## Pages

### KY Converter and Its Derivatives

DESIGN
• POWER =50W
• VIN=12V
•  VOUT=18V
·        OPERATING FREQUENCY OF THE SWITCH (MOSFET HERE) =195KHz
·        Gain formula of converter = 1+D
OUTPUT CURRENT
IOUT = POUT / VOUT
IOUT = 50W / 18V
IOUT = 2.77A
INPUT CURRENT
Assume that the converter efficiency is about 100%
POUT = PIN
I IN = PIN / VIN
I IN = 50W / 12V
I IN = 4.16A

VOLTAGE GAIN CALCULATION
Gain = VOUT  / VIN
VIN = 12V
VOUT = 18V
Gain = 18V /  12V
Gain = 1.5

DUTY CYCLE CALCULATION
Voltage  gain of converter = (1+D)
1.5 = (1+D)
D = 0.5
D = 50%

INDUCTOR VALUE CALCULATION

IN boost MODE (MODE 1), WHEN THE SWITCH S1 IS ON AND  S2 IS OFF, VOLTAGE ACROSS THE INDUCTOR

VL =2 VIN  - VOUT
VL =2* 12V  - 18V
VL =6V

FOR AN INDUCTOR VOLTAGE CURRENT BASIC RELATION IS
VL = L * dI / dt
THEN,  L = VL  *  dt  / dI
L =  V *  dt   / dI

HERE dt = DUTY CYCLE / FREQUENCY
Assume that operating frequency of the switch (mosfet here) =195 kHz
AND dI IS THE RIPPLE CURRENT OF INDUCTOR
IL = IIN= 4.16A
From the industrial viewpoint,the output inductor is generally designed to have no negative current when the output current is above 20%~40% of the rated output current . Therefore, in this paper, the boundary between the positive current and the negative current is assumed to be at 40% of the rated output current. Hence, the
value of Lo can be obtained as follows:
Assume that inductor ripple current = 30% of inductor current
dI =40%  *  IL
dI =40%  * 4.16A *2
dI = 3.328 A

L =  V *  dt   / dI
L = VL *  D   / (F * di)
L = 6V  * 0.5   / (195000 Hz * 3.328 A)
L = 4.6uH

CHARGE PUMP CAPACITOR VALUE
FOR A CAPACITOR VOLTAGE CURRENT BASIC RELATION IS
I = C * dV / dt

dV  is output ripple voltage. Assume that output ripple voltage is about 0.05% of output voltage
dV = 0.1% * 12V
dV =   0.012V
C = IIN * dt / dV
We have dt = duty ratio/frequency
C = IIN * D /  (F * dV )
C = 4.16A * 0.5/ (195000 Hz* 0.012 V)
C =888uF =1000 uF (standard value)

CHARGE PUMP CAPACITOR VALUE
FOR A CAPACITOR VOLTAGE CURRENT BASIC RELATION IS
I = C * dV / dt

dV  is output ripple voltage. Assume that output ripple voltage is about 0.05% of output voltage
dV = 0.1% * 18V
dV =   0.018V
C = IOUT * dt / dV
We have dt = duty ratio/frequency
C = I OUT * D /  (F * dV )
C = 2.77A * 0.5/ (195000 Hz* 0.018 V)
C =394uF = 470 uF (standard value)