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SWITCH-MODE POWER SUPPLIES AND SYSTEMS Lecture No 5 Silesian University of Technology Faculty of Automatic Control, Electronics and Computer Sciences Ryszard Siurek Ph.D., El. Eng. Continous/discontinuos current (magnetic flux) flow in output inductance of step-down regulator IL UIN t Uwe D U0 Ro ΔIL 2I 0cr U0 U0 U IN , U0 >U0 U0 t C L U1 IL D T L U0 U1 I0 I0cr critical current ΔIL L L T I0 t1 2I0cr 1 U0 ( 1) U -U IN 0 t t L L I0cr U0 1 t T (1 ) U0 (1 ) 2L 2L T I0cr I0<I0cr I0cr U0 U (1 ) IN (1 ) 2fL 2fL t T Step-down regulator output characteristic U0 UIN U IN U0 2LI0 1 U INT 2 0,5 0,5UIN For output current exceeding critical value output voltage depends linearly on duty cycle – stable feedback loop is easy to accomplish U0 U IN I0 For output current below critical value output characteristic bocomes significantly nonlinear, which makes difficult to maintain stable operation of closed feedback loop I0cr Critical current decrease may be obtained: - by increasing the switching frequency - by increasing the inductance of the output choke Step-down regulator - output voltage is always lower than the input voltage - output voltage rises to the maximum value of the input voltage in case of no-load condition - AC current component is the same for output inductor and capacitor „Step-up” (boost) switching regulator L ID IL TU T UIN t D Io IC C ~ UC U0 T UC Ro U0 Assumptions: 1. Diode D and transitor T are perfect (ideal) switches 2. Series resistance of the choke L is negligible (rL = 0) 3. Capacitance C is very large (DUc << Uo) EL I cycle U T IN D EC T – ON, D – OFF Io II cycle EL D UIN T EC T – OFF, D – ON Io Basic waveforms in step-up switching regulator I cycle - equivalent circuit ILmin rL=~ 0 I‘L L 0<t<t I0 ~ UC IT UIN T0 Ro U0 L rL , ~ UC << U0 UT I0 U0 iC (t) R0 i (t) I Lmine t T0 t U IN (1 e T0 ) rL t IT T ILmin t ILmax IL Calculation of IL – superposition method ' L t ΔIL' ILmin t ID ILmin t t t U t i L' (t) I Lmin (1 .....) IN (1 1 ...) T0 rL T0 <<1 U t U i L' (t) I Lmin IN I Lmin IN t L rL L rL inductor current swing U ΔIL' IN t L IC t ~ UC Uc(0) t t uC (t) I0 t 1 i (t) dt U (0) t C C C 0 C 0 II cycle - equivalent circuit rL=~ 0 UT U0 „ I L ILmax L UIN t<t<T I0 ~ UC UT Ro U0 t t IT T t L T0 rL I0 ~ UC << U0 inductor current swing in steady state: U0 R0 U U IN ΔI 0 (T t ) L '' L ΔIL' ΔIL'' ILmax IL ΔI IINAV ' L ILmin t ID U U IN U IN t 0 (T t ) L L Τ U0 U IN T -t t IC t Step-up regulator transfer function U0 UIN 1 1 Uo > UIN ~ UC t T 1 uC (t) iC (t)dt Cτ Continous/discontinuos current (magnetic flux) flow in step-up regulator inductance U0 IIN DIL IINcr t T ’ > Uwe from energy balance: I INAVU IN I0U 0 I INAV I0 I INcr U0 1 I0 U IN 1 DI L U IN t 2 2L I INcr U IN (1 ) 2fL The same as for step-down I0cr Step-up regulator - output voltage always higher than the input voltage - can not operate in no-load condition (output voltage rise out of control) - high value of RMS output capacitor current I0 „Step-up-step-down” (flyback) switching regulator T IT ID IL t UL T L ~ UC IC D UIN Io C U0 UC Ro U0 Assumptions: 1. Diode D and transitor T are perfect (ideal) switches 2. Series resistance of the choke L is negligible (rL = 0) 3. Capacitance C is very large (DUc << Uo) T D I cycle U IN EC EL T – ON, D – OFF T Io II cycle D EL EC Uwe T – OFF, D – ON Io Basic waveforms in flyback switching regulator I cycle - equivalent circuit IT ILmin 0<t<t I0 I‘L UL L UIN T0 L rL ~ UC UIN Ro U0 ~ UC << U0 I0 U0 iC (t) R0 U ΔI IN t L ' L inductor current swing II cycle - equivalent circuit „ ILmax IL I0 t<t<T t t T -U0 IT ILmin t ILmax IL ΔIL' ILmin ID ~ UC L UL t ILmax „ I0=ILavr Ro t U0 IC inductor current swing in steady state: Flyback regulator transfer function ΔIL'' U0 (T t ) L t ΔIL' ΔIL'' U0 UIN 1 ~ UC Uc(0) t t 1 uC (t) iC (t)dt C0 Continous/discontinuos current (magnetic flux) flow in flyback regulator inductance IL (Fm) continuous current flow critical current flow Ilmaxcr=DIL t IT discontinuous current flow t t1 T t The value of energy accumulated in the inductor by the end of I cycle is constant, so current decreasing below critical value (beginning of discontinuous current flow) must result in output voltage rise. ID T I0 UL I0cr iD (t)dt ... I0cr I <I 0 0cr 0 U0 (1 2 ) 2Lf U0 I0cr (1 2 ) 2Lf UIN t U0 I Lmaxcr U IN t L (1) U 2 2 from energy balance we obtain: 2 LI Lmaxcr 2 energy stored in the choke by the end of I cycle U02 Τ R0 -U IN 0 2LfI (2) -U0 energy transfered to the load during the pulse repetition period T LR0 UIN t L 2T t T 0,5 Uwe R0 U0 U IN 1 > 0,5 from equtions (1) & (2) we obtain: U0 0 < 0,5 U0 I0 2 2 UIN U0 2LfI0 I0cr I0 Flyback regulator - output voltage of opposite polarity, may be higher or lower than the input voltage - can not operate in no-load condition (output voltage rise out of control) - high value of RMS output capacitor current