Chapter 1Characteristics ofTunedLC CircuitsINTRODUCTIONFor any series orparallel LC circuit,the inductive reactanceXL and capacitive reactanceXc will beequalatsomefrequency. The frequency atwhich XL =Xc is called the resonantfrequency. When the values of L andC are known, the resonantfrequency canbe calculated as:1/o =(1.1)ITTJLCwhere /0 represents the resonantfrequency.In general,large valuesof L and Cprovide arelativelylow resonantfrequency,whereas smallervalues ofLand Cprovide ahigher resonantfrequency. The mostcommonapplication of resonanceisin radio-frequency(RF)circuits where tuningis important. Timing refers to anLCcircuit’sability toprovidemaximum voltageoutput atthe resonantfrequencycompared with the voltage output atfrequencies either above orbelowresonance.More specifically,tuning is used in RFcircuits whenit is desired topass only aspecific band orchannel offrequencies while atthe sametime completelyrejecting or blockingallothers. The useof tunedLCcircuits is foundin every television, video cassetterecorder (VCR), AM/FM receiver,and satellite tonamejustafew ofthe morepopular applications.1.1 CHARACTERISTICS OFA SERIES RESONANT LC CIRCUITFigure 1-1shows aseries LCcircuit. The seriesresistance rs is arepresentation ofthe coil’s owninternal resistance. Because thecircuitdoes contain someseries resistance, it canbe considered aseriesRLCcircuit. Since the values of L and C aregiven as25 p,H and 162.1pF respectively, the resonantfrequency f0 canbecalculated asfollows:1/o =2TT\[LC12 X 7T X-ÿ25 /AH X162.1pF=2.5MHzrs= 3.14 £21= 25gH—y-VY-VN_LA/W0VA= 150pV7TÿC= 162.1pFFig. 1-11