ISL6731A Datasheet, PDF (16/20 Pages) Intersil Corporation – Power Factor Correction Controllers

ISL6731A, ISL6731B
120
F_Z
F_P
100
G_ILOOP (s)
80
Gid (s)
60
Gci (s)
40
20
F_C
0
Gsm
-20
-4010
100
1k
10k
FREQUENCY (Hz)
100k
FIGURE 16. ASYMPTOTIC BODE PLOT FOR CURRENT LOOP GAIN
F_Z= -₂---_-----_----_R----¹-_i--_c----_----_C----_i--_c-
(EQ. 46)
F_P= -₂---_-----_----_R-----_i--_c----_-¹---_C-C---------_ii---pp---------+_{---------CC}---------_i-i--_c-_c--
(EQ. 47)
Use the following guidelines for locating the poles and zeros of
the compensation network.
Near the crossover frequency, the transfer function from duty
cycle to inductor current is well approximated by Equation 48:
G_ids= -_L---^V_B----^OS----_TU----^T-_---_s-
(EQ. 48)
The compensation gain uses external impedance networks as
shown in Figure 15, G_ci(s) is given by:
G_cis= Gmi _---_C-----_i-_c----+----¹-_C-----_i-_p----_---_---_s-  -_2-^{2-------------}_--^{-------}_-^_-------^ss-------_---------_FF------------_PZ---------++-----¹¹--
(EQ. 49)
The current gain and modulation gain Gsm is:
Gsm = _R---^R--_s--^c--_e--^s--_n-  ^R----₂-ⁱ--^s- _V----¹-_m---
(EQ. 50)
Where _M is the phase margin, which is 20°. F_P = 6kHz. This is
an aggressive example to fulfill a tight THD for light load.
Thus, the current loop compensation zero is:
F_Z=
-----------------------------¹----⁴----^k---^H-----^z------------------------------
tan _
atan


1_--6--4_--k--k_-H--H_---z--z_{-}
+
20 d e g_
=
0.78 k H z
(EQ. 53)
The total compensation capacitance is calculated:
C_ip + C_ic=







L^----_B^----_S^----_T^V----O-^---^-U-2^---T-^----f^--_c^---^--2-

-^A--_V--^I--^D-_m---^C--

R^--R---_S^--C--_E^--S--_N^--_{}

1^{-1----+-+----}^---ff^--_cc^----^--ff^--_pz^{------22-}_{} ^{(EQ. 54)}
C_ip + C_ic= 7.345nF
C_ip = C_ip + C_iC_f-^f-_p-^z-
The value of the noise filtering capacitor is:
C_ip = 7.345nF  ⁰----^.--⁷⁶---⁸-_H---^k--_z-^H-----^z- = 0.958nF
(EQ. 55)
(EQ. 56)
(EQ. 57)
The value of C_ic is:
C_ic = 7.345nF – 0.958nF = 6.378nF
(EQ. 58)
The value of R_ic is:
R_ic = ₂----_-----_---₀---_.--₇---₈----_k----_H--¹---_z----_---₆---_.--₃---₇----₈---_n----_F-- = 31.85k
(EQ. 59)
Select the R_C value from the standard value, we have:
R_ic = 30kΩ, C_ic = 6.8nF, C_ip = 1nF. Figure 17 shows the actual
bode plot of current loop gain.
100
F_Z
F_P
50
0
90
F_Z
F_P
where Vm is the amplitude of the PWM carrier. The open loop
gain of the current loop is:
G_ILOOPs= G_ids  G_sm  G_cis
(EQ. 51)
It is recommended to set the crossover frequency, F_C from 1/10
to 1/6 of the switching frequency with a phase margin of 60°. A
high frequency pole, F_P, is set at 1/2 of the switching frequency
for ripple filtering. In this example, we set the F_C at 14kHz.
F_Z=
-------------------------^F----^C---------------------------
tan



atan



F_{-F---C-P--}
+

_{M}
(EQ. 52)
60
60
45
30
0 ₁₀
100
1k
10k
100k
FREQUENCY (Hz)
FIGURE 17. BODE PLOT OF THE ACTUAL CURRENT LOOP GAIN
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February 13, 2015