代写EEME30004 Communications and Networks RF systems Homework #1代写Web开发

EEME30004 Communications and Networks

RF systems Homework #1

Q1: Below is the S matrix of a 4 port network.

(a) What fraction of the incident power at port 1 is reflected back to port 1 when all other ports are terminated with matched loads?

(b) What is the return loss at port 1 when all other ports are terminated with matched loads?

(c) What is the ratio of power transmitted from port 4 to port 2 if all other ports are terminated with matched loads?

(d) When port 3 is excited with an incident signal and all other ports are terminated with matched loads, what fraction of the incident power at port 3 is transmitted to each of the other ports?

(e) Is this network lossless?

(f) Is this network reciprocal?

Q2: Answer the following questions:

In Figure Q2, a load impedance zl  = 40 -j30 Ω, connected with a lossless transmission line with length l = 0.3λ . Its characteristic impedance z0  = 50 Ω . The operating frequency is 2 GHz.

Figure Q2

(a) Plot the normalized load impedance on the Smith chart and provide its corresponding reflection coefficient.

(b) Using the Smith Chart, determine the input impedance zin looking into the transmission line.

(c) Verify your result from part (b) analytically using the transmission line input impedance formula.

(d) Indicate whether the input impedance is capacitive or inductive.

Q3. The network below consists ofa lossless transmission line of characteristic impedance Z02 and electrical length l2 , terminated by a load Zl . At a distance l2 from the load, a  shunt capacitor c is connected to ground. From that node back to the source, there is a second lossless line  of  characteristic  impedance  Z01 and  electrical  length  l1.  Assume  a  single  operating frequency f0.

Given: Z01  = 50 Ω, Z02  = 75 Ω, l1 = 0.15λ of the Z01 line, l2  = 0.2λ of the Z02 line, Zl  = 30 —j20 Ω, f0  = 2 GHz

Figure Q3

(a) Plot the normalized load impedance on Smith chart (referenced to Z02). Use Smith chart to obtain the input impedance looking into the Z02 line (without considering shunt capacitance C).

(b) Covert the input impedance obtained in (a) to admittance. Then, calculate the value of  the shunt capacitance C to make this total admittance at the junction between the Z02 line and the Z01 line a pure conductance.

(c) Based on the result from (b), determine the input impedance looking into Z01 line. Obtain this value both graphically using Smith chart and analytically with the transmission line input impedance formula.

(d) Calculate the VSWR at the input (source) end of the Z01 line based on the result from (c).