Ch.5 Additional
Analysis Techniques
LEARNING GOALS
LINEARITY
SUPERPOSITION
THEVENIN’S AND NORTON’S THEOREMS
MAXIMUM POWER TRANSFER

Equivalent Circuits
Equivalent Circuits
s
v
a
b
R
s
i
a
b
R
𝑽
𝒔
= 𝑹. 𝑰𝒔

Linear System
Principles of Superposition (
중첩의 원리
)
𝑦 = 𝐻(𝑥)
is linear iff
𝑦 = 𝐻
𝛼
ଵ
𝑥
ଵ
+ 𝛼
ଶ
𝑥
ଶ
= 𝛼
ଵ
𝐻
𝑥
ଵ
+ 𝛼
ଶ
𝐻
𝑥
ଶ
for all possible input pairs
𝑥
ଵ
,
𝑥
ଶ
and for all possible scalars
𝛼
ଵ
,
𝛼
ଶ
정의
1
정의
2
𝑦 = 𝐻(𝑥)
is linear iff it meets the following two conditions
Additivity
:
𝐻
𝑥
ଵ
+ 𝑥
ଶ
= 𝐻
𝑥
ଵ
+ 𝐻
𝑥
ଶ
,
∀ 𝑥
ଵ
,
𝑥
ଶ
Homogeneity
:
𝐻
𝛼𝑥
= 𝛼𝐻
𝑥
,
∀ 𝛼
,
𝑥
일상 생활에서 찾아볼 수 있는
Linearity
Exchange Rates
Feet
F
in terms of centimeters,
C
C=30.48 * F
Travel
Distance
D
that a vehicle moves during
H
hours
(with a speed of 60 mph)
D = 60 * H
Are the followings linear?
Temperature Conversion
C = (5/9) (F-32)
Cell Phones
Monthly cost based on minutes/month
C = 0.05m + 20

Example 5.1: Find
V
out
.
]
[
1
2
V
V
V
out
=
=
ASSUME
Now use homogeneity
]
[
2
]
[
12
]
[
1
]
[
6
V
V
V
V
V
V
V
V
out
O
out
O
=
→
=
=
→
=
Source Superposition
=
+

Example 5.3