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