1. 2009 mid-term examination (100)
Microwave Engineering
Date: April 24, 2009.
1. Consider a sinusoidal wave function. Show that sin(ωt − kz )] is a wave
function and find out the direction of propagation. Hint:) set t = 0, z = 0 and
increase time while tracing a wavefront of sin(ω ⋅ 0 + k ⋅ 0) . (20)
Z − Z0
2. Consider a coaxial line with
Z 0 = 50Ω, f = 12.4 [GHz], Γ = L
Z L + Z 0 (80)
1)Calculate the reflection coefficient, Γ in terms of the magnitude and phase
when a resistor, R = 5 [Ω] is attached. (10)
2)Calculate the reflection and transmission powers for problem 1) when
Pi = 20 [dBm] . Hint:) PR =| Γ | 2 Pi , PT = (1− | Γ | 2 ) Pi ,
dBm = 10 log10 ( P / 1mW ) or P = 1mW * 10 dBm / 10 (20)
3)Calculate the reflection coefficient, Γ in terms of the magnitude and phase
when an inductor, L = 0.5[nH ] is attached. Hint:) Z L = jωL (20)
4)Calculate the reflection coefficient, Γ in terms of the magnitude and phase
when a real inductor, L = 0.5[nH ] and R = 20 [Ω] is attached. Hint:)
Z L = R + jωL (20)
5)Calculate the VSWR (Voltage Standing Wave Ratio) for problem 4). Hint:)

2. 1+ Γ
VSWR =
1 − Γ (10)