Please complete ONLY 12.2 and show your work! 2.1. Voltage and current standing

Question

Please complete ONLY 12.2 and show your work!

2.1. Voltage and current standing wave patterns for resistive loads. Consider a lossless trans- mission line of characteristic impedance Zo- 50 and a time-harmonic traveling wave of rms voltage Vi) 10 V on it. The wavelength along the line is ,-1 m. Find the magnitude and phase angle of the load reflection coef- ficient, the maxima and minima of the total voltage and of the total current of the line and their locations, and the standing wave ratio of the line, and sketch the voltage and cur- rent standing wave patterns along the line if it is terminated in a purely resistive load of resistance (a) RL-250 and (b) RL = 10 , respectively. 2.2. Standing wave patterns for reactive loads. Repeat the previous problem but for a purely reactive load of reactance (a) XL-50 and (b) XL :--50 , respectively.

Explanation / Answer

Given Z0=50 ohms

rms voltage=10 V

(a) Rl=250 ohms :

REflection coefficient   = (ZL - Z0)/(ZL + Z0)

= (250-50)/(250+50)

= (200/300)=0.66

Voltage Standing wAVE Ratio(VSWR):

VSWR = (1 + )/(1 - )

VSWR=(1+0.667)/(1-0.667)=1.337

(B)

Rl=10 ohms :

REflection coefficient   = (ZL - Z0)/(ZL + Z0)

= (10-50)/(10+50)

= (-40/60)=-0.66

Voltage Standing wAVE Ratio(VSWR):

VSWR = (1 + )/(1 - )

VSWR=(1-0.667)/(1+0.667)=0.1979

These are the rong results obtained in this section because VSWR Range is:1 to infinity.So it is not possible.

(12.2)

(a) Xl=50 ohms

Rl=50 ohms :

REflection coefficient   = (ZL - Z0)/(ZL + Z0)

= (50-50)/(50+50)

= (0/100)=0

Voltage Standing wAVE Ratio(VSWR):

VSWR = (1 + )/(1 - )

VSWR=(1+0)/(1-0)=1

That means there is no reflection takes place if IMPEDENCE Matchimg Takes place (zl=z0).

so VSWR=1, tHAT Means wave is properly travelling to other side without any reflections.

(b)

Xl=-50 ohms

Rl=-50 ohms :

REflection coefficient   = (ZL - Z0)/(ZL + Z0)

= (-50-50)/(-50+50)

= (-100/0)=infinite

Voltage Standing wAVE Ratio(VSWR):

VSWR = (1 + infinite)/(1 -infinite)=0

That means Entire wave is refected back to the source due to the complete  IMPEDENCE Miss Matchimg Takes place ( =0).

so VSWR=0.

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