SWITCH-MODE POWER SUPPLIES AND SYSTEMS Silesian University of Technology Faculty of Automatic Control, Electronics and Computer Sciences Ryszard Siurek Ph.D., El. Eng. Lecture No 5

ILIL  T II0II0 I 0cr critical current Continous/discontinuos current (magnetic flux) flow in output inductance of step-down regulator U1U1 ILIL I 0cr I 0 <I 0cr U we U0U0U0U0 L U0U0U0U0 L D U0U0U0U0 L U0U0 U 0 >U 0, D T U IN RoRo L CU1U1 II0II0  T t1t1t1t1

U0U0 II0II0 0,5U IN I 0cr Step-down regulator output characteristic For output current exceeding critical value output voltage depends linearly on duty cycle – stable feedback loop is easy to accomplish For output current below critical value output characteristic bocomes significantly nonlinear, which makes difficult to maintain stable operation of closed feedback loop 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 is always lower than the input voltage - output voltage rises to the maximum value of the input voltage - output voltage rises to the maximum value of the input voltage in case of no-load condition in case of no-load condition - AC current component is the same for output inductor and capacitor - AC current component is the same for output inductor and capacitor

L C Ro IoIo ILIL ICIC IDID U IN U0U0 Assumptions: 1. Diode D and transitor T are perfect (ideal) switches 2. Series resistance of the choke L is negligible (r = 0) 2. Series resistance of the choke L is negligible (r L = 0) 3. Capacitance C is very large (  U << U) 3. Capacitance C is very large (  U c << U o ) EELEEL EECEEC D T EELEEL EECEEC D T U IN I cycle II cycle T – ON, D – OFF T – OFF, D – ON IoIo IoIo „Step-up” (boost) switching regulator UTUT U0U0 UCUC ~ UCUC  T D T

t t t t t t UTUT ITIT ILIL IDID ICIC UCUC ~ T I cycle - equivalent circuit 0 < t <  U IN r= 0 r L = 0 ~ ILIL L I I Lmin U0U0 Ro II0II0 Calculation of I – superposition method Calculation of I L – superposition method ‘, I I Lmin  <<1 inductor current swing I Lmin Basic waveforms in step-up switching regulator I Lmax ~ UCUC UCUC ~ << U 0 U(0) U c (0) ITITITIT

r= 0 r L = 0 ~ ILIL L I I Lmax U0U0 Ro II0II0 ~ UCUC UCUC ~ << U 0 II cycle - equivalent circuit  t  T „ inductor current swing in steady state: Step-up regulator transfer function t t t t t t UTUT ITIT ILIL IDID ICIC UCUC ~ T I Lmin I Lmax U0U0 UTUT I I INAV U o > U IN U o > U IN U IN

Continous/discontinuos current (magnetic flux) flow in step-up regulator inductance I IN I INcr ILILILIL T The same as for step-down step-down U0U0 U we I 0cr   ’ >  I0I0I0I0 Step-up regulator - output voltage always higher than the input voltage - output voltage always higher than the input voltage - can not operate in no-load condition (output voltage rise - can not operate in no-load condition (output voltage rise out of control) out of control) - high value of RMS output capacitor current - high value of RMS output capacitor current from energy balance:

„Step-up-step-down” (flyback) switching regulator T L D C Ro IoIo ILIL ICIC IDID ITIT U IN U0U0 ULUL U0U0 UCUC ~ UCUC T Assumptions: 1. Diode D and transitor T are perfect (ideal) switches 2. Series resistance of the choke L is negligible (r = 0) 2. Series resistance of the choke L is negligible (r L = 0) 3. Capacitance C is very large (  U << U) 3. Capacitance C is very large (  U c << U o ) EELEEL EECEEC D T EELEEL EECEEC DT U IN U we I cycle II cycle T – ON, D – OFF T – OFF, D – ON IoIo IoIo

t t t t t t ULUL ITIT ILIL IDID ICIC UCUC ~ T I cycle - equivalent circuit 0 < t <  U IN ILIL L I I Lmin U0U0 Ro II0II0 ‘ inductor current swing I Lmin I Lmax ~ UCUC UCUC ~ << U 0 U(0) U c (0) ITITITIT Basic waveforms in flyback switching regulator ULUL U0U0 Ro II0II0 ~ UCUC I I Lmax ILIL „ L II cycle - equivalent circuit  t  T inductor current swing in steady state: Flyback regulator transfer function transfer function I Lmax I 0 =I Lavr „ -U 0 U IN

Continous/discontinuos current (magnetic flux) flow in flyback regulator inductance ILIL ITIT IDID ULUL  T t t t  m  t1t1t1t1 U IN U0U0 continuous current flow critical current flow discontinuous current flow I lmaxcr =  I L I0I0I0I0 I 0cr I 0 <I 0cr 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.

from energy balance we obtain: energy stored in the choke by the end of I cycle energy transfered to the load during the pulse repetition period T repetition period T (1) (2) from equtions (1) & (2) we obtain: I 0cr  0,5  > 0,5 I0I0I0I0  < 0,5 -U 0 U we Flyback regulator - output voltage of opposite polarity, may be higher or lower - output voltage of opposite polarity, may be higher or lower than the input voltage than the input voltage - can not operate in no-load condition (output voltage rise out of - can not operate in no-load condition (output voltage rise out of control) control) - high value of RMS output capacitor current - high value of RMS output capacitor current