Question

2.19 A 50 lossless transmission line is terminated in a load with impedance ZL = (30 − j50) . The wavelength is 8 cm. Determine: (a) The reflection coefficient at the load. (b) The standing-wave ratio on the line. (c) The position of the voltage maximum nearest the load. (d) The position of the current maximum nearest the load. (e) Verify quantities in parts (a)–(d) using CD Module 2.4. Include a printout of the screen display.

Answer 1

The answer is below

Step-by-step explanation:

The load impedance =
`z_L=(30-j50)\Omega\\`

Characteristic impedance (Zo) = 50 Ω

Wavelength (λ) = 8 cm = 0.08 m

a) The reflection coefficient at the load is given as:

`\Gamma=(Z_L-Z_o)/(Z_L+Z_o)=(30-j50-50)/(30-j50+50)=0.57\angle -79.8^o`

b) The standing wave ratio (VSWR) is given as:

`VSWR=(1+|\Gamma|)/(1-|\Gamma|)=(1+0.57)/(1-0.57) =3.65`

c) The position of the voltage maximum nearest the load is given asL

`d_(max)=(\theta_\Gamma*\lambda)/(4\pi)+(n\lambda)/(2)=(-79.8*0.08\ m)/(4\pi)*(\pi)/(180)+(n*0.08)/(2)=-0.00887+0.04=0.0311\ m\\\\d_(max)=3.11\ cm`

d) The current maximum occurs at the voltage minimum. Hence:

`d_(min)=d_(max)-(\lambda)/(4)=3.11\ cm-(8\ cm)/(4)=1.11\ cm`