# Transmission Lines 原文翻譯..

Z0 = characteristic impedance in ohms

R = conductor resistance in ohms per unit length

j = √-1

L = inductance in henrys per unit length

G = dielectric conductance in siemens per unit length

C = capacitance in farads per unit length

ω= frequency in radians per second

Z0 = 特性阻抗在歐姆

R = 兩個導體中每單位長度的串聯電阻，單位是 Ω/m。

j = √-1

L = 兩個導體中每單位長度的串聯電感，單位是 Η/m。

G = 每單位長度的並聯電導，單位是 S/m。

C = 每單位長度的並聯電容，單位是 F/m。

ω= 頻率在弧度每秒

=CHAPER 6 －Page 173=

In general the impedance is complex and is a function of frequency as well as the physical characteristics of the line.

For a lossless line, however, R and G are zero and Equation (6.2) simplifies to

Of course, there is no such thing as a completely lossless line, but many practical lines approach the ideal closely enough that characteristic impedance can be approximated by Equation (6.3).

This is especially true at high frequencies: as ω gets larger the values of R and G become less signify-cant in comparison with ωL and ωC.

For this reason, Equation (6.3) is often referred to as the high-frequency model of a transmission line.

Equation (6.3) gives a characteristic impedance that is a real number and does not depend on frequency or the length of the line, but only on such characteristics as the geometry of the line and the permittivity of the dielectric.

For coaxial cable, the characteristic impedance is given by:

Where

Z0 = characteristic impedance of the line

D = inside diameter of the outer conductor

d = diameter of the inner conductor

εr = relative permittivity of the dielectric, compared with that of free space. εr is also called the dielectric constant.

Z0 = 線的特性阻抗

D = 外面導管的內徑

d = 內在導管的直徑

εr = 電介質的相對電容率, 比較那自由空間。εr並且稱介電常數。

### 1 個解答

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最佳解答

Z0 = characteristic impedance in ohms

R = conductor resistance in ohms per unit length

j = √-1

L = inductance in henrys per unit length

G = dielectric conductance in siemens per unit length

C = capacitance in farads per unit length

ω= frequency in radians per second

Z0 = 特性阻抗單位為歐姆

R = 每單位長度的導體阻抗，單位是歐姆。

j = √-1

L = 每單位長度的電感係數，單位是 Η/m。

G = 每單位長度的電介質電導，單位是 S/m。

C = 每單位長度的電容量，單位是 F/m。

ω= 頻率單位為每秒弧度

=CHAPER 6 －Page 173=

In general the impedance is complex and is a function of frequency as well as the physical characteristics of the line.

For a lossless line, however, R and G are zero and Equation (6.2) simplifies to

一般來說阻抗是複雜的,牽涉頻率的作用和線的物理特性。

然而, 一條無損耗的導線, R與G為零(R=0,G=0)並且等式(6.2) 可簡化成

Of course, there is no such thing as a completely lossless line, but many practical lines approach the ideal closely enough that characteristic impedance can be approximated by Equation (6.3).

This is especially true at high frequencies: as ω gets larger the values of R and G become less signify-cant in comparison with ωL and ωC.

For this reason, Equation (6.3) is often referred to as the high-frequency model of a transmission line.

Equation (6.3) gives a characteristic impedance that is a real number and does not depend on frequency or the length of the line, but only on such characteristics as the geometry of the line and the permittivity of the dielectric.

For coaxial cable, the characteristic impedance is given by:

當然,沒有一條傳輸線是完全沒有損耗的,但許多現今的線已經非常接近理想其特性阻抗可簡化如等式 (6.3)。

尤其於高頻率時更為正確(接近): 當ω越大, 與 ωL 和ωC比較, R和G值相對影響較小。

因此, 等式(6.3) 通常適用於傳輸線的高頻率模型。

等式(6.3) 提供一個不取決於頻率或線的長度的實際的數字特性阻抗, 但只區限於線性幾何和電介質電容率之特性。

以同軸電纜, 其特性阻抗為:

Where

Z0 = characteristic impedance of the line

D = inside diameter of the outer conductor

d = diameter of the inner conductor

εr = relative permittivity of the dielectric, compared with that of free space. εr is also called the dielectric constant.

Z0 = 線的特性阻抗

D = 外面導管的內徑

d = 內在導管的直徑

εr = 相較於自由空間之電介質的電容率, 。εr也稱作介電常數。

參考資料： Own work
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