I-1

Group of exercises nr. 5 Scattering parameters

Exercise nr. 1 For the two-port network below, compute the scattering matrix, with respect to the reference impedances Zr1 = Z1 and Zr2 = Z2. Dati: Z1 = 30 Z2 = 60 ZP = Z2 AB = l1 = /3 BC = l2 = 3/8

1 2Z1 Z2

A B C

Zp

S11=0; S21=1/sqrt 2 e-j17/12 s22=-j0.5

Exercise nr. 2 For the two-port network below, compute the S11 and S21 scattering parameters with respect to the reference impedances Zr1 = Zr2 = Z0.

1 2Z2 Z1

A B C

Z1Z3

D EZ

Data: Z1 = 2Z0 Z2 = Z0/3 Z3 = Z0/2 ZE = j Z1 AB = /2 BC = 3/4 AD = 5/8 BE = /8

S11=-0.55-j0.72; s21=-0.27-j0.36; Exercise nr. 3

Consider the circuit below, consisting in a voltage generator connected to a load through a lossy transmission line and a two-port network inserted between section B and C, characterized by its scattering matrix S, with respect to the reference impedances Zr1 = Zr2 = Z0. Compute the power delivered to the load ZL. Data:

E = 10 V (peak value) Zg = Z0/2 Z = 2Z0 ZL = 5Z0/2 Z0 = 50 = 1 m AB = 11/4 dB = 0.8 dB/m

0.1 0.80.8 0.1

S = 0.2 W

E ZL Z , dB

Zg

S

A C B