MIC2169A Datasheet, PDF (11/17 Pages) Micrel Semiconductor – 500kHz PWM Synchronous Buck Control IC

MIC2169A
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:
f_LC  _{2  }
1
L  C_OUT
Therefore, f_LC = 3.6kHz
By looking at the phase curve, it can be seen that the output
capacitor ESR (0.050Ω) cancels one of the two poles (LC_OUT)
system by introducing a zero at:
f_ZERO

2


1
 ESR

C_OUT
Therefore, F_ZERO = 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.
00
Micrel
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.
The transfer function with R1, C1, and C2 for the internal
g_m error amplifier can be approximated by the following
equation:


Error Amplifier(z)

g_m





s

C1

1 R1  S 
C2 ^{}1 R1
C1
C1 C2 
C1 C2
S





The above equation can be simplified by assuming
C2<<C1,
Error Amplifier(z)

g_m




s

1 R1  S 
C11 R1
C1
C2

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 π × R1 × C1
Fpole = ¹/₂ π × C2 × R1
Fpole@origin = ¹/₂ π × 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 g_m = .005Ω^–1. It can be seen that at 50kHz, the error
amplifier exhibits approximately 45° of phase margin.
60 ⁶⁰
50
40
100
150
180
100
100
1.10³
1 ^.104
f
1 ^.105
1 ^.106
1000000
Figure 6. The Phase Curve with ESR = 0.002Ω
It can be seen from Figure 5 that at 50kHz, the phase is
approximately –90° versus Figure 6 where the number is
–150°. This means that the transconductance error ampli-
fier 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
amplifier phase boost of about 90°. Therefore, it is easier to
June 2005
11
20
.001
1 ^.103
1000
1 ^.104
1 ^.105
f
1 ^.106
1 ^.107
10000000
Figure 7. Error Amplifier Gain Curve
M9999-111803