|
MIC2168_05 Datasheet, PDF (11/14 Pages) Micrel Semiconductor – 1MHz PWM Synchronous Buck Control IC | |||
|
◁ |
MIC2168
30 30
Micrel, Inc.
00
7.5
50
15
100
37.5
60 60
100
100
1.103
1 .104
f
1 .105
1 .106
1000000
Figure 4. The Gain Curve for G(s)
00
50
100
150
180
100
100
1.103
1 .104
f
1 .105
1 .106
1000000
Figure 5. Phase Curve for G(s)
It can be seen from the transfer function G(s) and the gain
curve that the output inductor and capacitor create a two pole
system with a break frequency at:
fC =
1
2 Ã Ï â L Ã COUT
Therefore, fLC = 3.6kHz
By looking at the phase curve, it can be seen that the output
capacitor ESR (0.050â¦) cancels one of the two poles (LCOUT)
system by introducing a zero at:
fZERO =
1
2 Ã Ï Ã ESR Ã COUT
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 0.002â¦.
150
180
100
100
1.103
1 .104
f
1 .105
1 .106
1000000
Figure 6. The Phase Curve with ESR = 0.002â¦
It can be seen from Figure 5 that at 50kHz, the phase is
approximately â90° versus Figure 6 where the number is
â150°. This means that the transconductance error ampli-
ï¬er 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
RC and C2 compensation scheme allows a maximum error
ampliï¬er phase boost of about 90°. Therefore, it is easier to
stabilize the MIC2168 voltage control loop by using high ESR
value output capacitors.
gm Error Ampliï¬er
It is undesirable to have high error ampliï¬er 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 ampliï¬er gain
should be allowed to increase rapidly at low frequencies.
The transfer function with R1, C1, and C2 for the internal
gm error ampliï¬er can be approximated by the following
equation:
Error Amplifier (z) - gm Ã
1+ R1 Ã S Ã C1
s
Ã
(C1
+

C2)ï£ï£¬1
+
R1
Ã
C1 Ã
C1
C2 Ã
+ C2
S

The above equation can be simplified by assuming
C2<<C1,
Error Amplifier (z)
-
gm
Ã
 1+ R1 à S à C1
ï£ï£¬ s à (C1)(1+ R1 à C2 à S)


From the above transfer function, one can see that R1 and
C1 introduce a zero and R1 and C2 a pole at the following
frequencies:
Fzero= 1/2 Ï Ã R1 Ã C1
Fpole = 1/2 Ï Ã C2 Ã R1
Fpole@origin = 1/2 Ï Ã C1
Figures 7 and 8 show the gain and phase curves for the above
transfer function with R1 = 9.3k, C1 = 1000pF, C2 = 100pF,
and gm = .005â¦â1. It can be seen that at 50kHz, the error
ampliï¬er exhibits approximately 45° of phase margin.
April 2005
11
M9999-040805
|
▷ |