ISL6731A Datasheet, PDF (17/20 Pages) Intersil Corporation – Power Factor Correction Controllers

ISL6731A, ISL6731B
INPUT VOLTAGE SETTING
First, set the BO resistor divider gain, K_BO according to
Equations 1 and 2.
Assuming the converter starts at V_LINE = 80V_RMS, then the BO
resistor divider gain, K_BO, should be:
K_BO = ₈----₀---⁰-_V--^.--⁵-–--^V---₂---_V--- = 0.00641
(EQ. 60)
In this design, two 470kΩ resistors in series are used for R_IN2.
Therefore, R_IN1 is calculated:
R_IN1 = ₁-----⁰_–---^.--₀₀---_.0--₀--⁶-₀--⁴--₆--¹-₄---₁--  0.94M = 6.065k
(EQ. 61)
We choose R_IN1 = 5.76kΩ, the actual K_BO is calculated:
K_BO = -_R----_I--_N---^R-₁----^I-+-^N---_R-¹----_I--_N----₂- = 0.00609
(EQ. 62)
NEGATIVE INPUT CAPACITOR GENERATION
The ISL6731A and ISL6731B generate an equivalent negative
capacitance at the input to cancel the input filter capacitance.
Thus, more input capacitors can be used without reducing the
power factor.
The input equivalent negative capacitance is a function of the
current sensing gain, BO resistor divider gain and the
compensation components.
C_NEG= _{}K_BO  0.8 – _V----^V-_O---^m-_U----_T--_{ R}-----_C-^R---_S-^S---_A-^E---_i-^N-_D----_C-- C_ic + C_ip
(EQ. 63)
C_NEG=


0.00609

0.8
–
3^-1---9^-.-5-0^{--}
0^----.^--0^---7^--3-3^---k--^---1^---.^--9^--
 6.8
nF
+
1
nF
=
0.17  F
(EQ. 64)
This equivalent negative capacitor cancels the input filter
capacitor required for EMI filtering. Therefore, the displacement
power factor significantly improves.
For example, C_F1 = 0.68µF, C_F2 = C_F3 = 0.47µF, using the low
cost EMI filter shown in Figure 13. When V_LINE = 230VAC,
f_LINE = 50Hz, P_O = 300W.
Assuming 95% efficiency under the above test condition, the
resistive component of the line current, which is in phase to voltage:
I_a= -_V----_L---_I--_N----^P_E----^o-_---₀---_.--₉---₅-- = 1.373A
(EQ. 65)
The reactive current through the input capacitors:
I_c= V_LINE  2  f_LINE  C_F1 + C_F2 + C_F3 = 0.14A
(EQ. 66)
Thus, the displacement power factor is:
PF_DIS=
----------------^I--^a-----------------
I_a² + I_c²
=
0.9948
(EQ. 67)
The reactive current generated by the equivalent negative
capacitor is:
I_cneg= V_LINE  2  f_LINE  C_NEG = 0.015A
(EQ. 68)
With the equivalent negative capacitor, the total reactive current
reduces to:
I_c – I_cneg = 0.126A
(EQ. 69)
The displacement power factor increases to:
PF_DIS=
--------------------------^I--^a---------------------------
I_a² + I_c – I_cneg²
=
0.9958
(EQ. 70)
VOLTAGE LOOP COMPENSATION
The average boost diode forward current can be approximated by:
I_{Dave}= _V----^P-_O---ⁱ-_U-ⁿ---_T--
(EQ. 71)
Assuming the input current traces the input voltage perfectly. The
input power is in proportion to (V_COMP - 1V).
I_{Dave}=
R^-----_C^----_S^---R--^---S0^----.^E-5^---N--^---R^-----_I^--_S^-

-_V----_O--¹--_U----_T--





-_--_--₂--------₂----_--⁰--_-^.-_-²---_⁵--₂-----_---_K----_B----_O--_{}
 _COMP
(EQ. 72)
Where _COMP is the V_COMP - 1V. 1V is the offset voltage.
R_IS is the internal current scaling resistor. R_IS = 14.2kΩ.
I_{Dave}= 0.749 ^AV---  _COMP
(EQ. 73)
2.5V
FB
VOUT
R_FB2
Gmv
I_FB
R_FB1
COMP
Rvc
Cvp
Cvc
FIGURE 18. OUTPUT VOLTAGE SENSING AND COMPENSATION
Thus, the transfer function from V_COMP to V_OUT is:
G_PSs=
-^V----^O----^U----^T----^---^s---^
_COMP
=
C^-----_O^--1----^---s^-

-^I--^D----^--^a----^v---^e---^-
_COMP
(EQ. 74)
G_PSs=



I_{--CD-----O--a---v---es---}

^----_C^-----_O^1----_M^-----_P^--_{}
=
-_C0---^.-_O-⁷---⁴--_--⁹-_s-
As shown in Figure 18, the voltage loop gain is:
G_VLOOPs= G_PSs  G_DIV  Gmv  Z_COMPs
(EQ. 75)
(EQ. 76)
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FN8582.1
February 13, 2015