Microwave Engineering

LECTURE ‘S TOPICS
1- Revision on the previous lecture.

2- Smith chart in finding:
- Y from 𝐙
- 𝐙𝐢𝐧 , 𝚪, 𝛔 (VSWR)
- 𝐙𝐦𝐚𝐱 , 𝐙𝐦𝐢𝐧
- 𝐙𝐋 using 𝛔, 𝐝𝐦𝐢𝐧
2- Single stub matching (series-shunt)
3- 𝚪 , 𝛔 in case of single stub matching
(f≠ 𝐟𝟎 ).
4- Quarter Wave Transformer
5- Solved Examples

, LAST LECTURE REVISION
Voltage and current waves are given by:

𝐕 = 𝐕𝟏 𝐞−𝐣𝛃𝐳 + 𝐕𝟐 𝐞𝐣𝛃𝐳 (3.6)

I = 𝐈𝟏 𝐞−𝐣𝛃𝐳 − 𝐈𝟐 𝐞𝐣𝛃𝐳 (3.7)
𝐕𝟏 −𝐣𝛃𝐳 𝐕𝟐 𝐣𝛃𝐳
I= 𝐞 − 𝐞 (3.8)
𝐙𝐜 𝐙𝐜
Voltage and current waves using reflection coefficient:

𝐕 = 𝐕𝟏 𝐞−𝐣𝛃𝐳 + 𝚪 𝐞𝐣𝛉 𝐕𝟏 𝐞𝐣𝛃𝐳 (3.9)
𝐕𝟏 −𝐣𝛃𝐳 𝚪 𝐞𝐣𝛉 𝐕𝟏 𝐣𝛃𝐳
I= 𝐞 − 𝐞 (3.10)
𝐙𝐜 𝐙𝐜

,LAST LECTURE REVISION

𝑽𝒎𝒂𝒙
VSWR = 𝛔 = (3.11)
𝑽𝒎𝒊𝒏

𝐕𝐦𝐚𝐱 𝟏+ 𝚪
𝛔= = (3.12)
𝐕𝐦𝐢𝐧 𝟏− 𝚪

𝛔 −𝟏
𝚪 = (3.13)
𝛔 +𝟏

0< 𝚪 <𝟏 1<𝛔<∞

, LAST LECTURE REVISION
The ideal (matched) Tr. line has:

zero reflection 𝚪 = 0 VSWR = 1 (𝛔 = 1)

𝐙𝐋 + 𝐣𝐙𝐜 𝐭𝐚𝐧 𝛃𝐋
𝐙𝐢𝐧 = 𝐙𝐜
𝐙𝐜 + 𝐣𝐙𝐋 𝐭𝐚𝐧 𝛃𝐋



𝐕𝐦𝐚𝐱 𝐕𝟏 + 𝚪 𝐕𝟏 𝐕𝟏 𝟏 + 𝚪
Zmax = = = = Z𝐂 𝛔
𝐈𝐦𝐢𝐧 𝐈𝟏 − 𝚪 𝐈𝟏 𝐈𝟏 𝟏 − 𝚪



𝐕𝐦𝐢𝐧 𝐕𝟏 − 𝚪 𝐕𝟏 𝐕𝟏 𝟏 − 𝚪 𝟏
Zmin = = = = Z𝐂
𝐈𝐦𝐚𝐱 𝐈𝟏 + 𝚪 𝐈𝟏 𝐈𝟏 𝟏 + 𝚪 𝛔