S-8351A20MC-J2FT2X Datasheet, PDF (19/51 Pages) Seiko Instruments Inc – SWITCHING REGULATOR CONTROLLER

STEP-UP, BUILT-IN / EXTERNAL FET PFM CONTROL SWITCHING REGULATOR / SWITCHING REGULATOR CONTROLLER
Rev.3.0_01
S-8351/8352 Series
Integration of the equation (6) is as follows :
I_L
= I_PK
− 

V_OUT
+ V_D
L
− V_IN
 • t

(7)
During tON, the energy is stored in L and is not transmitted to VOUT. When receiving the output current (IOUT) from
VOUT, the energy of the capacitor (CL) is consumed. As a result, the pin voltage of CL is reduced, and goes to the
lowest level after M1 is turned ON (tON). When M1 is turned OFF, the energy stored in L is transmitted through the
diode to CL, and the voltage of CL rises rapidly. VOUT is a time function, and therefore indicates the maximum value
(ripple voltage (VP−P) ) when the current flowing through into VOUT and load current (IOUT) match.
Next, the ripple voltage is determined as follows.
IOUT vs. t1 (time) from when M1 is turned OFF (after tON) to when VOUT reaches the maximum level :
I_OUT
= I_PK
− 

V_OUT
+ V_D
L
− V_IN
 • t₁

(8)
∴
t₁
=
(I_PK
− I_OUT ) • _{}
V_OUT
L
+ V_D
−
V_IN

(9)
When M1 is turned OFF (tOFF), IL = 0 (when the energy of the inductor is completely transmitted).

V_OUT
L
+ V_D
−
V_IN

=
t_OFF
I_PK
Based on equation (7) :
(10)
When substituting equation (10) for equation (9) :
t₁
=
t_OFF
−

I_OUT
I_PK

•
t_OFF
(11)
Electric charge ΔQ1 which is charged in CL during t1 :
   ^ΔQ1 ⁼
0t1^{ILdt = IPK •}
t1_dt
0
−
V_OUT
+ V_D
L
−
V_IN
•
t1_tdt
0
= I_PK
• t₁
−
V_OUT
+ V_D
L
−
V_IN
•
1
2
t₁₂
(12)
When substituting equation (12) for equation (9) :
( ) ΔQ1
=
I_PK
−
1
2
I_PK − I_OUT
•
t₁
=
I_PK
+ I_OUT
2
•
t₁
(13)
A rise in voltage (VP−P) due to ΔQ 1 :
V_P−P
=
∆Q₁
C_L
=
1
C_L
•  ^IPK

+ I_OUT
2
 • t₁

(14)
When taking into consideration IOUT to be consumed during t1 and the Equivalent Series Resistance (RESR) of CL :
V_P−P
=
ΔQ₁
C_L
=
1
C_L
•  ^IPK

+ I_OUT
2
 • t1+  ^IPK

+ I_OUT
2
 • R_ESR

−
I_OUT • t₁
C_L
(15)
When substituting equation (11) for equation (15) :
V_P−P
=
(I_PK
− I_OUT )²
2I_PK
•
t_OFF
C_L
+  ^IPK

+ I_OUT
2
 • R_ESR

(16)
Therefore to reduce the ripple voltage, it is important that the capacitor connected to the output pin has a large
capacity and a small RESR.
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