Question

Consider the system with matching network shown in Fig. 3. 1) Select L and C such that the input impedance Zin is 50 Ohms resistive at the Industrial, Scientific, and Medical (ISM) band frequency of 27.12 MHz. same frequency. transformation at 13.56 MHz, and at the same time offer high-pass function. 2) Design a different matching networks that provide the same impedance transformation at the 3) Design a matching network with two L and one C that can provide the same impedance

Answer 1

Z_in = 50 Ohm, f = 27.12 MHz, R = 75 Ohm matching network Implies f = 27.12 MHz = 27.12 times 10^6 Hz, w = 2 pi f = 170 times 10^6 rad/sec Q = squareroot R/Z_in - 1 = squareroot 75/50 - 1 = 0.707 X_s = Q middot Z_n = 0.707 times 50 = 35.35 Ohm X_p = R/Q = 75/0.707 = 106 Ohm X_s = Lw Implies L = X_s/2 pi f = 35.35/170 times 10^6 = 208 nH X_p = 1/c w Implies w = 1/c X_p Implies c = 1/X_p w = 1/106 times 2 pi f = 55.5 p F 2) consider another matching network . Q = 0.707 X_s = Q middot Z_in = 35.35, X_p = R/Q = 106 Ohm X_s = 1/c w Implies w = 1/c X_s Implies c = 1/w X_s = 1/170 times 10^6 times 35.35 = 166 PF X_p = c w Implies L = X_R/w = 106/170 times 10^-6 = 0.0623 nH \r\n 3) f = 13.56 MHz Implies w = 2 pi f = 85.2 times 10^6 rad/sec Q = squareroot R/Z_in - 1

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