Cirrus Logic AN379 - Manual (Page 23)

AN379
AN379REV2 23
Calculate buck inductance L
BUCK
at maximum boost voltage V
BST(max)
and maximum voltage V
OUT(max)
. The
current through inductor L
BUCK
must reach peak current I
BUCKPK
during period T1
BUCK
. Solving Equation 18
on page 12 for inductor L
BUCK
returns Equation 53:
where
L
BUCK
= power inductor L2 and is selected as a standard inductor with an inductance of 47 H
Inductor L
BUCK
must not saturate up to a peak current of 1.2A, maintaining some margin against the calculated
peak current 1.0A.
Step 7) Determine the RMS Current in the Winding
The inductor winding is subject to the full waveform during periods T1
BUCK
and T2
BUCK
, as demonstrated in
Equation 19 on page 12. Use Equation 54 to solve for RMS current I
RMS
:
Step 8) Buck Inductor Specification
Use Equation 55 to calculate the new period T1
BUCK
using the actual value of inductor L
BUCK
:
Use Equation 56 to calculate the new switching period TT
BUCK(fb)
using the new period T1
BUCK
:
Specifications for buck inductor L
BUCK
can now be compiled to enable suppliers to design within size and cost
constraints.
Step 9) Determine Output Capacitor
Output capacitor C
OUT
ripple current I
Ripple(RMS)
is the difference between the RMS current in the winding of
L
BUCK
and the DC load current. Calculate ripple current I
Ripple(RMS)
from Equation 57:
Parameter Value
Output DC Power 5.15W
Converter Topology DCM Buck
Full-load Switching Frequency 138kHz
Inductance 47 H  10%
Peak Current in the Winding 1.0A
RMS Current in the Winding 527mA
L
BUCK
V
BST max  
V
OUT max  
–   T1
BUCK

I
BUCKPK
----------------------------------------------------------------------------------------------- 
32V 13.2V –   2.3s 
1.0A
----------------------------------------------------------- 43.2 H = = [Eq. 53]
I
RMS
I
BUCKPK
T
critical
3 TT
BUCK

-------------------------------  1.0A
1
3 1.2 
-----------------  527mA = = =
[Eq. 54]
T1
BUCK
I
BUCKPK
L
BUCK

V
BST max  
V
OUT max  
–  
-------------------------------------------------------------------
1.0A 47 H 
32V 13.2V –  
------------------------------------- 2.5 s = = = [Eq. 55]
TT
BUCK fb  
T1
BUCK
GAIN
TT


C max/max  
-------------------------------------------------
2.5 s 1.2 
0.413
------------------------------ 7.3 s = = = [Eq. 56]
I
Ripple RMS  
I
RMS
2
I
OUT
2
– = 0.53
2
0.43
2
–  A 0.31A = = [Eq. 57]