(PFC) PFC PFC (PFC) IEC1 (THD) AC PFC APPLICATION NOTE () 4 V ( ) (Figure Figure 4) 1MOSFET MOSFET trr PFC dl/dtrms Diode Bridge PFC Stage Power Supply + AC Line IN Controller + Bulk Capacitor LOAD Figure 1. Power Factor Corrected Power Converter PFC PFC (MC6MC68MC6)NCP165 W Semiconductor Components Industries, LLC, 14 November, 14 Rev. 1 Publication Order Number: AND81JP/D
AND81/D Diode Bridge Diode Bridge Icoil + L Icoil + L + IN V in IN V in V out The power switch is ON The power switch being about zero, the input voltage is applied across the coil. The coil current linearly increases with a (V in /L) slope. The power switch is OFF The coil current flows through the diode. The coil voltage is (V out V in ) and the coil current linearly decays with a (V out V in )/L slope. Coil Current V in /L Icoil_pk (V out V in )/L Critical Conduction Mode: Next current cycle starts as soon as the core is reset. Figure. Switching Sequences of the PFC Stage (Figure ) (V in /L) V in L (V out V in )/L V out PFC () (Figure 4)EMI( 1 nf 1. F) Figure (V in ) PFC1V in AC AC PWM PWM MOSFET (Figure Figure 4) Figure 4 8 AC EMI Icoil T Icoil_pk (eq. 1) <Icoil> T 1( T) Icoil_pk Icoil_pk(k*V in ) <Icoil> T Icoil T k*vin k* * * sin(t) (eq. ) AC
AND81/D V in L1 PFC Stage D1 AC Line Input Filtering Capacitor X1 Bulk Capacitor + C1 R7 Current Sensing Resistor Zero Current Detection PWM Latch S Output Buffer Current Envelope R Current Sense Comparator Q R1 R Multiplier Error Amplifier Vref C R R4 Figure. Switching Sequences of the PFC Stage PWM PWMMOSFET Peak Inductor Current (Icoil) T MOSFET DRIVE (Tac is the AC line period) Figure 4. Coil Current 8AC
AND81/D ton *L* Pin toff * *L* Pin * ( **sin(t)) *sin(t) ton * **sin(t) (eq. ) **sin(t) MC6 AC (ton) (V in /L) Icoil(t) Vin L *t (eq. 4) (ton) (Icoil_pk) Icoil_pk Vin L *ton (eq. 5) ton L * Icoil_pk (eq. 6) Vin (toff) (V in V out ) ((V out V in )/L)(Icoil_pk) Icoil(t) Icoil_pk Vin *t (eq. 7) L Icoil toff L * Icoil_pk (eq. 8) Vin ( T)tontoff T ton toff L * Icoil_pk * (eq. 9) Vin * ( Vin) (17) ACrms Icoil_pk * * Pin *sin(t) (eq. 1) AC(9)Icoil _pk T * * L* Pin *sin(t) * **sin(t) * ( Vin) (eq. 11) T *L* Pin * * ( Vin) (eq. 1) f *L* Pin 1 **sin(t) (eq. 1) (ACrms) 1 *L* Pin AC 1 **sin(t) ACAC 4
