110年 - 110 國立臺灣大學_碩士班招生考試_光電工程學研究所:電磁學(C)#105687

(c) (5%) Find β_i (in rad/m)?

(e) (5%) What is the wavelength of wave ①?

(f) (5%) What is the w elength of wave ②?

(8) (5%) If the time-averaged power flow density of wave① is P₁, what is the time-averaged power flow density of wave②?

2. (15%) A parallel-plate transmission line consists of an arrangement of two perfect dielectrics, as shown by the transverse cross section in the figure below. Note that μ₁ε₁ =μ₂ε₂, so that the TEM waves propagating in the two dielectrics are in phase at all points along the interface between the dielectrics. Neglect finging of fields and compute the values of L, C, and Z₀ of the line. (C is the capacitance per unit length; L is the inductance per unit length.)

3. (10%) The input impedance of a short-cireuited transmission line of length / is
A resonant system is formed by connecting two short-circuited transmission lines as follows
At the junction, . Please show that

(i) (10%) Please show that the total field E = E₁+E₂ is equal to

(ii) (10%) Please write down the values of d and a for each case below.