MIC2155 Datasheet, PDF (29/33 Pages) Micrel Semiconductor – 2-Phase, Single Output, PWM Synchronous Buck Control IC

Micrel, Inc.
Step 3: Determine the gain boost needed at the
crossover frequency (fc)
Typically, 50° of phase margin can be used for most
applications. This is a good tradeoff between an
overdamped system (slower response to transients) and
an underdamped system (overshoot or unstable
response to transients). It also allows some margin for
component tolerances and variations due to ambient
temperature changes. The phase margin at the
crossover frequency (fc) can be determined by plotting
the Gvd(s) phase on a bode plot or can be estimated
with the following formula:
⎡
⎢
fc
⎤
⎥
ϕ_M
=
tan^−1_{⎢⎢⎢⎢⎣1−}^Q_{⎜⎝⎛×ffocfo⎟⎠⎞2}
⎥
⎥
⎥
⎥⎦
+
tan^−1_{⎢⎣⎡}
fc
fz
⎤
⎥⎦
The additional phase boost required from the error
amplifier is:
ϕ_Boost = 52° − ϕ_M
Step 4: Determine the frequencies fz2 and fp1
The frequencies for the zero and pole (fz2 and fp1) are
calculated for the desired amount of phase boost at the
crossover frequency (fc).
fz2 = fc ×
1− [ sin ϕ_Boost ]
1+ [ sin ϕ_Boost ]
fp1 = fc ×
1+ [ sin ϕ_Boost ]
1− [ sin ϕ_Boost ]
Step 5: Determine the frequency for fz1
The low frequency zero, fz1, is initially set to one-fifth of
the LC resonant frequency. If it is set too low, it will force
the low frequency gain to be low and impact transient
response. If set too high, it will not add enough phase
boost at the LC resonant frequency. This could cause
conditional stability, which when the phase drops below -
180° before the gain crosses 0dB. If the DC gain should
drop in this situation, this may lead to an unstable
system.
fz2 = ^fo
5
Step 6: Determine the frequency for fp2
This is the high frequency pole, which is useful in
additional attenuation of the switching frequency. It
should initially be set at half of the switching frequency. If
it is set too low, it will lower the phase margin at the
crossover frequency, making it difficult to achieve the
MIC2155/2156
proper phase margin. If set too high, it will not provide
attenuation of the switching frequency, which could lead
to jitter of the switching waveform or instability under
certain conditions.
fp2 = ^fs
2
Calculating Error Amplifier Component Values
Once the pole and zero frequencies have been fixed, the
error amplifier’s resistor and capacitor values are
calculated.
R1 This value is chosen first. All other component values
are calculated from R1. A value of 10K is suggested. If
R1 is chosen too high, R2 may be very large and the
high impedances could be sensitive to noise. If the
remote sense amplifier is used, R1 must be large
enough so than not more than 500µA of current is drawn
from the amplifier.
R2 The value of R2 is determined from the mid-band
gain of the error amplifier. This gain depends on the
frequencies of the poles, zeros and LC filter resonant
frequency. Based on the amount of gain necessary at
the crossover frequency the mid-band gain and R2 value
is calculated using the following formula.
G_CO
=
Vm
H× Vin
× ⎜⎛
⎝
fo _⎟⎞²
fc _⎠
× ⎜⎛
⎝
fc
fz
⎟⎞ ×
⎠
fz2
fp1
R2 = R1× G_CO
The other component values are calculated as follows:
C2 =
1
2 × π × fz1× R2
C3 =
1
2 × π × fz2 ×R1
C3 =
C2
2 × π × (fp1× C2 × R2 − 1)
R3 =
1
2 × π × fp2 × C3
Compensation of the Current Sharing Loop
The control circuitry for Channel 2 forces the channel’s
output current to match the current in Channel 1. The
Channel 2 error amplifier compares the inductor currents
in the two channels and adjusts the duty cycle of
Channel 2 to control its output current. A block diagram
is shown in Figure 27.
May 2009
29
M9999-052709-A
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