AND81/D Figure 5. Switching Frequency Over the AC Line RMS Voltage (at the Sinusoid top) f(9) =1rms V out = 4 V ( = 18V %= 7V6%)V out AC (LLHLLLVa chl) Figure 7. Switching Frequency Over the AC Line Sinusoid @ ACf1 = VV out = 4V AC1 5 Figure 6. Switching Frequency vs. the Input Power (at the Sinusoid top) f( W) = 1 1 WPFC MHz MC6 4kHz Figure 8. Switching Frequency Over the AC Line Sinusoid @ 9 = 9V Figure 5(f ) AC 5
AND81/D EMIPFC ( ) (5 khz)emi. s (5 khz) PFCAC AC lin(t) *lac*sin(t) (eq. 14) Iin(t)ACIac AC lin(t) Icoil T Icoil_pk (eq. 15) <Icoil> T T Icoil_pk Icoil_pk * *lac*sin(t) (eq. 16) PFC1 ACrmsrms ( Pin * lac) Icoil_pk * * Pin *sin(t) (eq. 17) sin(t) 1 (Icoil_pk)H rms (Icoil_pk)H * * Pin (eq. 18) AC Icoil_max * * Pin max (eq. 19) LL <Pin>max LLAC rms rms1. rms rms 1. rms MOSFET < t < ton (IM(t) Vin * tl Icoil_pk * tton) (ID(t) Icoil_pk ( Vin) * tl Icoil_pk * (T t) ton<t<t (T ton) ) Trms (Icoil)rms T 1 T *ton Icoil_pk * t T *dt Icoil_pk * *dt T t ton ton T ton (eq. ) (Icoil)rms T 1 T *Icoil_pk ton * ton (T ton) * Icoil_pk *Icoil_pk * T T T ton Icoil_pk * T ton (eq. 1) T ton 6
AND81/D (Icoil)rms T 1 T *Icoil_pk *ton (T ton) ) * Icoil_pk * ( Icoil_pk (eq. ) (Icoil)rms T Icoil_pk * (eq. ) 1 T *ton T ton (Icoil)rms T Icoil_pk (eq. 4) AC rms17 (Icoil)rms T * * Pin *sin(t) (eq. 5) V in rms V in AC rms<(icoil)rms> T rms rms (eq. 6) Tac (Icoil)rms Tac * (Icoil)rms T *dt Tac = */AC( ms16.66 ms)ac PFCAC AC (Tac/) 5 Tac (Icoil)rms Tac * * * *sin(t) Pin *dt (eq. 7) rmsrms * * Pin *sin(t) ( * * Pin ) rmsrms ( ) Icoil(rms) * Pin (eq. 8) MOSFET 5% (Figure 9tt FR ) 7
AND81/D Figure 9. Turn Off Waveforms Figure 9 MOSFET () t (Figure 9) t FR * Icoil_pk psw * t t (eq. 9) FR T * Icoil_pk * t FR T tt FR Figure 9 T 9 () T L * Icoil_pk * Vin Vin. 99 psw Vin * ( Vin) * (t t FR) (eq. ) *L 1 AC psw (<psw>) (eq. 1) psw Tac Tac * Vin * ( Vin) * (t tfr) * dt *L psw t t FR *L * Tac Tac * Vin * * dt Tac Tac * Vin *dt (eq. ) 8
AND81/D V out ( * *) ( Tac Tac * Vin *dt) (eq. ) psw t t FR * * * * *L (eq. 4) psw *(t t FR)* * *L * 4 (L) L 4(V out /)MOSFET MC6 AC () PFC 1 tt FR MOSFETQ (Figure 1)t Q Q1 (Q/) (t = Q/I drive t = [Q1 + (Q/)]/I drive ) t FR Figure 1. Typical Total Gate Charge Specification of a MOSFET MOSFET (Qcc*Vcc*f)Qcc VccMOSFET Vccf PFC MOSFET MOSFET (1/*C parasitic *V *f)c parasitic V MC6 4 MOSFET Figure 4 RFI AC Icoil(t) Vin L *t (eq. 5) V in (Vin **sin(t) )L t 9
