ISL6721 Datasheet, PDF (16/22 Pages) Intersil Corporation – Flexible Single-ended Current Mode PWM Controller

ISL6721
The loop compensation is placed around the Error Amplifier
(EA) on the secondary side of the converter. The primary
side amplifier located in the control IC is used as a unity gain
inverting amplifier and provides no loop compensation. A
Type 2 error amplifier configuration was selected as a
precaution in case operation in continuous mode should
occur at some operating point.
V_OUT
V_ERROR
-
+ REF
FIGURE 8. TYPE 2 ERROR AMPLIFIER
Development of a small signal model for current mode
control is rather complex. The method of reference¹ was
selected for its ability to accurately predict loop behavior. To
further simplify the analysis, the converter will be modeled as
a single output supply with all of the output capacitance
reflected to the 3.3V output. Once the “single” output system
is compensated, adjustments to the compensation will be
required based on actual loop measurements.
The first parameter to determine is the peak current
feedback loop gain. Since this application is low power, a
resistor in series with the source of the power switching
MOSFET is used for the current feedback signal. For higher
power applications, a resistor would dissipate too much
power and current transformer would be used instead.
There is limited flexibility to adjust the current loop behavior
due to the need to provide overcurrent protection. Current
limit and the current loop gain are determined by the current
sense resistor and the ISET threshold. ISET was set at 1.0V,
near its maximum, to minimize noise effects. When
determining ISET, the internal gain and offset of the ISENSE
signal in the control IC must be taken into account. The
maximum peak primary current was determined earlier to be
1.87A, so a choice of 2.25A peak primary current for current
limit is reasonable. A current gain, A_EXT, of 0.5V/A was
selected to achieve this.
ISET = 2.25 • 0.8 • 0.5 + 0.100 = 1.00 V
(EQ. 26)
The control to output transfer function may be represented as²:
v_----o-
v_c
=
K•
-^R----^o----^•-----^L---^s----^•-----^f--^s---^w--
2
•
-¹----+-----^{ω----s------z--}
1
+
---^s---
ω_p
(EQ. 27)
If we ignore the current feedback sampled-data effects:
K
=
I_{--s---p----k---(--m-----a---x---)}
V_c(max)
R_o = LoadResis tance
(EQ. 28)
(EQ. 29)
L_s = SecondaryInduc tance
ω_p
=
---------²-----------
R_o • C_o
or
f_p
=
--------------¹---------------
π • R_o • C_o
ω_z = _R-----_c----¹_•----_C-----_o-
or
f_z = -₂----_•-----_π----_•----¹-_R----_c----_•-----_C----_o--
C_o = OutputCapaci tan ce
(EQ. 30)
(EQ. 31)
(EQ. 32)
(EQ. 33)
R_c = OutputCapaci tan ceESR
(EQ. 34)
V_c(max) = ControlVoltageRange
(EQ. 35)
The value of K may be determined by assuming all of the
output power is delivered by the 3.3V output at the threshold
of current limit. The maximum power allowed was
determined earlier as 15W, therefore:
I_spk(max)
=
-²----^•-----^V-P--------^oo------^uu-------^tt---^•----^t--^s---^w--
Tr
=
2_-----•_-----3--¹-----_.--⁵_--3------•_----5_----×_---1---0---^–_---⁶_-
2.33 ×10^–6
=
19.5
v_c(max)
=
V_I
S
E
N
S
E
•
A_EXT
•
A_C
S
•
---------¹-----------
A_COMP
=
2.93
A
(EQ. 36)
V
(EQ. 37)
where A_EXT is the external gain of the current feedback
network, A_CS is the IC internal gain, and A_COMP is the gain
between the error amplifier and the PWM comparator.
The Type 2 compensation configuration has two poles and
one zero. The first pole is at the origin, and provides the
integration characteristic which results in excellent DC
regulation. Referring to the Typical Application Schematic on
page 3, the remaining pole and zero for the compensator are
located at:
f_pc
=
-----------------^C-----¹---³----+-----^C-----¹---⁴------------------
2 • π • R₁₅ • C₁₄ • C₁₃
≈
---------------------¹-----------------------
2 • π • R₁₅ • C₁₄
(EQ. 38)
f_zc
=
---------------------¹-----------------------
2 • π • R₁₅ • C₁₃
(EQ. 39)
The ratio of R₁₅ to the parallel combination of R₁₇ and R₁₈
determine the mid band gain of the error amplifier.
A_midband
=
-^R----¹---⁵----^•-----⁽--^R-----¹---⁷----+-----^R----¹---⁸----⁾
R₁₇ • R₁₈
(EQ. 40)
From Equation 27, it can be seen that the control to output
transfer function frequency dependence is a function of the
output load resistance, the value of output capacitance, and
the output capacitance ESR. These variations must be
considered when compensating the control loop. The worst
case small signal operating point for the converter is at
16
FN9110.6
March 5, 2008