0.3
)
5
6kt
n
U. A
延万加
Unit
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.
L.ro
베
○
VDD
VDD
.
f
Widlar Current Source
temperaturedependence.tt
VDD
저항 이용해
IREF
정함
.
Rout
"
A
☒
&
W가
R
大
ve or
.
same
.
Widlar Current Source
VDD
IREF
Rout
Long
b
Small
b
일종의
feedback.tn
Small
aeesse.com
R
Large
Cascode Current Source
VDD
IREF
Rout
剡聃
ㅋ
ㅋ
ㅋ
Wilson Current Source
VDD
VDD
R=
s
The
IREF
of
Root
IREF
,
适
Small
Signal
Hand
=
Model
Analysis
.
To Route
R
C
L
Diode
Bipolar Junction Transistor Field Effect Transistor
(BJT)
(FET)
Area for Implementation on Integrated Circuit (IC) Chip
R
C
L
Diode
BJT
FET
Top view
VDD
VSS
W
L
M2
VDD
Via
M1
G-poly
Contact
P+
N+
N+
tox
P+
P+
N-well
P-sub
N+
OP Amp
R
Vi
C
+
Vo
R2
R1
Vi
R2
-
Vo
+
C
R1
Vi
C
R1
Vi
+
+
Vo
Vo
𝑅𝑅𝐹𝐹
𝑉𝑉1
𝑉𝑉1
𝑉𝑉2
𝑅𝑅1
𝑅𝑅2
+
Vo
𝑉𝑉2
𝑉𝑉3
𝑉𝑉4
𝑅𝑅𝐹𝐹
𝑅𝑅1
𝑅𝑅2
𝑅𝑅3
𝑅𝑅4
+
Vo
Propagation of Signal Polarity
D
G
S
G -> S : Same
G -> D : Opposite (w/ gain)
S -> D : Same (w/ gain)
D -> S : Negligible (Same)
Differential-mode and Common-mode
VDD
RL
VO
VI-
VI+
ISS
RSS
Differential-mode and Common-mode
VCM ={(VI+)+(VI-)}/2 : 평균
VDM =(VI+)-(VI-)
VDD
: 차이
RL
ACM = VO/VCM
VO
ADM = VO/VDM
CMRR = ADM/ACM
VCM-½VDM
VCM+½VDM
ISS
RSS
Half-circuits for Vo at Differential and Common-modes
VDD
RL
CM
DM
VDD
VDD
RL
VO
RL
VO
VCM-½VDM
VCM+½VDM
ISS
RSS
VCM
2RSS
VO
-½VDM
Differential-mode and Common-mode
VDD
ACM = ∆VO/VCM
ADM = ∆VO/VDM
CMRR = ?
RL
RL
VO-
VO+
VI-
VI+
ISS
RSS
Differential-mode and Common-mode
VDD
RL
RL+∆RL
VOVI+
VO+
gm+∆gm
gm
ISS
RSS
VI-
Open-circuit time constant vs. Short-circuit time constant
𝑠𝑠
𝑠𝑠
𝑠𝑠
)(1 +
) ��� (1 +
)
𝜔𝜔𝑧𝑧1
𝜔𝜔𝑧𝑧2
𝜔𝜔𝑧𝑧𝑘𝑘
𝐴𝐴0
𝑠𝑠
𝑠𝑠
𝑠𝑠
)(1 +
) ��� (1 +
)
(1 +
𝜔𝜔𝑝𝑝1
𝜔𝜔𝑝𝑝2
𝜔𝜔𝑝𝑝𝑛𝑛
(1 +
=
𝐴𝐴0
1
1
1
1 + 𝑠𝑠
+
+��� +
+���
𝜔𝜔𝑝𝑝1 𝜔𝜔𝑝𝑝2
𝜔𝜔𝑝𝑝𝑛𝑛
(𝑠𝑠 + 𝜔𝜔𝑧𝑧1 )(𝑠𝑠 + 𝜔𝜔𝑧𝑧2 ) ��� (𝑠𝑠 + 𝜔𝜔𝑧𝑧𝑘𝑘 )
𝐵𝐵0
(𝑠𝑠 + 𝜔𝜔𝑝𝑝1 )(𝑠𝑠 + 𝜔𝜔𝑝𝑝2 ) ��� (𝑠𝑠 + 𝜔𝜔𝑝𝑝𝑛𝑛 )
≡
=
𝐵𝐵0
𝑠𝑠 𝑛𝑛 + 𝑠𝑠 𝑛𝑛−1 𝜔𝜔𝑝𝑝1 + 𝜔𝜔𝑝𝑝2 +��� +𝜔𝜔𝑝𝑝𝑛𝑛 +���
2
1
1
2
Frequency response
|H(jω)| (dB)
Vo /Vs = H (s )
A
0dB
-20dB/dec
ωp2 ωp3
ωp1
ωBW
(1 + s / ωp1)(1 + s / ωp 2 )(1 + s / ωp 3 )
-40dB/dec
ω (log)
0
-45°
ωBW = A* ωp1 : GBW
-90°
-270°
ω (log)
A
-60dB/dec
∠H(jω)
-180°
=
Phase margin
Ex) Two negative real poles, PM=90°
A=ωBW/ωp1
ωBW
ωp1
0.1ωp1
10ωp1
0.1ωp2
10ωp1<ωBW<0.1ωp2
ωp2
ω
ω
Ex) Two negative real poles, PM=45°
A=ωBW/ωp1
ωBW=ωp2
ωp1
0.1ωp1
ω
ω
10ωp1<0.1ωp2
Ex) Two negative real poles, PM=60°
tan-1(ωBW/ωp2)=30°
A=ωBW/ωp1
ωBW ωp2=√3*ωBW
ωp1
0.1ωp1
10ωp1
10ωp1<0.1ωp2
ω
ω
Ex) Two negative real poles, PM=30°
From ωp2/ωp1=A/(ωBW/ωp2)2,
tan-1(ωBW/ωp2)=60°
A=ωBW2/(ωp1*ωp2)
ωp2=ωBW/√3
(ωBW/ωp2)2
ωBW
ωp1
0.1ωp1
10ωp1
10ωp1 < 0.1ωp2
(one ex.)
ω
ω
Ex) Two poles at 0, PM=0°
|A| at DC=∞
|A|
-40dB/dec
ωBW
∠A
ω
ω
-180°
PM=0° : Two poles at the origin
ωp1=ωp2 =0
Voltage Source vs. Current Source
I
I
V
V
Requirements of Input & Output Resistance
∞
Vi
∞ ∞
0
A
Vo
Vi
A=Io/Vi
A=Vo/Vi
0
Ii
0 ∞
0
A
A=Vo/Ii
A
Io
Vo
Ii
A
Io
A=Io/Ii
Feedback
Steps to Understand Feedback Circuit
1. Check if loop forms a negative feedback
2. Check if loop gain is large enough
3. Estimate output which makes input be negligible
(=> 출력단의 전류 또는 전압을 입력의 함수로 고정되게 함)