Ch7 dc-dc Switch-mode converters
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in a step-up converter, id=iL
I oB = (1 − D) I dB = (1 − D) I LB
I oB TsVo D(1 − D) 2 = 2L
I oB max = TV 2 TsVo = 0.074 s o 27 L L
Io = (1 − D ) Id
When D=1/3,
Ts Vo (1 − D)Ts VVo = 8C L
• In switch-mode dc power supplies, the percentage ripple in the output voltage is usually specified to be less than 1%.
15
Based on MATLAB the simulation of step-down converter • The curve as follows :
② When toff:
D on; L release energy;
10
3) continuous-conduction mode: iL(t)>0
① Analysis: ② In steady-state, inductor current flows continuously.
(Vd − Vo )ton = Vo (Ts − ton ) or : Vo ton = =D Vd Ts Vo = DVd
5
• A simple approach that shows the evolution:
ton Vo = ⋅Vd Ts
Stepping down a dc voltage.
6
• The methods for controlling the output voltage:
① Keeping a constant frequency of the switch (i.e. a constant switching time period Ts=ton +toff ), and adjusting the on duration of the switch to control Vo——pulse width modulation (PWM). where, switch duty ratio D ,which is defined as the ratio of the on duration to the switching time period, is varied. ② Adjusting both the switching frequency and the on duration of the switch. ③ keeping the on duration of the switch constant, and adjusting the switching frequency.
ቤተ መጻሕፍቲ ባይዱ
4
7-2 Control of dc-dc converters dc• Switch-mode dc-dc converters utilize one or more switches to transform dc from one level to another. • In a dc-dc converter with a given input voltage, the average output voltage is controlled by controlling the switch on and off durations( ton and toff ).
19
2) continuous-conduction mode iL(t)>0
① Analysis:
② In steady-state, inductor current flows continuously; and the time integral of the inductor voltage over one time period must be zero. Vd ton + (Vd − Vo )toff = 0
7
Pulse-Width Modulation in DC-DC Converters
① ② ③ ④
The switch control signal; The control voltage signal; The switch frequency; When Vcontrol>Vst, ton; when Vcontrol<Vst, toff;
18
1) Fundamental analysis: ① When the switch is on: the diode is reversed biased, L energy storage ; ② When the switch is off: the diode is on, the output stage receives energy from the inductor as well as from the input. ③ The output filter capacitor is assumed to be very large.
Io ∆1 = (Q Pd = Po ) I d ∆1 + D
and , I d = I L =
iL , peak 2
③ Neglecting power losses,
Pd = Po Vd I d = Vo I o Io 1 = Id D
11
4) Boundary between cont./ discont. conduction
I LB =
t D Ts V T 1 i L m ax = on (V d − V o ) = (V d − V o ) = d s D (1 − D ) = I oB 2 2L 2L 2L
?whend12somaxlbi?inastepupconverteridilwhend134discontinuousconductionmodevdconstant41112222onssolblpeakdotdttviivvdddlll??????8sotvl?max41lblbiidd??11obdblbididi????212soobtviddl??1odidi??max2007427sosoobtvtvill??2max271obobiddi???oftenoccursatlightloads1110dsdosodvdtvvtvdsov????????11ododippid?????q12lpeakdliandiid????1122ddssdovsoidtdltvidl?????5outputvoltageripple?inacontinuousconductionmodethepeakpeakvoltagerippleis
16
17
7-4 step-up (boost) converter
Its main application is in regulated dc power supplies and the regenerative braking of dc motors. Output voltage must be greater than the input.
Vo Q iLpeak = ∆1Ts L D + ∆1 I 0 = iLpeak 2 Io ∴∆1 = 4 I LB max D Vo D2 ∴ = Vd D 2 + 1 ( I o ) I LB max 4
14
6) Output voltage ripple In the previous analysis, the output capacitor is assumed to be so large as to yield vo(t)=Vo. However, the ripple in the output voltage with a practical value of capacitance can be calculated. In a continuous-conduction mode,
The output voltage is held constant.
t DTs TV 1 I LB = iL , peak = on Vd = Vo (1 − D) = s o D(1 − D) 2 2L 2L 2L
When D=1/2,
I LB max
TsVo = 8L
So,
I LB = 4 I LB max D(1 − D)
2
Classification:
1) step-down (buck) converter 2) step-up (boost) converter 3) step-down/step-up (buck-boost) converter 4) cuk converter 5) full-bridge converter • Only the step-down and the step-up are the basic converter topologies.
