代做EEME30004 Communications and Networks RF systems Homework #2代写Processing

EEME30004 Communications and Networks

RF systems Homework #2

Q1: Design a matching network, assuming zs   = 50 Ω and zl   = 20 + j100 Ω . The operating frequency is 1 GHz.

Figure Q1

Design a LC matching network (only two lumped components). Get all possible combinations of this LC matching network with the help of Smith Chart, and obtain their actual values.

Q2 A load impedance zl  = 100 + j80 Ω is to be matched to a 50 Ω line using a single shunt- stub matching network. Find two designs using open-circuited stubs and two designs using short-circuited stubs via  Smith Chart. The characteristic impedance of lines are 50 Ω . (4 possible matching networks in total, get the electrical lengths of transmission lines in fractions of wavelength).

Q3 A quarter-wave transmission line is inserted between zl  and zs  as the impedance matching network.

Figure Q3

(a) Determine the characteristic impedance z0  of the quarter-wave transmission line above if zl  = 100 Ω and zs  = 40 Ω .

(b) Discuss if zl  is a complex impedance, can the single quarter-wave transmission line offer a perfect match as seen in Figure Q3 assume you can select z0  (real value)?

(c) If this quarter-wave transmission line is implemented on a substrate with an effective dielectric constant of εeff  = 3, what is the physical length of this line if operating frequency is 1.5 GHz.

Q4 Design a matching network for the diagram below. zl   = 40 + j60 Ω and zs   = 50 Ω .

Figure Q4

(a) Design a LC matching network (one choice is enough). Calculate their actual values assuming the operating frequency is 2 GHz.

(b) Design a transmission line based matching network using a shunt stub (assuming the characteristic impedance of the designed matching network transmission lines is 50 Ω) using Smith Chart. The requirement is that choose the design with the shortest length among all possibilities. (show your steps on Smith chart)