AND81/D Icoil T pt 1 T * ton RonMOSFET ton 6 (eq. 7) pt Ron T * Vin ton L * t *dt 1 *Ron* Vin L * ton T Icoil_pk Vin * tonl pt 1 (eq. 8) * Ron * Icoil_pk * ton T ( 1 * Ron * Ipk *dipk dmosfet) MOSFET ton Ron * Icoil(t) *dt 1 T * Ron * Vin L *t *dt (eq. 6) (d = ton/t) 1 (toff)ton( )(T = ton + Toff) 1 (CCM)CCM d ton T 1 Vin (eq. 9) 98 (eq. 4) pt 1 * Ron * Icoil_pk *1 Vin (Icoil_pk) Icoil_pk * * Pin *sin(t) ( 17) V in Icoil_pk( **sin(t) )( * * Pin *sin(t) ) 4 pt 1 (eq. 41) *Ron** * Pin *sin(t) *1 **sin(t) pt 8 *Ron* Pin *sin (t) * * sin (t) (eq. 4) 4V in AC p Tac 8 *Ron* Pin Tac * Tac * sin (t) * sin (t)(.5)<sin (t)> sin () 1 cos() sin( ) sin( ) sin() * cos() * sin (t) *dt (eq. 4) sin (t) *sin(t) sin(t) (eq. 44) 4 4 444 p Tac 8 *Ron* Pin Tac * Tac * sin(t) * * * sin(t) * * sin(t) *dt 4 * 4 * (eq. 45) 1
AND81/D p Tac 8 *Ron* Pin 46 * 1 * p Tac 4 * Ron * Pin * 4 * *1 8* * * 4 * * * * (eq. 46) (eq. 47) (/V out )MOSFET MOSFET MC6 AC () PFC p Tac Ron * (IM)rms rms((i M )rms) (IM)rms * Pin * 1 8* * (eq. 48) * PFC MOSFET MC6 MC6 ( Figure 15 ) ( ) PFC MC6 PFC MC6 MC6 (I M )rmsrms prs 6 4 * Rs * Pin *1 8* * (eq. 49) * <prs> 6 Rs MC6 Rs Rsrms prs 6 Rs * (Icoil(rms) ) (eq. 5) Icoil(rms)rms8 Icoil(rms) * Pin. prs 6 4*Rs * Pin (eq. 51) 11
AND81/D prs 6 prs 6 (eq. 5) prs 6 prs 6 1 8* * * 8/.85 prs 6 prs 6 1.85 * Vm VmAC (eq. 5) RMS Id Iload ICout (eq. 54) (eq. 55) Id Iload ICout Iload ICout ( ) Id Iload Pout (eq. 56) rms rms rms AC Figure 4 (Icoil_pk) Icoil(t) Icoil_pk * toff t (eq. 57) toff rms1 rms Id(rms) T 1 toff (eq. 58) T * Icoil_pk * toff t toff *dt 1 rms Id(rms)T toff * Icoil_pk (eq. 59) *T Icoil_pk17 Id(rms)T * * Pin * toff *sin(t) (eq. 6) T tofft toff T* Vin (eq. 61) T* **sin(t) * * (eq. 6) Id(rms)T * Pin * sin(t) * V in rms rms rms (eq. 6) Tac Id(rms) Tac * 8* * Pin * * sin (t) * dt MOSFET(sin (t)) And : Then : sin (t) sin(t) * sin (t) sin(t) * 1 cos(t) 1 * sin(t) 1 * sin(t) * cos(t) sin(t) * cos(t) 1 *(sin( t) sin(4t) ) sin (t) 4 * sin(t) 1 4 * sin(t) 6 Id(rms) Tac * Tac 8* * Pin * * sin(t) * sin(t) *dt 4 4 (eq. 64) 1
AND81/D Id(rms) 16 * * Tac * Pin * ( *Tac ) Id(rms) 16 * cos(tac) ) **(cos() 4 * Pin * * (1 cos() ) * cos() 1 4 *Tac 1 *Tac cos(tac) cos() 1 (eq. 65) (eq. 66) (cos) Id(rms) 16 * * Pin * 6 * 8* 1 1 * (eq. 67) rms Id(rms) * (eq. 68) 9* * Pin * rms Id(rms) 4 (eq. 69) * * * Pin * rms Figure 11 (I1)(I) Ic(t) I1(t) I(t) (eq. 7) AC1 rms111 rms Ic(rms) Tac (eq. 71) Tac * (I1 I) *dt (I1 I) (eq. 7) Ic(rms) Tac Tac * [I1 I ( * I1 * I)] * dt (eq. 7) Ic(rms) I1(rms) I(rms) 4 Tac Tac * I1 * I * dt V in DRV PFC Stage L D V out Figure 11. Output Capacitor Current I1 Power Switch Ic I Load (I1(rms)) rms (I(rms)) rms I1I PFC () rms Ic(rms) I1(rms) I(rms) (eq. 74) rms Ic(rms) * * Pin 9* ** I(rms)rms I(rms) (eq. 75) 1
