Post on 23-Feb-2022
Capacitor
3
• Capacitor (캐패시터 or 콘덴서)
- Capacitor 내부의 전기장에 전기에너지를 저장할 수 있
도록 고안된 전기소자
Pusan National University
AC
d
메탈필름 세라믹 전해
바리콘
Capacitor
4
• Capacitance : 𝑞 = 𝐶𝑣
- 정전용량의 단위 : Farad = Coulomb/Volt
- Capacitor의 전압-전류 관계
Pusan National University
00
1 1( ) ( ) ( )
t t
t
dq dv dvq Cv C i C
dt dt dt
v i t dt i t dt v tC C
Capacitor
5
• Instantaneous power to the capacitor
• Energy stored in the capacitor
Pusan National University
dvp vi Cv
dt
( )( )
2
( )( )
22
1( ) ( ) ( )
2
1 1( ( ) 0) or ( )
2 2
v tt t v t
vv
dvw p t dt C v t dt C v t dv Cv
dt
q qw Cv v v
C C
Capacitor
6
• Capacitor의 특징
- A capacitor acts as an open circuit to DC (𝑖 = 𝐶𝑑𝑣
𝑑𝑡)
- The voltage on a capacitor cannot change abruptly
- The ideal capacitor does not dissipate energy
- A non-ideal capacitor can be modeled as the parallel
circuit with ideal capacitor and leakage resistance
Pusan National University
Capacitor
8Pusan National University
Example 6.4
Determine the current through a 200uF capacitor whose voltage is shown in the Fig.
Capacitor
9Pusan National University
Example 6.5
Obtain the energy stored in each capacitor in the figure under DC conditions
Series & Parallel Capacitors
10
• Capacitor의 병렬연결
Pusan National University
1 2
1 2
1
1 2
(by KCL)N
N
N k
k
eq N
i i i i
dv dv dv dvC C C C
dt dt dt dt
C C C C
Series & Parallel Capacitors
11
• Capacitor의 직렬연결
Pusan National University
1 2
0 0 01 2
01 2
1 2
(by KVL)
1 1 1( ) ( ) ( )
1 1 1( )
1 1 1 1
N
t t t
t t tN
t
tN
eq N
v v v v
i t dt i t dt i t dtC C C
i t dtC C C
C C C C
Series & Parallel Capacitors
12Pusan National University
Example 6.6
Find the equivalent capacitance between terminals a and b of the following circuit :
Series & Parallel Capacitors
13Pusan National University
Example 6.7
Find the voltage across each capacitor for the following circuit :
Inductor
14
• Inductor (인덕터 or 코일)
- Inductor 내부의 자기장에 전기에너지를 저장할 수 있
도록 고안된 전기소자
Pusan National University
2N AL
솔레노이드 코일
칩인덕터
초크 코일
Inductor
15
• Inductance : 𝑣 = 𝐿𝑑𝑖
𝑑𝑡
- Inductance의 단위 : [H], Henry
- Inductance의 전압-전류 관계
Pusan National University
00
1 1( ) ( ) ( )
t t
ti v t dt v t dt i t
L L
Inductor
16
• Instantaneous power to the inductor
• Energy stored in the inductor
Pusan National University
dip vi L i
dt
( )
2
( )
2
1( ) ( ) ( )
2
1( ( ) 0)
2
i tt t t
i
diw p t dt L i t dt L i t di Li
dt
w Li i
Inductor
17
• Inductor의 특징
- A inductor acts as a short circuit to DC (𝑣 = 𝐿𝑑𝑖
𝑑𝑡= 0)
- The current though an inductor can’t change abruptly
- The ideal inductor does not dissipate energy
- A non-ideal inductor can be modeled as the series
circuit with ideal inductor and winding resistance
Pusan National University
Inductor
19Pusan National University
Example 6.10
Consider the following circuit. Under DC conditions, find: (a) 𝑖, 𝑣𝐶and 𝑖𝐿, (b) the energy stored in the capacitor and inductor
Series & Parallel Inductors
20
• Inductor의 병렬연결
Pusan National University
1 2
1 0 2 0 00 0 0
1 2
1 0 2 0 00
1 2
1 2
(by KCL)
1 1 1( ) ( ) ( )
1 1 1( ) ( ) ( )
1 1 1 1
N
t t t
Nt t t
N
t
Nt
N
eq N
i i i i
vdt i t vdt i t vdt i tL L L
vdt i t i t i tL L L
L L L L
Series & Parallel Inductors
21
• Inductor의 직렬연결
Pusan National University
1 2
1 2
1 2
1 2
(by KVL)N
N
N
eq N
v v v v
di di diL L L
dt dt dt
diL L L
dt
L L L L
Series & Parallel Inductors
22Pusan National University
Example 6.11
Find the equivalent inductance of the circuit shown in the following figure
Series & Parallel Inductors
23Pusan National University
Example 6.12
For the following circuit, ሻ𝑖(𝑡ሻ = 4(2 − 𝑒−10𝑡 mA. If 𝑖2(0ሻ = −1mA, find (a) ሻ𝑖1(0 ; (b) ሻ𝑣(𝑡ሻ, 𝑣1(𝑡 , and ሻ𝑣2(𝑡 ; (c) ሻ𝑖1(𝑡 and ሻ𝑖2(𝑡
Applications - Integrator
24
• Inverting invertor에 capacitor를 활용하여 적분기 구성
Pusan National University
0
(0 ),
1( )
i o oR C
ti o
o i
v d v dvi i C C
R dt dt
v dvC v v t dt
R dt RC
Applications - Integrator
25Pusan National University
Example 6.13
If 𝑣1 = 10cos2𝑡 [mV] and 𝑣2 = 0.5𝑡 [mV], find 𝑣𝑜 in the op-amp circuit in the following figure. Assume that the voltage across the capacitor is initially zero.
Applications - Differentiator
26
• Inverting invertor에 capacitor를 활용하여 미분기 구성
Pusan National University
,i o iC R o
dv v dvi C i v RC
dt R dt
Applications - Integrator
27Pusan National University
Example 6.14
Sketch the output voltage for the following circuit. Assume that 𝑣𝑜 = 0 at 𝑡 = 0.
iv
Applications – Analog Computer
28
• Analog computer는 미분방정식을 풀기 위한 목적으로 개
발되었으며, op-amp를 이용하여 구현
•𝑑𝑥
𝑑𝑡는
𝑑2𝑥
𝑑𝑡2를 적분하여, 𝑥는
𝑑𝑥
𝑑𝑡를 적분하여 계산, ሻ𝑓(𝑡 는 외부
의 signal generator를 이용하여 입력
Pusan National University
2
2
2
2
( ), 0
( )
d x dxa b cx f t t
dt dt
d x f t b dx cx
dt a a dt a
Applications – Analog Computer
29Pusan National University
Example 6.15
Design an analog computer circuit to solve the differential equation :
Subject to 𝑣𝑜(0ሻ = −4, 𝑑𝑣𝑜
𝑑𝑡|𝑡=0 = 1.
2
22 10sin 4 , 0o o
o
d v dvv t t
dt dt