### AN009 CN

```Application Note

AN009 – Jul 2014
Buck 转换器的电流纹波系数
Current Ripple Factor of a Buck Converter

1. 介绍 .........................................................................................................................................................2
2. 纹波系数 ..................................................................................................................................................3
3. 电感的面积积 ...........................................................................................................................................4
4. 一个设计示例 ...........................................................................................................................................6
5. 总结 .........................................................................................................................................................7
AN009
1
Buck 转换器的电流纹波系数
1. 介绍
Buck 转换器被广泛应用于大量的降压应用中，板上负载点转换器是这种应用的典型例子。从原理上看，它就是用一个功率开关和

Q1
L
Vsw
Vsw
Vin
Vin
+
iL
C
D1
∆iL
Vo
R Vo
Io
0
-
t
Ton
Toff
Ts
(b)
(a)

VL (t)  Vin  Vo ; 0  t  Ton (Q1 “ON”)
(1)

V  Vo
iL (t)  iL (0)  in
t
L
(2)

VL (t)  Vo ; Ton  t  Ts (Q1 “OFF”)
AN009
(3)
2
Buck 转换器的电流纹波系数

V
iL (t  Ton )  iL (Ton )  o  (t  Ton )
L
(4)

Vo Ton

 D (duty cycle)
Vin Ts
(5)

2. 纹波系数

ΔiL
iL
Io
0
t
Ton
Toff
Ts

iL  iL (Ton)  iL (0)
(6)

Io 
iL (Ton)  iL (0)
2
AN009
(7)
3
Buck 转换器的电流纹波系数

γ
iL
Io
(8)

Conduction Mode, DCM)。由于连续导通模式下功率元件所受电流应力较低，工作在满载状态下的 Buck 转换器一般都被设计成

Δi
γ L 
Io
Vin  Vo
 D  Ts V  (1 D)  D  T
V  (1 D)  Ts
s
L
 in
or o
Io
L  Io
L  Io
(9)

3. 电感的面积积

L  ipk  N  Bm  AC
(10)

I
N  A WT  N  rms  k w  Wa
J
(11)

AN009
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Buck 转换器的电流纹波系数
AP  Ac  Wa 
L  ipk  Irms
k w  J  Bm
(12)

i 2
Irms  Io2 + L
12
(13)

AP 
Vo  Io
1 D  Ts 
k w  J  Bm

γ2
 1 γ 
4

 
γ2 
   1

12 
 
γ
(14)

5
Relative Inductor Size
D=0.1
D=0.3
4
D=0.5
D=0.7
3
D=0.9
Optimum
2
1
0
0
0.5
1
1.5
Ripple Factor (γ)

AN009
5
Buck 转换器的电流纹波系数
4. 一个设计示例

Vin = 4 ~ 12V, Vout = 1.8V, Io = 6A, ΔVo = 10mV （输出电容上的纹波电压）。

Ripple Current
Ripple Current
(A)
RMS (A)
0.3
1.80
0.52
1.56
0.15
0.3
1.80
0.52
1.89
0.1
0.3
1.80
0.52
2.00
Input Voltage (V)
Duty Cycle
Ripple Factor
4
0.30
8
12
Inductance (μH)

Optimal Ripple
Ripple Current
Ripple Current
Factor
(A)
RMS (A)
0.30
0.42
2.52
0.73
1.11
8
0.15
0.45
2.7
0.78
1.26
12
0.1
0.48
2.88
0.83
1.25
Input Voltage (V)
Duty Cycle
4
Inductance (μH)

MLCC 作为输出电容，它们都具有极低的串联等效电阻，因此要得到纹波电压指标是很容易的。
AN009
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Buck 转换器的电流纹波系数
5. 总结

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AN009