Rainbow Electronics MAX1585 User Manual
Page 23
If Z
COUT
is not less than Z
RHP
/ 10 (as is typical with
ceramic output capacitors) and continuous conduction
is required, then cross the loop over before Z
RHP
and f
0
:
f
C
< f
0SC
/ 10, and f
C
< Z
RHP
/ 10
In that case:
C
C
= (V
IN
/ V
RAMP
)(V
FB
/ V
OUT
)(g
M
/ (2
π x f
C
))
Place:
1 / (2
π x R
C
x C
C
) = 1 / (2
π x R
LOAD
x C
OUT
), so that
R
C
= R
LOAD
x C
OUT
/ C
C
Or, reduce the inductor value for discontinuous operation.
AUX3 Step-Down Compensation
It is expected that most AUX3 step-down applications
employ continuous inductor current to optimize induc-
tor size and efficiency. To ensure stability, the control-
loop gain should cross over (drop below unity gain) at
a frequency (f
C
) much less than that of the switching
frequency.
The relevant characteristics for voltage-mode step-
down compensation are as follows:
• Transconductance (from FB3 to CC3), g
MEA
(135µS)
• Oscillator ramp voltage, V
RAMP
(1.25V)
• Feedback regulation voltage, V
FB
(1.25V)
• Output voltage, V
OUT3
, in V
• Output load equivalent resistance, R
LOAD
, in
Ω =
V
OUT3
/ I
LOAD
• Characteristic impedance of the LC output filter, R
O
= (L / C)
1/2
The key steps for AUX3 step-down compensation are
as follows:
1) Place f
C
sufficiently below the switching frequency
(f
OSC
/ 10).
2) Calculate C
OUT
.
3) Calculate the complex pole pair due to the output
LC filter.
4) Add two zeros to cancel the complex pole pair.
5) Add two high-frequency poles to optimize gain and
phase margin.
If we assume V
IN
= 5V, V
OUT
= 3.3V, and I
OUT
=
300mA, then R
LOAD
= 11
Ω. If we select f
OSC
= 500kHz
and L = 10µH, select the crossover frequency to be
1/10 the OSC frequency:
f
C
= f
OSC
/ 10 = 50kHz
For 3.3V output, select R14 = 30.1k
Ω and R15 =
18.2k
Ω. See the Setting Output Voltages section.
Calculate the equivalent impedance, R
EQ
:
R
EQ
= R
SOURCE
+ R
L
+ ESR + R
DS(ON)
where R
SOURCE
is the output impedance of the source
(this is the output impedance of the step-up converter
when the AUX3 step-down is powered from the step-
up), R
L
is the inductor DC resistance, ESR is the filter-
capacitor equivalent resistance, and R
DS(ON)
is the
on-resistance of the external MOSFET.
The output impedance of the step-up converter
(R
SOURCE
) is approximately 1
Ω at f
0
. Since the sum of
R
L
+ ESR + R
DS(ON)
is small compared to 1
Ω, assume
R
EQ
= 1
Ω. Choose C
OUT
so R
O
is less than R
EQ
/ 2:
C
OUT
> L / [(R
EQ
/ 2)
2
] = 10µH / 0.25 = 40µF
Choose C
OUT
= 47µF:
C4 = (V
IN
/ V
RAMP
)(1 / [2
π x R14 x f
C
])
= (5 / 1.25)(1/ [2
π x 30.1k x 50kHz) = 423pF
Choose C4 = 470pF.
Cancel one pole of the complex pole pair by placing
the R4 C4 zero at 0.75 f
0
. The complex pole pair is at
the following:
f
0
= 1 / [2
π(L x C
OUT
)
1/2
]
= 1 / [2
π(10µH x 47µF)
1/2
] = 7.345kHz
Choose R4 = 1 / (2
π x C4 x 0.75 x f
0
)
= 1 / (2
π x 470pF x 0.75 x 7.345kHz)
z
Choose R4 = 61.9k
Ω (standard 1% value). Ensure that
R4 > 2 / g
MEA
= 14.8k
Ω. If it is not greater, reselect
R14 and R15.
Cancel the second pole of the complex pole pair by
placing the R14 C20 zero at 1.25 x f
0
.
C20 = 1 / (2
π x R14 x 1.25 x f
0
)
= 1 / (2
π x 30.1k x 1.25 x 7.345kHz) = 576pF
Choose C20 = 560pF.
Roll off the gain below the switching frequency by plac-
ing a pole at f
OSC
/ 2:
R22 = 1 / (2
π x C20 [f
OSC
/ 2])
= 1 / (2
π x 560pF x 250kHz) = 1.137kΩ
Choose R22 = 1.2k
Ω.
If the output filter capacitor has significant ESR, a zero
occurs at the following:
Z
ESR
= 1 / (2
π x C
OUT
x R
ESR
)
Use the R4 C22 pole to cancel the ESR zero:
C22 = C
OUT
x R
ESR
/ R4
If C22 is calculated to be <10pF, it can be omitted.
MAX1584/MAX1585
5-Channel Slim DSC Power Supplies
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