MIC2155 Datasheet, PDF (30/33 Pages) Micrel Semiconductor – 2-Phase, Single Output, PWM Synchronous Buck Control IC

Micrel, Inc.
MIC2155/2156
Channel 2
Transconductance E/A
RZ1
CZ1
Ramp
Modulator
V_IN
Q1
Driver
Q2
Filter
R2
C2
R_L2
L2
Channel 1 I_L
R_L1
L1
R1
C1
C_O
Figure 27. Current Sharing Loop and Transfer Functions
Unlike the voltage output amplifier used for Channel 1
compensation, a transconductance amplifier is used for
the Channel 2 compensation since only a pole/zero
combination is required for compensation. The
transconductance amplifier transfer function is:
Gea(s) = gm × ^{1+ s × Rz1× Cz1}
s × Cz1
where:
Rz1 and Cz1 are the external components connected to
the COMP2 pin
gm is the transconductance of the internal amplifier.
The pole and zero frequencies are:
f_POLE
=
2×
gm
π × Cz1
f_ZERO
=
1
2 × π × Rz1× Cz1
The gain of the modulator is:
g_MOD
=
1
V_M
where V_M is the peak-to-peak amplitude of
the internal sawtooth.
The gain of the feedback circuit is output current divide
by V_EA
H = R_L2
The filter transfer function is the output current over the
applied voltage
G_FILTER(s)
=
V_IN − V_OUT
s ×L2
The open loop transfer function is:
G_OL2(s) = G_EA(s) × G_MOD × H × G_FILTER(s) =
gm × (1+ s ×Rz1× Cz1)× R_L2 × (V_IN − V_OUT )
(s × Cz1)× Vm × (s ×L2)
The loop is inherently stable because the phase shift is
only 90 degrees. The error amplifier pole and zero is
selected to achieve a desired crossover frequency. In
this example, the desired crossover frequency is 50kHz.
The transfer function of the filter, modulator and
feedback is plotted in Figure 28.
50
V_IN = 12V
V_OUT = 1.8V
L = 1.5µH
0
Gain
-50
Phase
-100
10
100 1k 10k 100k 1M
FREQUENCY
Figure 28. Current Sharing Loop Gain/Phase
May 2009
30
M9999-052709-A
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