Course: BEng (Hons) in Electrical and Electronic Engineering

1. EEEE 6490345 RF AND MICROWAVE ELECTRONICS
Transmission Line
FACULTY OF ENGINEERING AND COMPUTER TECHNOLOGY
BENG (HONS) IN ELECTRICALAND ELECTRONIC ENGINEERING
Ravandran Muttiah BEng (Hons) MSc MIET

2. Power
Example 1:
Consider the transmission line circuit shown in figure 1. Compute the
incident power, the reflected power and the power transmitted into the
infinite 75 Ω line. Show that power conservation is satisfied.
Figure 1: Transmission line circuit
1
50 Ω
𝑍1 = 75 Ω10 V 𝑍o = 50 Ω
λ 2
𝑃trans𝑃inc
𝑃ref

3. 2
Solution:
𝑍in = 𝑍o
𝑍𝑙 + j𝑍o tan 𝛽𝑙
𝑍o + j𝑍𝑙 tan 𝛽𝑙
Since, 𝑙 =
λ
2
, tan 𝛽𝑙 = tan
2π
λ
λ
2
= tan π = 0
𝑍in = 𝑍o
𝑍𝑙 + 0
𝑍o + 0
𝑍𝑙 = 𝑍1 = 75 Ω
𝑅g = 50 Ω
𝑅L = 75 Ω𝑉g = 10 V
Source impedance
Terminal
impedance
Characteristics
impedance
𝑍o = 50 Ω
𝐼g
+ -
+
-
Figure 2

4. 3
Power delivered by source =
1
2
𝑉g 𝐼g cos 𝜃
𝑍in =
1
2
10
10
50 + 75
=
1
2
100
125
= 0.4W
Power dissipated in 50 Ω,
𝑃r =
1
2
𝐼g
2
𝑅g =
1
2
10
50 + 75
2
50 = 0.16W
Power transmitted down the line or Power delivered to load 𝑃L,
𝑃L =
1
2
𝐼g
2
𝑅L
=
1
2
10
50 + 75
2
75
= 0.24 W

5. 4
Incident power is also the input power.
𝑃inc =
1
2
𝐼g
2
𝑍o
=
1
2
10
50 + 50
2
50
= 0.25 W
50 Ω
50 Ω𝑉g = 10 V 𝑍o = 50 Ω
𝐼g
+ -
+
-
Figure 3
𝑃inc

6. 5
𝑅g = 50 Ω
𝑅L = 75 Ω𝑉g
S11 or Гin
𝐼g
+ -
+
-
Figure 4
Input reflection coefficient, Гin =
75 − 50
75 + 50
=
25
125
= 0.4
Reflected power, 𝑃r = 𝑃inc Гin = 0.25 0.4 = 0.1 W
Transmitted power = Incident power – Reflected power = 0.25 − 0.1 W
= 0.24 W
Power from source, 𝑃g = Dissipated power + Transmitted power
= 0.16 + 0.24 W = 0.4 W