MIC2124 Datasheet, PDF (15/24 Pages) Micrel Semiconductor – Constant Frequency, Synchronous Current Mode Buck Controller

Micrel, Inc.
Feedback Loop Compensation
The MIC2124 controller comes with an internal error
amplifier used for optimizing control loop stability by
placing a capacitor C1 in series with a resistor R1 and
another capacitor C2 in parallel from the COMP pin to
ground.
Figure 6. Loop Compensation
a. Power Stage
The adaptive on-time current mode control applied in
MIC2124 controller eliminates the double-pole in the
power stage, which is caused by the output inductor and
output capacitor. At the frequency range which is far
below the switching frequency (f < f_SW/6), the transfer
function from the output of the error amplifier to the buck
converter output can be approximated by the following
equation:
G(s)_con
≈ G_C
× ^{1 + s × COUT}
1+
× ESR _COUT
s
(29)
ϖ_p
where:
G_C
= ^RLOAD
Ri
×
1+
1
R_LOAD
×^D
f_SW × L 2
ϖ_p
=
C _OUT
1
× R_LOAD
+
f_SW
1
× L × C_OUT
×^D
2
C_OUT = total output capacitors
ESR_COUT = electrical series resistance of the output
capacitor
R_LOAD = load resistance
Ri = 2.4 x Rds(on)_bottom (low-side MOSFET Rds(on))
f_SW = switching frequency
L = inductance of the output inductor
D = duty cycle
According to equation (29), there is a pole and zero pair
set by the load resistance R_LOAD, the output capacitor,
June 2010
MIC2124
and the output inductor in the power stage:
f _z(con)
=
1
2π × C_OUT × ESR _COUT
(30)
f_p(con)
=
1 _×(
2π C_OUT
1
× R_LOAD
+
f_SW
1
× L × C_OUT
× ^D)
2
(31)
Therefore, type II compensation, which is comprised by
C1, R1 and C2, is able to achieve a stabilized loop for
MIC2124 in most applications.
b. g_m Error Amplifier
It is undesirable to have high error amplifier gain at high
frequencies because high frequency noise spikes would
be picked up and transmitted at large amplitude to the
output; thus, gain should be permitted to fall off at high
frequencies. At low frequency, it is desired to have high
open-loop gain to attenuate the power line ripple. Thus,
the error amplifier gain should be allowed to increase
rapidly at low frequencies.
The transfer function with R1, C1, and C2 for the internal
g_m error amplifier can be expressed as:
⎡
⎤
G(s)_err
=
g_m
×
⎢
⎢
⎢
⎢
s
×
⎣
(C1 +
1 + s × R1× C1
C2) × ⎜⎛1 + s × R1×
⎝
C1×
C1 +
⎥
⎥
C2
C2
⎟⎞
⎠
⎥
⎥
⎦
(32)
One pole and one zero can be seen from the above
transfer function at the following frequencies:
f _{z( err )}
=
1
2π × R1× C1
(33)
f _{p( err )}
=
1
2π × R1× ^{C1× C2}
(34)
C1 + C2
c. Total Open-Loop Response
The open-loop response for the MIC2124 controller is
easily obtained by combining the power stage, the
feedback resistor divider, and the error amplifier gains
together.
G(s) _total
=
R_FB2
R_FB1 + R_FB2
× G(s)_con × G(s)_err
(35)
where R_FB1 and R_FB2 are the voltage divider resistors, as
shown in the typical application schematic on Page 1.
It is desirable to have the gain curve intersect zero dB at
tens of kilohertz, this is commonly called crossover
frequency; the phase margin at crossover frequency
should be at least 45°.
12V to 1.8V @ 10A application is applied as an example
to demonstrate the loop compensation for MIC2124. In
this application:
15
M9999-060810-D