Question

3) For the following r-network at 1 GHz, calculate a) The admittance matrix b) The impedance matrix c) The ABCD matrix (30 points) 1/π nH 11, 2 O-

Answer 1

For the following T-network at 1GHZ, calculate a) the admittance matrix b) the impendence matrix c) the ABCD matrix Given that f = 1GHZ X_L = 2 pi fl = 2 pi times 1 times 10^9 times 1/pi times 10^-9 X_L = j_2 ohm X_L = 1/2 pi f c = 1/ 2 pi times 1 times 10^9 times 1/pi times 10^- 9 X_L = 1/2 X_L = -j 0.5 ohm The T - network becomes \r\n a) Admittance matrix I_1 = y_11 v_1 + y_12 v_2 I-2 = y_21 v_1 + y_22 v_2 short port - 2(v_2 = 0) current floor low resistance then circuit becomes V_1 = j_2 I_1 rightarrow (1) I_1/v_1 = 1/j-2 y-11 = -j 0.5 ohm I_1 = -I_2 Eq(1) becomes v_1 = j_2(- I_2) I_2/v_1 = -1/j_2 I_2/v_1 = j 0.5 ohm y_21 = j 0.5 \r\n short part -1(v_1 = 0) apply in loop - 1 v_2 = -j 0.5(I_1 + I_2)