MIC2159 Datasheet, PDF (12/17 Pages) Micrel Semiconductor – SYNCHRONOUS-itty™ Step-Down Converter IC

Micrel
connected to the output capacitor, COUT, with its
electrical series resistance (ESR) as shown in Figure 3.
The transfer function G(s), for such a system is:
Figure 3. The Output LC Filter in a voltage Mode Buck
Converter
G(s)=
s(DCR⋅
1+ESR⋅ s⋅C_OUT
C_OUT+ESR⋅C_OUT) +s²(L
⋅
C_OUT)
+
1
Plotting this transfer function with the following assumed
values (L=2 µH, DCR=0.009Ω, COUT=1000µF,
ESR=0.050Ω) gives lot of insight as to why one needs to
compensate the loop by adding resistor and capacitors
on the COMP pin. Figures 4 and 5 show the gain curve
and phase curve for the above transfer function.
MIC2159
gain curve that the output inductor and capacitor create
a two pole system with a break frequency at:
f_LC = _{2⋅π â‹}
1
L⋅C_OUT
Therefore, fLC = 3.6kHz
By looking at the phase curve, it can be seen that the
output capacitor ESR (0.050Ω) cancels one of the two
system poles (LCOUT) by introducing a zero at:
f_ZERO=
2⋅π
⋅
1
ESR⋅C_OUT
Therefore, FZERO = 6.36kHz.
From the point of view of compensating the voltage loop,
it is recommended to use higher ESR output capacitors
since they provide a 90° phase gain in the power path.
For comparison purposes, Figure 6, shows the same
phase curve with an ESR value of 0.002Ω.
Figure 4. The Gain Curve for G(s)
Figure 5. Phase Curve for G(s)
It can be seen from the transfer function G(s) and the
October 2006
Figure 6. The Phase Curve with ESR = 0.002Ω
It can be seen from Figure 5 that at 50 kHz, the phase is
approximately –90° versus Figure 6 where the number is
–150°. This means that the transconductance error
amplifier has to provide a phase boost of about 45° to
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.
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M9999-101206