AND81/D I = V out /RR7 Ic(rms) 1(rms) (eq. 76) R 4 Tac Tac * 1* R *dt rms Ic(rms) Id(rms) R * * Id R Ic(rms) * 9* * Pin * R * R Pout = V out /R Ic(rms) * 9* * Pin * R * Pout (eq. 77) (eq. 78) (eq. 79) Ic(rms) I I ( )(9 Ibulk Cbulk * ddt ) 79 () (ESR Figure 1) PFCMOSFET ESR (ESR*I)I ESRESR*(Id I) Id PFC ESR PFC PFC () () Figure 1Figure 14 V in Driver PFC Stage Figure 1. ESR of the Output Capacitor Id ESR Ic I Load Bulk Capacitor 14
AND81/D Figure 1. Output Voltage Ripple PFC PFC PFC Figure 14. Output Voltage Ripple ( )AC 15
AND81/D 1 lin * Pin *sin(t) (eq. 8) ( )( **sin(t) )Iin Pin * Pin * sin (t) (eq. 81) ( *Pin) PFC I * Pin I C*dVdt * Pin I Cbulk * d dt (eq. 8) 818 d 1 dt Cbulk ** * Pin * sin (t) * Pin (eq. 8) * d dt * Pin * * sin (t) 1 Cbulk (eq. 84) d() * * d cos(t) 1 * sin (t) dt dt * Pin Cbulk * * sin(t) (eq. 85) <V out > * Pin *sin(t) 1 Cbulk * * (eq. 86) (eq. 87) * Pin *sin(t) 1 Cbulk * * V out * Pin *sin(t) * 1 Cbulk * * (eq. 88) 1 () * Pin *sin(t) 1 11 Cbulk * * * Pin *sin(t) Cbulk * * * Pin *sin(t) 1 Cbulk * * 1 1 Pin *sin(t) * Cbulk * * (eq. 89) 8889 * Pin *sin(t) (eq. 9) * Cbulk * * (sin(t) 1) (sin(t) 1) ()pk pk * Pin Cbulk * * ()pk pk * sin(t) (eq. 91) (eq. 9) 16
AND81/D PFC 1 AC PFC MOSFET PFC 17
AND81/D Peak Coil Current: Icoil_pk * * Pin *sin(t) Maximum Peak Current: Icoil_max * * Pin max LL RMS Coil Current: Icoil(rms) * Pin Average Diode Current: Id Iload Pout RMS Diode Current: Id(rms) 4 * * * Pin * Switching Frequency: f *L* Pin 1 **sin(t) Switching Losses: psw *(t t FR)* *L Conduction Losses: Pon 4 *Ron* Pin * * 4 *1 8* * * L1 D6 V out I load AC Line M1 CONTROLLER + C1 LOAD R7 R5 MC6 like Current Sense Resistor (Rs = R5) Dissipation: prs 6 4*Rs * Pin MC6 like Current Sense Resistor (Rs = R7) Dissipation: prs 6 4 *Rs* Pin *1 8* * * Capacitor Low Frequency Ripple: * Pin ()pk pk Cbulk * * RMS Capacitor Current: Ic(rms) * * Pin Iload(rms) 9* * * If load is resistive: Ic(rms) * 9* * Pin * R : AC line rms voltage LL: lowest level : AC line angular frequency <Pin>: Average input power <Pin>max: Maximum pin level : Output voltage Pout: Output power Iload: Load current Iload(rms): RMS load current : Efficiency Ron: MOSFET on resistance t, t FR : Switching times (see Switching Losses section and Figure 1) Cbulk = C1: Bulk capacitor value Rs: Current sense resistance L: Coil inductance Figure 15. Summary 18
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