STEP-UP, 1.2 MHz HIGH-FREQUENCY, PWM CONTROL SWITCHING REGULATOR CONTROLLER
Rev.4.0_00
S-8337/8338 Series
Seiko Instruments Inc.
15
Change in current (IL) flowing through the diode into VOUT during tOFF:
L
V
L
V
dt
dl
IN
D
OUT
L
+
=
…………………………………………………………..…………………(6)
Integration of the above equation is as follows:
t
L
V
I
IN
D
OUT
PK
L
+
=
…………………………………………………………………………(7)
During tON, energy is stored in L and is not transmitted to VOUT. When receiving output current (IOUT)
from VOUT, the energy of the capacitor (CL) is used. 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 via the diode to CL, and the pin voltage of CL rises drastically. Because VOUT is a time
function indicating the maximum value (ripple voltage: Vp-p) when the current flowing through the
diode into VOUT and the load current IOUT match.
Next, this 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:
1
IN
D
OUT
PK
OUT
t
L
V
I
+
=
………………………………………………….………………...…(8)
()
+
=
∴
IN
D
OUT
PK
1
V
L
I
t
……………………………………………………………...…...(9)
When M1 is turned ON (after tOFF), IL = 0 (when the energy of the inductor is completely transmitted):
Based on equation (7),
PK
OFF
IN
D
OUT
I
t
V
L
=
+
…………………………………………………………………..………….(10)
When substituting equation (10) for equation (9):
OFF
PK
OUT
OFF
1
t
I
t
=
…………………………………………………………………………………(11)
Electrical charge
ΔQ
1 which is charged in CL during t1:
2
1
IN
D
OUT
1
PK
1
t
0
IN
D
OUT
1
t
0
PK
L
1
t
0
1
t
2
1
L
V
t
I
tdt
L
V
dt
I
dt
I
Q
+
=
∫
+
∫
=
∫
=
Δ
……….…...(12)
When substituting equation (12) for equation (9):
()
1
OUT
PK
1
OUT
PK
1
t
2
I
t
I
2
1
I
Q
+
=
=
Δ
…………………………………………………….…….(13)
A rise voltage (Vp-p) due to ΔQ1:
1
OUT
PK
L
1
p
t
2
I
C
1
C
Q
V
+
=
Δ
=
…………………………………………………………..……………(14)
When taking into consideration IOUT consumed during t1 and ESR
*1 (R
ESR) of CL:
L
1
OUT
ESR
OUT
PK
1
OUT
PK
L
1
p
C
t
I
R
2
I
t
2
I
C
1
C
Q
V
+
+
=
Δ
=
…………….………………….(15)
*1.
Equivalent Series Resistance