
RT8805C
Preliminary
12
DS8805C-03 August 2007
www.richtek.com
LGATE. OCP function monitors both channels, either
one can activate OCP. If the OC protection occurs three
times, OCSD (Over Current Shut Down) will be activated
and shut down the chip.
e. When fault conditions occur or SS < 0.4V, the current
sense function will be disabled.
Power Good
PGOOD goes high when soft-start voltage > 3.7V, and no
fault conditions.
Feedback Loop Compensation
The RT8805C is a voltage mode controller ; the control
loop is a single voltage feedback path including an error
amplifier and PWM comparator. In order to achieve fast
transient response and accurate output regulation, an
adequate compensator design is necessary. The goal of
the compensation network is to provide adequate phase
margin (greater than 45 degrees) and the highest 0dB
crossing frequency. To manipulate loop frequency response
under its gain crosses over 0dB at a slope of -20dB/
decade.
1) Modulator Frequency Equations
RT8805C is a voltage mode buck converter using the high
gain error amplifier with transconductance (OTA,
Operational Transconductance Amplifier), as Figure 6
shown.
The Transconductance:
Δ
V
M
= (EA+) - (EA-) ;
Δ
I
OUT
= E/A output current.
M
OUT
Δ
V
Δ
I
GM
=
Figure 6. OTA Topology
This transfer function of OTA is dominated by a higher DC
gain and the output filter (L
OUT
and C
OUT
) with a double
pole frequency at F
LC
and a zero at F
ESR
. The DC gain of
the modulator is the input voltage (V
IN
) divided by the
peak to peak oscillator voltage V
RAMP
.
OUT
OUT
P(LC)
F
C
L
2
1
×
×
=
π
The next step of compensation design is to calculate the
ESR zero. The ESR zero is contributed by the ESR
associated with the output capacitance. Note that this
requires that the output capacitor should have enough ESR
to satisfy stability requirements. The ESR zero of the
output capacitor expressed as follows :
1
F
OUT
×
×
π
ESR
C
2
Z(ESR)
=
2) Compensation Frequency Equations
The compensation network consists of the error amplifier
and the impedance networks as Figure 7 shown.
Figure 7. Compensation Loop
π
π
×
×
×
×
Z1
P1
F
P2
F
1
F
=
2
R2
C2
= 0
1
=
C1 C2
2
R2
C1+C2
Figure 8 shows the DC-DC converter's gain vs. frequency.
The compensation gain uses external impedance networks
to provide a stable, high bandwidth loop. High crossover
frequency is desirable for fast transient response, but often
jeopardize the system stability. In order to cancel one of
the LC filter poles, place F
Z1
before the LC filter resonant
frequency. In the experience, place F
Z1
at 10% LC filter
resonant frequency. Crossover frequency should be higher
than the ESR zero but less than 1/5 of the switching
frequency. The F
P2
should be place at half the switching
frequency.
The first step is to calculate the complex conjugate poles
contributed by the LC output filter.
The output LC filter introduces a double pole, 40dB/decade
gain slope above its corner resonant frequency, and a total
phase lag of 180 degrees. The resonant frequency of the
LC filter expressed as follows :
V
OUT
R
OUT
GM
EA+
EA-
-
+
+
-
GM
V
REF
V
COMP
C2
R2
C1
R
F
V
OUT
FB
R1