9-3: General Transmission Line Equations

1

• 9-3 General Transmission Line Equations
• Telegraphers equations
• They are derived from circuits, and are easy to
  remember, since they are generalized Faraday
  equations.

(9.31)
(9.33)
2

• In the frequency domain
• Note that
• For parallel-plate transmission lines

(9.35)
(9.23)
(9.13)
(9.15)
(9.29)
3

• 9-3.1 Wave characteristics on infinite
  transmission lines.
• From the two telegraphers equations of (9.35),
  we have
• Where
• fields

(9.36)
(9.37)
(8.44)
4

• The characteristic impedance
• Versus for fields

(9.41)
(8.54)
5

• 9-4 Wave characteristics on Finite Transmission
  Lines
• where

(9.93a)
(9.93b)
(9.94)
6

• General Solution of Lossless Transmission Line
• Note the coordinate just reversed!!!!
• The voltage wave
• where
• and

(1)
(2)
(3)
7

• At the load end, z0
• i.e.
• Voltage coefficient of the reflection at the load
  end

(4)
8

• Equations (1) and (3) may be rewritten as
• The input impedance

(5)
(6)
(9.109)
9

• For lossy line, we replace j by

(9.103)
10

• Special cases
• Open circuits
• Short circuits
• Quarter-wave transformer

(9.110)
(9.116)
(9.111)
(9.117)
(9.114)