DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY ROOKEE

EC-631 Prob. Sheet-3

1. Consider a two-port microwave network whose impedance matrix is known. Determine the circuit parameters if the network is represented by the following circuit.

Z1 Z2

ZC

l

t1t2

2. Determine the admittance matrix of the microwave two-port junction whose equivalent circuit is

shown in the figure below.

Y

t1 t2

ZC

l

3. Assuming that the S-parameters of microwave 2-port to be known, determine the Z- and Y-

parameters of the network.

4. A microwave 2-port has a scattering matrix {S}. If two such networks are connected in cascade, determine the S-matrix of the composite network.

5. A certain 2-port has a scattering matrix given by

0.1 0 0.8 90[ ]

0.8 90 0.2 0S

Determine whether the network is (i) reciprocal (II) lossless. If a short circuit is placed at port-2, what will be the return loss at port-1?

6. For a lossless 2-port junction, following S parameters were measured:

11 22

1 2 1 2

3 3

j jS S

A matched generator with power output of 100 mW is connected at the input port and output port is terminated in a normalized load impedance ZL = 2. Find (i) VSWR at the generator end, (ii) power delivered to the load, and (iii) power dissipated in the generator impedance.

7. For the following microwave network, evaluate (i) the power delivered to the load impedance ZL

and (ii) VSWR on the two transmission line sections. Assume ZL = 2 Z1, X1 = X2 = Z1, Vg = 5 V(peak).

Z1

Z1

l = /4

jX1

jX2 ZLZ1

l = 3/4

Vg

8. Starting with the defining equations, determine the wave-amplitude transmission matrix for a shunt susceptance jB connected across a transmission line of unit characteristic impedance.