MIC2155_0911 Datasheet, PDF (29/35 Pages) Micrel Semiconductor – Two-Phase, Single-Output, PWM Synchronous Buck Control IC

Micrel, Inc.
The Modulator Gain is proportional to the input voltage
and inversely proportional to the internal ramp voltage
generated by the oscillator. The MIC2155/6 peak-peak
ramp voltage is 1V:
G_MOD
=
⎜⎜⎝⎛
V_IN
V_RAMP
⎟⎟⎠⎞
The output voltage divider attenuates V_OUT and feeds it
back to the error amplifier. The divider gain is:
H = ^R4 = ^VREF
R1+ R4 V_OUT
The modulator, filter and voltage divider gains can be
multiplied together to show the open loop gain of these
parts:
G_VD(s) = G_FILTER (s) × H× G_MOD
This transfer function is plotted in Figure 25. At low
frequency, the transfer function gain equals the
modulator gain times the voltage divider gain. As the
frequency increases toward the LC filter resonant
frequency, the gain starts to peak. The increase in the
gain’s amplitude equals Q. Just above the resonant
frequency, the gain drops at a -40db/decade rate. The
phase quickly drops from 0° to almost 180° before the
phase boost of the zero brings it back up to -90°. Higher
values of Q will cause the phase to drop quickly. In a
well damped, low Q system the phase will change more
slowly.
90
45
0
Gain
-45
Phase
-90
-135
-180
10 100 1k 10k 100k 1M
FREQUENCY
Figure 25. G_VD Transfer Function
MIC2155/2156
As the frequency approaches the zero frequency (Fz),
formed by Co and it’s ESR, the slope of the gain curve
changes from -40db/dec. to -20db/dec and the phase
increases. The zero causes a 90° phase boost. Ceramic
capacitors, with their smaller values of capacitance and
ESR, push the zero and its phase boost out to higher
frequencies, which allow the phase lag from the LC filter
to drop closer to -180°. The system will be close to being
unstable if the overall open loop gain crosses 0dB while
the phase is close to -180°. If the output capacitance
and/or ESR is high, the zero moves lower in frequency
and helps to boost the phase, leading to a more stable
system.
The error amplifier is a type III which has two zeros, two
poles and a pole at the origin. This type of error amplifier
works well when Ceramic output capacitors make up the
majority of C_OUT because it introduces an extra zero that
helps improve phase margin:
Gea(s) =
⎜⎛1 +
⎝
ω^{sz1 ⎟⎠⎞⎜⎝⎛1 +}
s
ωz2
⎟⎞
⎠
s
ωpo
⎜⎜⎝⎛^{1 +}
ω^{sp1 ⎟⎟⎠⎞⎜⎜⎝⎛1 +}
s
ωp2
⎟⎟⎠⎞
Where:
ωz1 = ¹
R2 × C2
ωz2 =
1
(R1+ R3) ⋅ C3
ωpo = ¹
R1× C1
ωp1 =
1
C1× C2
⋅ R2
C1+ C2
ωp2 = ¹
R3 × C3
Figure 26 shows the bode plot of the error amplifier
transfer function.
November 2009
29
M9999-111209-B