ISL6844 Datasheet, PDF (4/10 Pages) Intersil Corporation – ISL6844 Reference Design: ISL6844EVAL3Z

Application Note 1612
C_E = Equivalent capacitor reflected to the auxiliary output.
ESR = Equivalent series resistance of the output capacitor.
K = I_SPK(MAX)/V_C(MAX).
The equivalent load reflected to the auxiliary output can be
estimated from:
R_E
=
-----------^V----^a2---^u----^x-----------
P_OUT(Total)
(EQ. 20)
=
-⁽--¹---⁵----^V-----⁾--²-
3W
=
75 Ω
The equivalent capacitor reflected to the auxiliary output can be
estimated from:
C_E
=
C_au
x
+
--^N----^S----¹---
N_aux
⋅
C
OUT
1
+
--^N----^S----²---
N_aux
⋅
C
OUT2
=
1
μ
F
+
1_----5_--
15
⋅ 10μF +
1_----5_--
15
⋅
10 μ F
=
21 μ F
(EQ. 21)
The value of I_SPK(MAX) can be determined by assuming that the
auxiliary output delivers all of the output power.
2 ⋅ ^P-----^O----^U----^T----⁽--^M-----^A----^X----⁾
I_SPK(MAX)
=
-----------------^V----^A----^U----^X-----------
D₂
2 ⋅ -⁴----^W-----
=
--------¹----⁵----^V--
0.5
=
1.067 A
(EQ. 22)
P_OUT(MAX) = The maximum power allowed = 4W
V_C(MAX) has value of 1.1V, clamped by ISL6844’s internal circuit.
Along with the result from Equation 22, K has a value of 0.97.
Replaces K and the results from Equation 21 and Equation 22
into Equation 19, yields
G_vc
=
15.87
⋅
-------------------------¹---------------------------
(1 + s ⋅ 7.875×10^–4)
(EQ. 23
Note that with the low ESR values of the output ceramic
capacitor, the zero due to their ESR is located at the frequency
significantly higher than the switching frequency. As the result,
the impact of capacitor’s ESR is neglected for compensator
design.
From Equation 20, it shows that when the total output power
reduces, the equivalent load resistor increases. This increases
the DC-gain in Equation 19, also the pole is moved to the lower
frequency.
40
1W TOTAL OUTPUT
3W TOTAL OUTPUT
20
0
20
40
10
100
1 ^.10³
1 ^.10⁴
1 ^.10⁵
1 ^.10⁶
FREQUENCY (Hz)
FIGURE 3. GAIN OF G_VC
From Equation 23, the pole of the control-to-output transfer
function for 3W output is located at 202Hz. Setting the
closed-loop’s bandwidth of 10kHz, the feedback compensation
must have a mid-band gain of 3.11 (10dB). The mid-band gain is
determined by
A_{mid – band}
=
R_-----2---4-
R₂₂
(EQ. 24)
Therefore, R₂₄ is selected to be 16.2kΩ.
The first zero of compensation is set at 1/3 of the crossover
frequency, 3.33kHz. C₉ can be calculated from:
C₉
=
---------------------------------¹-----------------------------------
2 ⋅ π ⋅ 3.33×10³ ⋅ 16.2×10³
(EQ. 25)
= 2.95nF
2.7nF is used for C₉.
The second zero of compensation is set at half of the switching
frequency. C₁₀ can be calculated from:
C₁₀
=
--------------------------------¹----------------------------------
2 ⋅ π ⋅ 150×10³ ⋅ 16.2×10³
(EQ. 26)
= 65.5pF
68pF is used for C₁₀.
4
AN1612.1
November 28, 2011