Cirrus Logic AN379 - Manual (Page 22)

AN379
22 AN379REV2
It is desirable to maintain a minimum margin of 8V and to use a FET with a breakdown voltage of 50V. Solving
Equation 44 for voltage V
Margin
yields Equation 45:
Step 3) Determine the Buck Stage Timing
The buck stage operates in DCM at all times. Gain factor GAIN
TT
is defined as constant equal to 1.2. Solving
Equation 11 on page 11 for critical period (T1
BUCK
+T2
BUCK
) yields Equations 46:
Solving Equation 12 on page 11 for period T3
BUCK
yields Equation 47:
Step 4) Calculate Peak Current on the Buck Inductor
Use Equation 13 on page 11 to determine the peak current at the highest I
BUCKPK
. Solve Equation 48 for peak
current I
BUCKPK(max)
:
Step 5) Calculate Buck Sense Resistor
The voltage drop across sense resistor R
Buck(Sense)
must equal 0.525V when a maximum current of 1.0A
flows through sense resistor R
Buck(Sense)
. Using Equation 14 on page 12, solve Equation 49 for sense
resistor R
Buck(Sense)
:
where
R
BUCK(Sense)
= resistor R2 and selected as 0.51 
Choosing a 0.51Ω standard value will assure margin against resistor tolerance. To prevent false triggering by
the comparator, pin BUCKSENSE has an internal blanking time of 250 ns. To reduce switching spikes, it is
recommended to add an additional 10
 resistor in series with pin BUCKSENSE.
Step 6) Calculate the Buck Inductance
Use Equation 6 on page 10 for the critical duty cycle at maximum boost output voltage V
BST(max)
and output
voltage V
OUT(max)
. Solve Equations 50 for critical duty cycle ∆
C(max/max)
:
Use Equations 16 and 17 on page 12 to express periods T1
BUCK
and T2
BUCK
using switching period TT
BUCK
,
critical duty cycle ∆
C
, and the effect of period T3
BUCK
. Calculate periods T1
BUCK
and T2
BUCK
at maximum
voltage V
BST(max)
and V
OUT(max)
using Equations 51 and 52, respectively:
V
M in arg
V
Breakdown
= 38V – 50V 38V – 12V = = [Eq. 45]
T1
BUCK
T2
BUCK
+
TT
BUCK fb   
GAIN
TT
--------------------------------
6.67 s
1.2
------------------ 5.56 s = = = [Eq. 46]
T3
BUCK
TT
BUCK fb  
GAIN
TT
1 –   
GAIN
TT
------------------------------------------------------------------------
6.67 s 1.2 1 –   
1.2
----------------------------------------------- 1.1 s = = = [Eq. 47]
I
BUCKPK max  
2 I
OUT
GAIN
TT
  2 430mA 1.2   1.0A = = = [Eq. 48]
R
BUCK Sense  
V
BUCKPK th  
I
BUCKPK
---------------------------------
0.525V
1.0A
------------------- 0.525  = = = [Eq. 49]

C max/max  
V
OUT max  
V
BST max  
---------------------------- =
12V 1.2V +  
32V
---------------------------------- 41.3% = = [Eq. 50]
T1
BUCK
TT
BUCK fb  
T3
BUCK
–   
C max/max  
 6.67 s 1.1s –   0.413  2.3 s = = = [Eq. 51]
T2
BUCK
TT
BUCK fb  
T3
BUCK
–   1 
C max/max  
–    6.67 s 1.1s –   0.587  3.3 s = = = [Eq. 52]