Microwave CAD and Measurements, Final Exam. Problems

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PIN = abcd: 휴대전화 끝 4 자리 (예: 010-8028-3194, a = 3, b = 1, c = 9, d = 4), 단 각 숫자가 0인 경우 순차적으로 1, 2, 3, 4로 대체 (예: 010-1234-0097인 경우 a = 1, b = 2, c = 9, d = 7)

The impeance of the following circuit is Z₂. Element values: C = 10a (nF), L_S = 100b (pH), R_S = d/10 (Ω), R_D = c (GΩ). Neglect C_P.

Fig. 1 Capacitor equivalent circuit

1. (10점) Find the self-resonant frequency f_r (Hz) of the circuit in Fig. 1. (10 points)

2. (20점) At the self-resonant frequency, calculate Z₂ and Z₁ = 1/(jωC).

The impeance of the following circuit is Z₂. C = 0.1a pF, R = b ohm, L = c + 0.1d uH

Fig. 2 Inductor equivalent circuit

3. (10점) Find the self-resonant frequency f_r (Hz) of the circuit in Fig. 2

4. (20점) At the self-resonant frequency, calculate Z₂ and Z₁ = jωL.

5. (30점) Write a Python code for calculating Z₂ and calculate Z₂ at f = 0.1 f_r, 0.5 f_r, 1.0 f_r, 2 f_r, and 10 f_r.

6. (20점) For a planewave propagating in +z direction in a medium with ε_r = a and μ_r = c, f = b (GHz),

E = (E_x, E_y, E_z) = (0, d, 0) V/m

1) find the wavelength λ (m),

2) find H = (H_x, H_y, H_z) = ( , , ) A/m

7. (20점) A planewave is incident from medium 1 to medium 2 with the incident electric field parallel to the plane of incidence. The angle of incidence is 45º.

Medium 1: ε₁ = bε₀, μ₁ = dμ₀

Medium 2: ε₂ = cε₀, μ₂ = aμ₀

Find the reflection coefficient Γ and the transmission coefficient τ.