

2I 0cr U 0



U IN L U 0

 

U IN

t 

U 0 ( 1



L



1)

t

I 0cr



U 0 1 2L (1

 

)

t  

U 0 T 2L (1

 

)

  t

T I 0cr



U 0 2fL (1

 

)



U IN 2fL



(1

 

)

U 0 U IN

Step-down regulator output characteristic

U 0



1



U IN U 2LI IN T



0 2 U 0

 

U IN

For output current exceeding critical value output voltage linearly on duty cycle depends – stable feedback loop is easy to accomplish

0,5U IN

 

0,5

 For output current below critical value output characteristic bocomes significantly nonlinear, which makes difficult to maintain stable operation of closed feedback loop

I 0 I 0cr

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

U IN

L „Step-up” (boost) switching regulator

I L

t

T T

U T

D

I D

C

I C I o

~

U C U C

Ro

U 0 U 0

Assumptions: 1.

2.

3.

Diode D and transitor T are perfect (ideal) switches Series resistance of the choke L is negligible (r

L

= 0) Capacitance C is very large (

D

U c

<< U

o

)

E L

D

E L

I cycle

U IN

T

E C

I o

II cycle

U IN

T D

E C

T – ON, D – OFF T – OFF, D – ON

I o

Basic waveforms in step-up switching regulator I cycle - equivalent circuit 0 < t <

t

r L = 0

‘

I L

L

I Lmin I 0 U T ~ U C

Ro

I T U IN U 0 T 0 L



r L

Calculation of I

L

,

~ U C << U 0 I 0



U 0 R 0

– superposition method

 

i C (t) i L ' (t)



I Lmin e



t T 0



U IN r L (1



e



t T 0 ) I T I Lmin I L I Lmin I D I Lmin

t

I C i ' L (t)



I Lmin (1



t T 0 .....)



U IN r L (1



1



t T 0 ...)

<<1

i ' L (t)



I Lmin



U IN r L t L r L



I Lmin



U IN L t

inductor current swing

ΔI ' L



U IN L

t

U C U c (0) ΔI ' L

t

I Lmax T u C (t)



1

C t 0



i C (t) dt



U C (0)



I 0 C t

t

0 t t t t t t

II cycle - equivalent circuit

t <

t

<

T

r L = 0 I L

„

L

I Lmax I 0 U IN U T U 0 ~ U C

Ro

T 0



L r L U C << U 0 I 0



U 0 R 0

inductor current swing

ΔI L ' '

 

U 0



U IN L (T

 t

)

in steady state:

ΔI ' L

 

ΔI ' ' L U IN

t

L



U 0



U IN L (T

 t

) U 0



T Τ -

t

U IN

Step-up regulator transfer function

U T I T I L I Lmin I D I C

U 0



U IN

1 1

 

U o > U IN

U C U 0

t

ΔI ' L I Lmax T u C (t)



1 C

τ



T

i C (t) dt I INAV t t t t t t

Continous/discontinuos current (magnetic flux) flow in step-up regulator inductance

I IN U 0

 D

I L

t

from energy balance:

I INAV U IN



I 0 U 0 I INAV I INcr

 

I 0 2 U 0

D

I L U IN

 

U IN 2L I 0

t

1 1

 

T

I INcr



I INcr



U IN 2fL



)

The same as for step-down

U we I 0cr



’ >

 

I 0

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

„Step-up-step-down” (flyback) switching regulator T

U IN

t

T

I T U L I L

L

I D

D C

I C I o

~

U C U C

Ro

U 0 U 0

Assumptions: 1.

Diode D and transitor T are perfect (ideal) switches 2.

3.

Series resistance of the choke L is negligible (r

L

= 0) Capacitance C is very large (

D

U c

<< U

o

) T D

E C

I cycle

U IN

E L

T – ON, D – OFF

I o

II cycle

U we

T

E L

D

E C

T – OFF, D – ON

I o

Basic waveforms in flyback switching regulator L I cycle - equivalent circuit 0 < t <

t

I T I Lmin I 0 I L

‘

~ U C U L U IN

L

U 0 T 0



L r L ~ U C << U 0

inductor current swing Ro

U L I T I 0



U R 0 0

 

i C (t) ΔI L '



U IN L

t

I Lmin I L

II

I Lmax

„

I L I 0

t <

t

<

T

I Lmin I D ~ U C

Ro

U 0 I C

inductor current swing

ΔI ' L '

 

U 0 L (T

 t

)

in steady state: Flyback regulator transfer function

ΔI ' L

 

ΔI ' ' L

U 0

 

U IN

1

  

U C U c (0) ΔI ' L U IN

t

I Lmax I Lmax u C (t)



1 C t 0



i C (t) dt T -U 0

„

I 0

=I

Lavr t t t t t t

I L

Continous/discontinuos current (magnetic flux) flow in flyback regulator inductance

(F

m

)

continuous current flow critical current flow

I lmaxcr

=

D

I L I T

t

discontinuous current flow

t 1 T t

The value of energy accumulated in the inductor by the end of I cycle is constant, so current

t

decreasing below critical value (beginning of discontinuous current flow) must result in output voltage rise.

I D I 0 I 0cr I 0