Cirrus Logic AN379 - Manual (Page 12)

AN379
12 AN379REV2
Step 5) Calculate Buck Sense Resistor
The CS1680 current sense threshold V
BUCKPK(th)
is set by the buck sense resistor. The voltage drop across
sense resistor R
BUCK(Sense)
equals threshold V
BUCKPK(th)
at a maximum peak current I
BUCKPK(max)
. Calculate
resistor R
BUCK(Sense)
using Equation 14:
It is recommended to use a slightly smaller value for sense resistor R
BUCK(Sense)
to leave some margin for
component tolerances and series voltage drops that were not considered.
Step 6) Calculate the Buck Inductance
Typically, 24V < V
BST
< 32V and V
OUT
< 15V. Increasing inductance L
BUCK
increases period TT
BUCK
. Use
Equation 6 on page 10 to define critical duty cycle

C
at maximum output voltage V
OUT(max)
and maximum
boost voltage V
BST(max)
. Solve Equation 15 for duty cycle

C(max/max)
:
Use Equation 6 on page 10 to express times T1
BUCK
and T2
BUCK
using time TT
BUCK(fb)
, critical duty cycle
∆
C
,
and the effect of period T3
BUCK
. Calculate times T1
BUCK
and T2
BUCK
at maximum voltages V
BST(max)
and
V
OUT(max)
using Equations 16 and 17, respectively:
Define the buck inductance relationship at maximum boost voltage V
BST(max)
and maximum output voltage
V
OUT(max)
. The current through inductor L
BUCK
must reach peak current I
BUCKPK
during period T1
BUCK
.
Calculate buck inductance L
BUCK
using Equation 18:
Step 7) Determine the RMS Current in the Winding
To define the buck inductor and determine the output capacitor it is necessary to determine current I
RMS
. The factor
3 in the denominator accounts for the triangular shape of the current in the inductor winding. Calculate RMS
current I
RMS
using Equation 19:
where
T
critical
= time when the current is present in the winding
TT
BUCK
= time (T1
BUCK
+T2
BUCK
+T3
BUCK
) (see Figure 4b on page 8)
R
BUCK Sense  
V
BUCKPK th  
I
BUCKPK
--------------------------------- = [Eq. 14]

C max/max  
V
OUT max  
V
BST max  
---------------------------- = [Eq. 15]
T1
BUCK max  
1
F
BUCKSW
-------------------------- T3
BUCK
–
V
OUT max  
V
BST max  
----------------------------  TT
BUCK fb  
T3
BUCK
–   
C max/max  
 = = [Eq. 16]
T2
BUCK max  
1
F
BUCKSW
-------------------------- T3
BUCK
– 1
V
OUT max  
V
BST max  
---------------------------- –  TT
BUCK fb  
T3
BUCK
–   1 
C max/max  
–    = = [Eq. 17]
L
BUCK
V
BST max  
V
OUT max  
–   T1
BUCK max  

I
BUCKPK
------------------------------------------------------------------------------------------------------------  [Eq. 18]
I
RMS
I
BUCKPK
T
critical
3 TT
BUCK

-------------------------------  = [Eq. 19]