Solution Electromagnetic Fields and Waves - Iskander - 8.14

Student Answer Electromagnetic Fields and Waves Chapter 8

8.14. A slotted wave guide dimensions 𝑎 = 7.6 𝑐𝑚 and 𝑏 = 3.8 𝑐𝑚 is used to measure the wave guide wavelength and the operating frequency. If the distance between two successive minima is 9 𝑐𝑚, and assuming 𝑇𝐸10 mode of operation in air, calculate the following: (a) Wave-guide wavelength 𝜆𝑔 , cutoff frequency, and operating frequency (assuming operating frequency is 20% higher than operating frequency). (b) Propagation constant and intrinsic impedance. Ans. (a) 1

Distance of two successive minima is 2 𝜆𝑔 1 𝜆 = 9 × 10−2 2 𝑔 𝜆𝑔 = 18 × 10−2 𝜆𝑔 = 18 𝑐𝑚 Cutoff frequency 𝑓𝑐𝑜,𝑚𝑛 =

1 2𝜋√𝜇𝜀

𝑓𝑐𝑜,𝑚𝑛 =

𝑓𝑐𝑜,10

√(

𝑚𝜋 2 𝑛𝜋 2 ) +( ) 𝑎 𝑏

𝑐 𝑚 2 𝑛 2 √( ) + ( ) 2 𝑎 𝑏

2 2 3 × 108 1 0 √ = ( ) +( ) 2 7.6 × 10−2 3.8 × 10−2

𝑓𝑐𝑜,10 = 1.97 × 109 𝑓𝑐𝑜,10 = 1.97 𝐺𝐻𝑧 Operating frequency 𝑓𝑜𝑝 = 1.2𝑓𝑐𝑜 𝑓𝑜𝑝 = 2.36 × 109 𝑓𝑜𝑝 = 2.36 𝐺𝐻𝑧

muhsin.web.id

1

(b) Propagation constant 𝑚𝜋 2 𝑛𝜋 2 𝛾 = √( ) + ( ) − 𝜔 2 𝜇𝜀 𝑎 𝑏 2

2𝜋𝑓𝑜𝑝 𝑚𝜋 2 𝑛𝜋 2 𝛾 = √( ) + ( ) − ( ) 𝑎 𝑏 𝑐

2

𝛾 = √(

2 2 1𝜋 0𝜋 2𝜋(2.36 × 109 ) ) +( ) −( ) 7.6 × 10−2 73.8 × 10−2 3 × 108

𝛾 = 𝑗27.0993 Intrinsic impedance 𝑍𝑚𝑛 =

𝑍10 =

𝑍𝑖 2 𝑓 √1 − ( 𝑐𝑜,𝑚𝑛 ) 𝑓𝑜𝑝

𝑍𝑖 2 𝑓 √1 − ( 𝑐𝑜,10 ) 𝑓𝑜𝑝

𝑍10 =

120𝜋 2 √1 − ( 1 ) 1.2

𝑍10 = 682.0030 Ω

Muhsin 1101121302 School of Electrical Engineering Telkom University

muhsin.web.id

2