Application Note AN-1150 - International Rectifier

For a Constant Power Load, the shunt impedance and the system load cancel
each other out and the equivalent impedance is infinite, in which case the
transfer function reduces to:
vout
1
=
i sC
chg
In the power stage transfer function, this is represented by a pole at the origin.
Under a Constant Current Load, since the impedance of a current source is
infinitely high, the equivalent impedance is effectively just the shunt impedance:
vout
RL
=
i 1 + sC RL
In the power stage transfer function, this is represented by a pole:
1
f
PS
= 2π
⋅C
R
chg
Next (i CHG /i L ) transfer function has to be evaluated. Assuming 100% efficiency,
recognize that:
V IN .I L = V OUT I OUT
I OUT is same as the DC component of the boost diode current (I CHG ). Hence
V IN .I L = V OUT I CHG
Applying linearization and small-signal analysis, for a given DC operating point
defined by V IN & V OUT yields the relationship between i CHG & i L :
i CHG /i L = V IN /V OUT
Assuming a resistive load, the overall power stage transfer function can now be
written as:
V
G(
s)
=
V
IN
OUT
out
out
out
RL
×
1+
sC
L
/ 2
out
R
2
L
OCC PFC Modulator, H 3 (s)
In order to derive i L /v m , the One Cycle Control PWM modulator control law is
employed:
v
m
G
DC
⋅ RS
⋅iL
=
M (d)
where M(d) = V OUT /V IN for a given DC operating point defined by the DC bus
voltage V OUT and RMS input voltage V IN . This ultimately yields
L
H
3
( s)
= =
vm
i
V
OUT
V
R
in
S
G
DC
www.irf.com AN-1150
20