electric circuit for physicists 電子回路論 第9回
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Electric Circuit for Physicists 電子回路論 第9回 Figure part
東京大学理学部・理学系研究科 物性研究所 勝本信吾
Shingo Katsumoto
Characteristic impedance
・・・ ・・・
dx
𝑉 𝑉 + 𝑑𝑉
𝐽 𝐽 + 𝑑𝐽
Pure reactance transmission line
L
C
L
C
L
C
L
・・・ ・・・
Coaxial cable setup
a b
r
ε, µ
Connection and termination
𝑍0 𝑍1
x 0 −l
SWR measurement SWR Meters: Desktop types
Cross-meter
Handy type
Connection and termination
𝑍0 𝑍1
x 0 −l
Exercise 4-3
𝑍0
x 0 −1km
𝑍0
0.6iΩ
4x10−6iS
Short
Open
Connection and termination
𝑍0 𝑍0′
5.2.3 Smith chart, Immittance chart
y = 4
x = 4
y = 2
y = 2 −
y = 4 −
y = 0
Re Z
Im Z
Re r
Im r
Z Z0
r : reflection coefficient
𝑟 =𝑉−𝑉+
=𝑍 − 𝑍0𝑍 + 𝑍0
Re r
Im r
5.2.3 Smith chart, Immittance chart
x=2 x=4
𝑟 = 𝑢 + 𝑖𝑖
5.2.3 Smith chart, Immittance chart
y =0
y =0.2
y =0.5
y =1 y =2
y =4
y =−4
y =−2 y =−1
y = −0.5
y = −0.2
𝑟 = 𝑢 + 𝑖𝑖
5.2.3 Smith chart, Immittance chart
x=2 x=4
y =0
y =0.2
y =0.5
y =1 y =2
y =4
y =−4
y =−2 y =−1
y = −0.5
y = −0.2
𝑟 = 𝑢 + 𝑖𝑖 Smith chart
5.2.3 Smith chart, Immittance chart
𝑟 = 𝑢 + 𝑖𝑖 Smith chart
Admittance chart
5.2.3 Smith chart, Immittance chart
𝑟 = 𝑢 + 𝑖𝑖 Immittance chart
5.3 S matrix (S parameters)
S
𝑎1 𝑏1
𝑏3 𝑏4
𝑎3
𝑎4
𝑎2 𝑏2
5.3 S-matrix (S-parameters) Simplest case:
𝑍𝑆 𝐽1
𝑉1 𝑉2
𝐽2
5.3 S-matrix (S-parameters) Simplest case:
𝑍𝑆
𝑍𝑆
𝑍0 𝑉2 𝑉1
𝐽1 𝐽2
𝑉1
𝐽1
𝑉2
𝐽2
𝑍0
𝑎2 = 0
𝑎1 = 0
𝐸1
𝐸2
𝑍0
𝑍0
Cascade connection of S-matrices
S-parameter representation of high-frequency devices
S-parameter representation of high-frequency devices
S-parameter representation of high-frequency devices
S11 S12
S21 S22
S-parameter and impedance matching
Practical impedance matching with Simth chart
5.4 Giving mass to LC transmission line
C
K
C
K
C
K
L L L
5.4 Giving mass to LC transmission line
𝜔
𝜔0
k
𝜔 = 𝑐∗𝑘
ℏ𝜔0 = 𝑚∗𝑐∗2
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