《电路》（英文版）10-2 Series resonance

810-2 Series resonance L Z=R+JOL-j 1 =R+J(oL oC +Vr 十E C The resonant frequency. =0 oroL= oc So that @r LC √LC 矿u(t)=√2 V cos a, t and i(t)=√2cosa,t R L ()==Li(t) cos"@t Vc I V/R R J@,c jo, C RO,C-90 ()=v2 √2J coS(ot-90) sino. Ro C Ro C C、22 L 2 wc(t)=Cuc 2 Ro C snot 2 2 R

§10-2 Series resonance C Z R j L j   1 = + − ) 1 ( C R j L  = +  − The resonant frequency: C or L C L r r r r     1 0 1 − = = t R V If t V t and i t  r r ( ) = 2 cos ( ) = 2 cos t R LV w t Li t L r 2 2 2 2 ( ) cos 2 1 ( ) = =  • • •  −  =  =  = 90 R C V j C V / R j C I V r r r C t R C V t R C V t r r r r C       sin 2 cos( 90 ) 2 ( ) = − = t R LV t R C V w t C C r r r C C     2 2 2 2 2 2 2 2 2 sin sin 2 2 1 2 1 ( ) = = = LC LC r r 2 1 1 So that  = →  =

/w(t)+w,(t)/ LⅣ2/R2 ∴Q=2丌 2丌 (2/R)(2n/) Z R ROC RVC R B VRERlER-=v R VL=jO LI=jo l=jov R C jov Oc r o>>I series resonance--voltage resonance

R （ r ） c L V / R )( / LV / R P T [w (t ) w (t )] Q     2 2 2 2 2 2 = +  = L R Q B r = − = =  2 1 • • • • = = =V R V V R R I R • • • • = = = jQV R V V L jr L I jr L • • • • = − = − = − jQV R V C I j C V j r r C   1 1 • I • V • C V • L V C L R R C R L r r 1 1 = = =   Q>>1 series resonance--voltage resonance

Frequency characteristIcs(AL, Ac, X,z,y, vso) Z=R+jX=R+j(XL +Xo=R+jOL-=z29

Frequency characteristics(XL , XC , X , z , y,  vs ) .   = + = + + = +  − = z C Z R jX R j XL XC R j L ) 1 ( ) ( XL XC X R r  z r  y  r  / 2 − / 2  z

Resonant curves L,VC, VR,I vS O) +vl C C (o) R2+(oL-1/C 丿aL V()= R2+(oL-1/aC)2 V(a)= 0→0 aC R+(aL-1/aC) max →0 VRO=RIO V→0 (DC)(@) V→V L

Resonant curves (V ,V ,V ,I vs) L C R 2 2 ( 1/ ) ( ) R L C V L VL     + − = 2 2 ( 1/ ) ( ) C R L C V VC     + − = 2 2 ( 1/ ) ( ) R L C V I    + − = V () RI() R = V  VC VL I 0 r ( ) 0 DC I VC V = = ( ) max r VL VC I  = − − V V V I L C → → → →  0 0 

L1 C1 Om VDc 2.2k 0 15V 300Hz 1. 0KHZ 3. 0KHZ 10KHZ 30KHZ 100KHZ 口v(V1:+,V1:-)◇V(C1:2,C1:1)W(R1:2,R1:1)△V(L1:1,L1:2)

Frequency 300Hz 1.0KHz 3.0KHz 10KHz 30KHz 100KHz V(V1:+,V1:-) V(C1:2,C1:1) V(R1:2,R1:1) V(L1:1,L1:2) 0V 5V 10V 15V R 1 2.2k V- V1 3 0Vdc C 1 2400p V￾V+ V- V+ V+ V+ 0 L1 200m 1 2 V-