and MICROWAVE RF ENGINEERING E&CE 493/671 Assignment #1
Due Date: Feb 8th, 2008
Problem #1 (25 marks)
(a) (b) Obtain expressions for the voltage and current standing-wave patterns on a lossless opencircuited transmission line. Sketch these patterns. A transmission line with Zc = 50 ohms is terminated in an impedance 25 j50 ohms. Find the reflection coefficient, standing-wave ratio, and fraction of the incident power delivered to the load. On a transmission line with Zc = 50 ohms, the voltage at a distance 0.40 from the load is 4 j2. The corresponding current is 2 amp. Determine the normalized load impedance.
(c)
Problem #2 (25 Marks)
For a discontinuity in a microstrip, the following scattering-matrix parameters were measured: 1 2 2 1 2 SA11 = + j SA12 = j SA22 = - j 3 3 3 3 3
(a) Find the parameters of equivalent ZA and YA networks that will represent the 2-port network whose scattering matrix is SA. (b) Find the overall scattering matrix of the following network: SA
0.50
SA
0.4
SA
( c ) If the overall network is terminated by a load with a reflection coefficient L . Find the reflection coefficient at the input of networks #4 , #2 and #1. #1-SA
0.2
#2-SA
0.7
#3-SA
0.5
#4-SA
Load L
Problem #3 (25 Marks)
A four-port network has the scattering matrix shown below. (a) Is this network lossless? (b) Is this network reciprocal? (c) What is the return loss at port 1 when all other ports are matched? (d) What is the scattering between matrix ports 2 and 4, when all other ports are matched? (e) What is the reflection coefficient seen at port 1 if a short circuit is placed at the terminal plane of port 3, and all other ports are matched?
- 1 of 3 -
0.1 1 [S ] = 2 1 2
/ 90 o / - 45o / - 45o 0
1 2
/ - 45o 0 0
1 2 0 0 1 2
/ 45o
1 2
/ 45o
/ - 45o
1 o / 45 2 1 o / - 45 2 0 0
Problem #4 ( 25 Marks)
A four-port network has the scattering matrix shown below. If ports 3 and 4 are connected together with a lossless matched transmission line with an electrical length of 120, find the scattering matrix between ports 1 and 2.
0.6 / 90o 0 [S ] = 0 0 .8 / 0 0 0.707 / - 45 0.707 / 45 0
o o
0 0.707 / 45 0.707 / - 45o 0
o
0 .8 / 0
0 0 0.6 / 90o
a) Find the reflection coefficient at port 1 and if port 3 is matched, port 2 is terminated by an open circui...