I oB
27 = D(1 − D) 2 I oB ,max 4
22
4) Discontinuous-conduction mode----Vd constant
often occurs at light loads
23
Vd DTs + (Vd − Vo )∆1Ts = 0 so, Vo ∆1 + D = Vd ∆1
⑤
D=
ton Vcontrol = ∧ Ts Vst
8
7-3 step-down (buck) converter step• The main application is in regulated dc power supplies and dc motor speed control. • The foregoing circuit (fig. 7-2) has two drawbacks: 1) in practice the load would be inductive; 2) the output voltage fluctuates between zero and Vd. • Usually, we use a low-pass filter, consisting of an inductor and a capacitor, to diminish the fluctuations, shown in fig.7-4.
Vo Ts 1 = = Vd toff 1 − D ∴Vo = Vd 1− D
③ Neglecting power losses,
Pd = Po Vd I d = Vo I o Io = (1 − D) Id
20
3) Boundary between cont./ discont. conduction
Ch7 dc-dc Switch-mode converters
7-1 introduction 7-2 control of dc-dc converters 7-3 step-down (buck) converter 7-4 step-up (boost) converter 7-5 buck-boost converter
1
7-1 introduction
Switch-mode dc-dc converters are used to convert the unregulated dc input into a controlled dc output at a desired voltage level. Functional block diagram:
9
1) Circuit configuration:
Switch, diode, L and C
Assume: Vd is ideal; L and C are large enough;
2) Fundamental analysis:
① When ton:
switch is on; D off; L energy storage; iL increase.
When D=1/2,
I LB max
Vd Ts = 8L
So,
I LB = 4 I LB max D(1 − D)
12
5) Discontinuous-conduction mode----Vd constant
13
(Vd − Vo ) DTs + (−Vo )∆1Ts = 0 Vo D ∴ = Vd D + ∆1
3
1) 2) 3) 4)
Assume that that: the converters are analyzed in steady state; the switches are ideal; the losses in the inductive and the capacitive elements are neglected; the dc input voltage has zero internal impedance.
in a step-up converter, id=iL
I oB = (1 − D) I dB = (1 − D) I LB
I oB TsVo D(1 − D) 2 = 2L
I oB max = TV 2 TsVo = 0.074 s o 27 L L
Io = (1 − D ) Id
When D=1/3,
Ts Vo (1 − D)Ts VVo = 8C L
• In switch-mode dc power supplies, the percentage ripple in the output voltage is usually specified to be less than 1%.
15
Based on MATLAB the simulation of step-down converter • The curve as follows :
② When toff:
D on; L release energy;
10
3) continuous-conduction mode: iL(t)>0
① Analysis: ② In steady-state, inductor current flows continuously.
(Vd − Vo )ton = Vo (Ts − ton ) or : Vo ton = =D Vd Ts Vo = DVd
5
• A simple approach that shows the evolution:
ton Vo = ⋅Vd Ts
Stepping down a dc voltage.
6
• The methods for controlling the output voltage:
① Keeping a constant frequency of the switch (i.e. a constant switching time period Ts=ton +toff ), and adjusting the on duration of the switch to control Vo——pulse width modulation (PWM). where, switch duty ratio D ,which is defined as the ratio of the on duration to the switching time period, is varied. ② Adjusting both the switching frequency and the on duration of the switch. ③ keeping the on duration of the switch constant, and adjusting the switching frequency.
ቤተ መጻሕፍቲ ባይዱ
4
7-2 Control of dc-dc converters dc• Switch-mode dc-dc converters utilize one or more switches to transform dc from one level to another. • In a dc-dc converter with a given input voltage, the average output voltage is controlled by controlling the switch on and off durations( ton and toff ).
19
2) continuous-conduction mode iL(t)>0
① Analysis:
② In steady-state, inductor current flows continuously; and the time integral of the inductor voltage over one time period must be zero. Vd ton + (Vd − Vo )toff = 0
7
Pulse-Width Modulation in DC-DC Converters
① ② ③ ④
The switch control signal; The control voltage signal; The switch frequency; When Vcontrol>Vst, ton; when Vcontrol<Vst, toff;
18
1) Fundamental analysis: ① When the switch is on: the diode is reversed biased, L energy storage ; ② When the switch is off: the diode is on, the output stage receives energy from the inductor as well as from the input. ③ The output filter capacitor is assumed to be very large.
