MIC2168A Datasheet, PDF (15/18 Pages) Micrel Semiconductor – 1MHz PWM Synchronous Buck Control IC

Micrel
The transfer function with R1, C1, and C2 for the
internal g_m error amplifier can be approximated by the
following equation:
⎡
⎤
Error
Amplifier(s)
=
gm
×
⎢
⎢
⎢
⎢⎣ ^s
×
(C1 +
1 + R1× S ×
C2)_⎜⎛1 + R1×
⎝
C1
C1× C2 × S
C1 + C2
⎥
⎥
⎟⎞
⎠
⎥
⎥⎦
MIC2168A
The above equation can be simplified by assuming
C2<<C1,
Error
Amplifier(s)
=
gm
×
⎜⎛
⎝
s
×
1 + R1× S ×
(C1)(1 + R1×
C1
C2
×
S)
⎟⎞
⎠
Figure 7. Error Amplifier Gain Curve
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:
1
F_ZERO =
2 × π × R1× C1
1
F_POLE =
2 × π × C2 × R1
1
F_POLE @origin =
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 gm = .005Ω^–1. It can be seen that at
50kHz, the error amplifier exhibits approximately 45° of
phase margin.
Figure 8. Error Amplifier Phase Curve
Total Open-Loop Response
The open-loop response for the MIC2168A controller is
easily obtained by adding the power path and the error
amplifier gains together, since they already are in Log
scale. It is desirable to have the gain curve intersect
zero dB at tens of kilohertz, this is commonly called
crossover frequency; the phase margin at crossover
frequency should be at least 45°. Phase margins of 30°
or less cause the power supply to have substantial
ringing when subjected to transients, and have little
tolerance for component or environmental variations.
Figures 9 and 10 show the open-loop gain and phase
margin. It can be seen from Figure 9 that the gain curve
intersects the 0dB at approximately 50kHz, and from
Figure 10 that at 50kHz, the phase shows approximately
50° of margin.
January 2010
15
M9999-011510