초고주파공학 중간고사 문제 (2021-4-23, 15:00-15:50), eCampus에 15:50 이전까지 답지 문서 또는 사진제출

학번 ( ) 성명 ( ) 이동전화번호( )

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)

배점: 소문제당 10점

1. Transmission line R, L, G, C parameter calculation:

We have a transmission line operating at 100 MHz with R = a /1000 Ω/m, L = 100b nH/m, G = c/1000 S/m, C = 10d pF/m. Write down a Python code to calculate the following. Run it on www.online-python.com. Submit the source code and the result of your program execution by capturing the PC screen.

1) the characteristic impedance Z₀ (Ω),

2) the attenuation constant α (Np/m),

3) the phase constant β (rad/m)

Hint: complex arithmetic

math.sqrt(z): take a square root of a complex number z

z.real: take the real part of a complex number z

z.imag: take the imaginary part of a complex number z

2. Input reflection coefficient, input impedance, and delivered power:

A load Z_L at z = 0 is connected with a tranmision line of length l with Z₀ and β.

Z_L = 10(d - jc) Ω

Z₀ = 10a Ω

l = 0.2 wavelength (tranmssion line length)

Find at z = −l,

1) the load reflection coefficient

2) the input reflection coefficient Γ(−l)

3) the input impedance Z(−l) (Ω)

4) the power delivered to the load when a power of 1 watt is incident on the transmissio line at z = −l.

3. L, C parameters of a coaxial cable:

For a coaxial cable with

the radius of the center conductor r₁ = a mm

the radius of the outer conductor r₂ = a+5b mm

the dielectric constant of the material between the inner and outer conductors ε_r = c

the relative permittivity of the material between the innder and outer conductos μ_r = d

find

1) the inductance per unit lenght L,

2) the capacitance per unit length C,

3) the characteristic impedance Z₀.

4. Impedance Smith chart, admittance Smith chart:

With Z₀ = 10d Ω,

1) draw R = 10a Ω curve and X = −10b Ω curve on the impedance Smith chart.

2) draw G = 1/(10c) S and B = 1/(10a) S curve on the admittance Smith chart.

5. Conjugate matching:

Zs = 10(a + jd) Ω, V_S = c exp(jb)

1) Find Z_L for maximum power transfer to Z_L.

2) In this case, find the power dissipated in Z_L

6. A quarter-wave transformer:

Z₀ = 10d Ω, Z_in = 100a Ω

Γ_L: magnitude = c/10, phase = 20b deg.

1) Find the minimum value of l in terms of the wavelength on the transmission line.

2) Find the input impedance Z₁ in the figure.

3) Find Z_T.

7. LC matching:

A load impedance Z_L = 20c + j50d Ω is to be transformed to Z_in = Z₀ = 30a Ω at 100 MHz.

1) Use the Python code given in the lecture webpage to find all possible LC matching networks. Run it on www.online-python.com. Submit the source code and the result of your program execution by capturing the PC screen.

2) Draw all of your matching networks.

Hint: The Python code for this problem is available on the lecture web page as 06-python.txt