Io ∆1 = (Q Pd = Po ) I d ∆1 + D
and , I d = I L =
iL , peak 2
③ Neglecting power losses,
Pd = Po Vd I d = Vo I o Io 1 = Id D
11
4) Boundary between cont./ discont. conduction
I LB =
t D Ts V T 1 i L m ax = on (V d − V o ) = (V d − V o ) = d s D (1 − D ) = I oB 2 2L 2L 2L
?whend12somaxlbi?inastepupconverteridilwhend134discontinuousconductionmodevdconstant41112222onssolblpeakdotdttviivvdddlll??????8sotvl?max41lblbiidd??11obdblbididi????212soobtviddl??1odidi??max2007427sosoobtvtvill??2max271obobiddi???oftenoccursatlightloads1110dsdosodvdtvvtvdsov????????11ododippid?????q12lpeakdliandiid????1122ddssdovsoidtdltvidl?????5outputvoltageripple?inacontinuousconductionmodethepeakpeakvoltagerippleis
16
17
7-4 step-up (boost) converter
Its main application is in regulated dc power supplies and the regenerative braking of dc motors. Output voltage must be greater than the input.
Vo Q iLpeak = ∆1Ts L D + ∆1 I 0 = iLpeak 2 Io ∴∆1 = 4 I LB max D Vo D2 ∴ = Vd D 2 + 1 ( I o ) I LB max 4
14
6) Output voltage ripple In the previous analysis, the output capacitor is assumed to be so large as to yield vo(t)=Vo. However, the ripple in the output voltage with a practical value of capacitance can be calculated. In a continuous-conduction mode,
The output voltage is held constant.
t DTs TV 1 I LB = iL , peak = on Vd = Vo (1 − D) = s o D(1 − D) 2 2L 2L 2L
When D=1/2,
I LB max
TsVo = 8L
So,
I LB = 4 I LB max D(1 − D)
2
Classification:
1) step-down (buck) converter 2) step-up (boost) converter 3) step-down/step-up (buck-boost) converter 4) cuk converter 5) full-bridge converter • Only the step-down and the step-up are the basic converter topologies.
I oB
27 = D(1 − D) 2 I oB ,max 4
22
4) Discontinuous-conduction mode----Vd constant
often occurs at light loads
23
Vd DTs + (Vd − Vo )∆1Ts = 0 so, Vo ∆1 + D = Vd ∆1
⑤
D=
ton Vcontrol = ∧ Ts Vst
8
7-3 step-down (buck) converter step• The main application is in regulated dc power supplies and dc motor speed control. • The foregoing circuit (fig. 7-2) has two drawbacks: 1) in practice the load would be inductive; 2) the output voltage fluctuates between zero and Vd. • Usually, we use a low-pass filter, consisting of an inductor and a capacitor, to diminish the fluctuations, shown in fig.7-4.
Vo Ts 1 = = Vd toff 1 − D ∴Vo = Vd 1− D
③ Neglecting power losses,
Pd = Po Vd I d = Vo I o Io = (1 − D) Id
20
3) Boundary between cont./ discont. conduction
Ch7 dc-dc Switch-mode converters
7-1 introduction 7-2 control of dc-dc converters 7-3 step-down (buck) converter 7-4 step-up (boost) converter 7-5 buck-boost converter
1
7-1 introduction
Switch-mode dc-dc converters are used to convert the unregulated dc input into a controlled dc output at a desired voltage level. Functional block diagram:
9
1) Circuit configuration:
Switch, diode, L and C
Assume: Vd is ideal; L and C are large enough;
2) Fundamental analysis:
① When ton:
switch is on; D off; L energy storage; iL increase.
When D=1/2,
I LB max
Vd Ts = 8L
So,
I LB = 4 I LB max D(1 − D)
12
5) Discontinuous-conduction mode----Vd constant
13
(Vd − Vo ) DTs + (−Vo )∆1Ts = 0 Vo D ∴ = Vd D + ∆1
3
1) 2) 3) 4)
Assume that that: the converters are analyzed in steady state; the switches are ideal; the losses in the inductive and the capacitive elements are neglected; the dc input voltage has zero internal impedance.