13-4GCL并联谐振电路

§13-4GCL并联谐振电路Y(jω)==G+j()=|Y|∠θ(ω)|Y|=θ(ω)=IsUC1L..G2C1L2tg1C1LGIL.IC.Is.IG.GjωL1jCIs=Is∠φis固定、ω可变G—C、L损耗电导Iｌ.1.谐振条件总B=0→ω0C–=0→Y(jω)=G→Is和U同相∴ω0=—并联谐振频率2.ω=ω0时电压、电流、阻抗Z0===R0—谐振阻抗(最大、呈电阻性)U0===R0Is(最大、且U0和I0同相)10L..1LC1Yj()1GIsY0.IsG0.....IL0=U0=Is=-jQIsIC0=jω0CU0=jω0CR0Is=jQIsIR0=GU0=IsQ==ω0CR0=—并谐电路的品质因数IC0=IL0=QIs(电流谐振)IL=QIs—环流BW=ωC2-ωC1=Q↑→BW↓Q↓→BW↑1j0LjR00L...........R00LR0CL0Q3.频率特性H(jω)======H(jω)==R0=,IsR0=U0UIs..1GjC1L1G11jCG1LGCG1LG00CG001LG00CR00R00LQ00UIs..1G11jQ001G..∴并谐:==θ(ω)==φu-φis串谐:==θ(ω)==φi-φusUU0UU0..11Q2002tg1Q00II0II0..11Q2002tg1Q004.有载Q值—QL并：Q=ω0CR0=—空载Q值(并谐回路Q值)R0q=R0‖Rs‖RL(有载谐振阻抗)QL==ω0CR0q=—有载Q值(要求Rs、RL大)(适用电流源)串：Q==(空载Q值)(LC回路Q值)QL=(要求Rs、RL小)(适用电压源)R00LR0q0LR0qR0Q0LR10CR0LRRsRL例：R=10KΩ，L=1mH，C=0.1uF，is=求：①ω0、Q、Z0、ρ、BW②u、iR、iL、iC解：ω0===rad/sQ=ω0CR==100ρ==ω0L==100Z0=R=10KΩ，BW==rad/s10cos105t30°mA1LC1103×107105IL.IC.Is.IR.LCR+U-105×107×104LC10C0Q103.②ω0=ω0=rad/s(并谐)，U0=IsZ0=∠30°(V)IR0=Is=∠30°(mA)，IC0=jQIs=∠120°(A)IL0=-jQIs=∠-60°(A)∴u0(t)=(V)iR0(t)=(mA)iC0(t)=(A)iL0(t)=(A)10510021021212........100cos105t30°10cos105t30°cos105t120°cos105t60°例：Is=10mA、L=100uH、R=10Ω、C=400pF、RL=100KΩ，求谐振时R0、U0、IL、BW解：ω0===rad/sQ====50(空载Q值)Z0===25KΩReq=R0‖RL==20KΩ1LC1104×4×10105×1060LRLCR1044×101010Q2R502×1025×10025100×103Is.jωLRRL1jL+U0-.U0=IsReq==200(V)QL=Qeq=ω0CReq===40BW===rad/sIL=QLIs==0.4A10×103×20×103ReqR0Q2025×500QL5×106401.25×10540×102Is.jωLRRL1jL+U0-.IL.例：L=100uH、C=100pF、Q=50、Us=150V、Rs=25KΩ，求ω0、I0、U0、IL解：ω0===rad/sR0===50KΩReq=R0‖Rs==16.7KΩIs===6mAU0=IsReq==100(V)1LC1104×1010107500C501012×107×10250255025×103UsRs15025×1036×103×16.7×103+Us-.CRsLI.I0=×Is=2mAIL=QLIs=QI0=100mA252550Is.CRsR0I.LI0.IL.IC.例：串谐的等效电路Z=jX=X=0→ω0=，Z0=0Ω并谐的等效电路Y===jBB=0→ω0=，Z0==∞jL1C1LCjωLZ→jωLZ→1jC1jCjC1jLjC1L1LC1Y0例：Q=100(空载)，N=100T，L=400uF，C=100pF，Rs=8KΩ，使并谐电路获最大功率，抽头N1=？解：Rs’=，m=Q=→r====20ΩN1rCLisRsNRCLis’Rs’1m2RsN1N0Lr0LQLCQ4×1041010100R=匹配：====m==∴N1==20TQ2r1m2RsQ2rm2RsQ2r8×1031002×204×1022×101N1N2×101×100例：谐振时IRL=15A、I=9A，求IC解：谐振时U和I同相，IRL滞后U角φL，IC超前U90°角I=IRL+ICI=IRLcosφL，cosφL===，φL=53.1°IC=IRLsinφL=15sin53.1°=15×=12A或IC===12A......IIRL9153545IRL2I215292...+U-.I.IC.IRL.rCLφ+1+jU.I.IC.IRL.U=U∠φu，I=I∠φiφi=φuφ=φu-φi=0°cosφ=1—单口的功率因数，Q=UIsinφ=0(无功功率)cosφL—电感支路的功率因数IRLsinφL—感性分量电流IRLcosφL—电阻性分量电流Z0=(最大，呈电阻性)..Q2r