What is Velocity Factor / Quarter-Wave Matching Transformers / Stub Matching

Chapter 5.8 Velocity Factor

Electronic Communication – Theory and Problems – Second Edition Book
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Electronic Communication – Theory and Problems – Second Edition Book

  • TRANSMISSION LINES[CHAP.5140VLPino =RLPron _V2rJRLPinoVfnc!RLv2ÿVLVrcnKr -— =Kr2(5.8)Pinc5.8VELOCITYFACTORThus farin thischapter, thespeed ofelectromagnetic waves on atransmission line has beenapproximated as beingequal tothespeed of electromagnetic waves in free space; 3 X108 meters/s.Thisis notexactly true.In fact,the ratio ofthespeed ofelectromagnetic waves on aparticular transmission lineto that in free space is known asthe velocity factor k. Thevelocity factor for mostcommontransmissionlines varies from alow of0.55 forcertain twisted pairs to0.98for smallconductorswidely spaced asopen-wire lines.5.9QUARTER-WAVE MATCHING TRANSFORMERSQuarter-wavelength sections of trans¬mission line canbe used to match aload toatransmission when theresistance of theloadis notequal tothecharacteristic impedanceof the transmissionline. Since the quarter-wavelength section ofline functions some¬what as amatching transformer, itis referredtoas a quarter-wave matchingtransformer.The proper valueofcharacteristicimpedanceforthe quarter-wave transmission line sec¬tion canbe found fromzo2zoZTZL\ZT= —ZLI___4_IFig. 5-6Zo2(5.9)z,where ZT is theimpedance seenlooking into the quarter-wave matchingsection whenit is attached totheload ZL, and Z0 is the characteristicimpedance ofthe quarter-wave matching section necessary toprovideamatch. SeeFig. 5-6.5.10 STUB MATCHINGEither because aload has areactive component orbecause aresistive load is notmatched tothecharacteristicimpedance oftheline, theimpedance seenfromthe input endof atransmission line canhaveareactive component. In order toeliminate the standing waves onsuch atransmissionline, it is necessarytoeliminate thereactive component ofimpedance as seenlooking into the line from theinput end. Oneway todo this is toplace ashort section of transmission line, eitheropen-circuited orshort-circuited, inparallel with the transmission line atalocation close tothe load end oftheline. Such ashort section of