MIC2155_0911 Datasheet, PDF (30/35 Pages) Micrel Semiconductor – Two-Phase, Single-Output, PWM Synchronous Buck Control IC

Micrel, Inc.
Z2
1
Z0 =
1
2^{.π .}( R1 R3) ^.C3
2 ⋅ π ⋅ R1⋅ C2
P1
1
2^{.π . C2.C1}
._R2
C2 C1
20^.log ^R2
R1
Z1
1
2^{.π .}R2^.C2
P2
1
2^{.π .}R3^.C3
MIC2155/2156
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 G_VD(s) phase on a bode plot or can be estimated
with the following formula:
Figure 26. Type III Error Amplifier Gain/Phase
Error Amplifier Design Procedure
Step 1: Decide on the crossover frequency
To maximize transient response, the open loop
bandwidth should be made reasonably high. Initially, the
bandwidth can be selected to be 1/10 of the output
switching frequency. This may be improved once the
design is built and measurements are made. An initial
bandwidth of 100kHz for the 2155 and 60kHz for the
2156 are good choices.
Step 2: Determine the gain required at the crossover
frequency
G_Boost is how much gain boost is needed so the open
loop transfer function crosses 0dB at the pre-determined
crossover frequency. This can be measured by plotting
the G_VD(s) transfer function or can be estimated with the
following formula:
G_Boost
=
H× V_IN
1
× ⎜⎛ ^fo ⎟⎞² × ⎜⎛ ^fc ⎟⎞
V_{M ⎝} fc _{⎠ ⎝} fz _⎠
Where: fo = LC filter resonant frequency
fc= open loop bandwidth chosen in Step 1
fz = zero formed by C_OUT and its ESR
H = voltage divider attenuation
V_M=amplitude of the internal sawtooth ramp (V_M=1)
V_IN= Input voltage to the power supply
⎡
⎢
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
November 2009
30
M9999-111209-B