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AOZ1977
RFB = = = 2.5 ?
ISET Voltage 0.5 V
0.2 A
V IN 2
f Z 2 =
2 ? ? L ? I O ? V O
RS = -------------------------------------------------------------------------- = ---------------- = 0.55 ?
2 ? ? C C ? G VEA
2 ? ? C O ? R L
2 ? ? C C ? R C
2 ? ? C O ? ESR CO
Current Sense Resistors
There are two current sense resistors in this application,
an LED current sense resistor RFB and a Boost switch
current sense resistor RS.
RFB LED current sense resistor is set by:
------------------------------------ ------------
LED Current
LED current is a function of ISET voltage and RFB
resistance. ISET voltage is generated by connecting a
resistor divider (Rr1 and Rr2 on page 1) from 1.2 V
VREF pin to ISET and GND pins. To minimize power
consumption, it is recommended that the total resistance
for the divider is approximately 20 k ? .
RS boost switch current sense resistor is set by:
0.3 V 0.3 V
LEDInductor Peak Current 0.55 A
For typical application, it is recommend to set the voltage
at CS to approximately 0.3 V when inductor current
reaches the peak.
Boost Feedback Loop Compensation
The AOZ1977 employs peak current mode control for
easy use and fast transient response. Peak current mode
control eliminates the double pole effect of the output
L&C filter. It greatly simplifies the compensation loop
design.
With peak current mode control, the boost power stage
can be simplified to be a one-pole, one left plane zero
and one right half plane (RHP) system in frequency
domain. The pole is the dominant pole and can be
calculated by:
1
f P 1 = -----------------------------------
The zero is a ESR zero due to the output capacitor and
its ESR. It is can be calculated by:
1
f Z 1 = ------------------------------------------------
where;
C O is the output filter capacitor,
R L is load resistor value, and
ESR CO is the equivalent series resistance of output capacitor.
The RHP zero has the effect of a zero in the gain causing
an imposed +20 dB/decade on the roll off, but has the
effect of a pole in the phase, subtracting 90 o in the
phase. The RHP zero can be calculated by:
-------------------------------------------
The RHP zero obviously can cause the instable issue if
the bandwidth is higher. It is recommended to design the
bandwidth to lower than the one half frequency of RHP
zero.
The compensation design is actually to shape the
converter close loop transfer function to get desired gain
and phase. Several different types of compensation
network can be used for AOZ1977. For most cases, a
series capacitor and resistor network connected to the
COMP pin sets the pole-zero and is adequate for a stable
high-bandwidth control loop.
In the AOZ1977, FB pin and COMP pin are the inverting
input and the output of internal transconductance error
amplifier. A series R and C compensation network
connected to COMP provides one pole and one zero.
The pole is:
G EA
f P 2 = -------------------------------------------
where;
G EA is the error amplifier transconductance, which is
200 x 10 -6 A/V,
G VEA is the error amplifier voltage gain, which is 1000 V/V, and
C C is the compensation capacitor.
The zero given by the external compensation network,
capacitor C C and resistor R C is located at:
1
f Z 2 = -----------------------------------
Choosing the suitable C C and R C by trading-off stability
and bandwidth.
Rev. 2.1 May 2012
www.aosmd.com
Page 12 of 16
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