ex5_2011-12
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I-1 Exercise nr. 1 For the two-port network below, compute the scattering matrix, with respect to the reference impedances Z r1 = Z ∞1 and Z r2 = Z ∞2 . Dati: Z ∞1 = 30 Ω Z ∞2 = 60 Ω Z P = Z ∞2 AB = l 1 = λ/3 BC = l 2 = 3λ/8 1 2 Z ∞1 Z ∞2 A B C Z p S11=0; S21=1/sqrt 2 e-j17/12 s22=-j0.5 Exercise nr. 2 For the two-port network below, compute the S 11 and S 21 scattering parameters with respect to the reference impedances Z r1 = Z r2 = Z 0 . 1 2 Z ∞2 Z ∞1 A B C Z ∞1 Z ∞3 D E Z Ε Data: Z ∞1 = 2Z 0 Z ∞2 = Z 0 /3 Z ∞3 = Z 0 /2 Z E = j Z ∞1 AB = λ/2 BC = 3λ/4 AD = 5λ/8 BE = λ/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 Z r1 = Z r2 = Z 0 . Compute the power delivered to the load Z L . Data: E = 10 V (peak value) Z g = Z 0 /2 Z ∞ = 2Z 0 Z L = 5Z 0 /2 Z 0 = 50 Ω λ = 1 m AB = 11λ/4 α dB = 0.8 dB/m 0.1 0.8 0.8 0.1 S ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ 0.2 W E Z L Z ∞ , α dB Z g S A C B
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Transcript of ex5_2011-12
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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
