MIC2159_09 Datasheet, PDF (13/16 Pages) Micrel Semiconductor – SYNCHRONOUS-itty Step-Down Converter IC

Micrel, Inc.
achieve a closed loop phase margin of 45° at a
crossover frequency of 50kHz for Figure 4, versus 105°
for Figure 6. The simple R1,C1 and C2 compensation
scheme allows a maximum error amplifier phase boost
of about 90°. Therefore, it is easier to stabilize the
MIC2169A voltage control loop by using high ESR value
output capacitors.
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
gm error amplifier can be approximated by the following
equation:
⎡
⎤
Error
_
Amplifier(z)
=
g_m
⋅
⎢
⎢
⎢
⎢
⎣
S
⋅
(C1+
1+ R1⋅ S ⋅ C1
C2)⋅⎜⎛1+R1⋅ ^{C1⋅C2⋅S}
⎝
C1+ C2
⎟⎞
⎠
⎥
⎥
⎥
⎥
⎦
The above equation can be simplified by assuming
C2<<C1,
Error
_ Amplifier
(z)
=
g_m
⋅
⎡
⎢
⎣
S
⋅
1 + R1⋅
(C1) ⋅ (1 +
S ⋅ C1
R1⋅ C2
⋅
⎤
S )^⎥⎦
From the above transfer function, one can see that R1
and C1 introduce a zero and R1 and C2 a pole at the
following frequencies:
F_zero= 1/2 π × R1 × C1
F_pole = 1/2 π × C2 × R1
F_pole@origin = 1/2 π × C1
Figures 7 and 8 show the gain and phase curves for the
above transfer function with R1 = 9.3k, C1 = 1000pF, C2
= 100pF, and gm = .005Ω–1. It can be seen that at 50
kHz, the error amplifier exhibits approximately 45° of
phase margin.
MIC2159
Figure 7. Error Amplifier Gain Curve
Figure 8. Error Amplifier Phase Curve
Total Open-Loop Response
The open-loop response for the MIC2159 controller is
easily obtained by adding the power path and the error
amplifier gains together, since they already are in Log
scale. 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°. Phase margins of 30° or less
cause the power supply to have substantial ringing when
subjected to transients, and have little tolerance for
component or environmental variations.
Figures 9 and 10 show the open-loop gain and phase
margin and it can be seen from Figure 9 that the gain
curve intersects the 0dB at approximately 50kHz, and
from Figure 10 that at 50kHz, the phase shows
approximately 50° of margin.
March 2009
13
M9999-030509-B