Microwave Engineering Problems and Solutions for Lectures in Week 9 to Week 13

Week 9: Capacitor equivalent circuit

Neglect R2 and R1. Find the self-resonante frequency f.

(Answer)

Week 10: Inductor equivalent circuit

R = 20 Ω, L = 3.5 μH, C = 0.7 pF

1) Calculate the self-resonant frequency f₀ neglecting R.

2) Find the impedance Z at 0.2f₀ and 5f₀ including R.

(Answer)

1)

2)

Week 11:

1. Parallel-plate capacitor

S= 1 cm², d = 0.1cm, f = 1 MHz, ε' = 3ε₀, ε'' = 0.001ε'

Find the values of C and R

(Answer)

2. Solenoid inductor

S= 1 cm², d = 0.1 cm, f = 1 MHz, μ' = 3μ₀, μ'' = 0.001μ'

Find the values of R and L.

(Answer)

3. Find the conductor loss power density p_c, dielectric loss power density p_d, and dielectric stored power density w_e in a medium with

ε' = 3ε₀, ε'' = 0.001ε', σ = 100, | E | = 10 V/m, f = 100 MHz

(Answer)

4. Find the magnetic loss power density p_m, and magnetic stored power density w_m in a medium with

μ' = 3μ₀, μ'' = 0.001μ', | H | = 10 A/m, f = 100 MHz

(Answer)

5. Planewave

ε = 9ε₀, μ = μ₀, f = 100 MHz

Find the intrinsic impedance η, propagation constant k, and wavelength λ.

(Answer)

Week 12:

1. Planewave in lossy media

ε' = 4ε₀, ε'' = 0.1ε', μ' = 9μ₀, μ''= 0, f = 3 GHz

1) Find the attenuation constant α, propagation constant β, and skin depth δ_s.

2) Write a Python code and show the execution result.

(Answer)

2) Omitted

2. Surface impedance

μ = μ₀, f = 3 GHz, σ = 10⁷ S/m

Find the surface impedance Z_s.

(Answer)

Week 13:

1. Planewave reflection and transmission, normal incidence

ε₁ = ε₀, ε₂=4ε₀, μ₁ = μ₂ = μ₀

Find the reflection coefficient Γ and transmission coefficient τ.

(Answer)