MIC2159 datasheet(13/17 Pages) MICREL

13 / 17 page

Micrel

MIC2159

October 2006

M9999-101206

The transfer function with R1, C1, and C2 for the internal

gm error amplifier can be approximated by the following

equation:

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

⋅

Amplifier

Error

)

(

)

(

The above equation can be simplified by assuming

C2<<C1,

()⎥⎦

⎤

⎢

⎣

⎡

⋅

Amplifier

Error

)

(

)

(

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 gm = .005Ω–1. It can be seen that at 50

kHz, the error amplifier exhibits approximately 45° of

phase margin.

Figure 7. Error Amplifier Gain Curve

Figure 8. Error Amplifier Phase Curve

Total Open-Loop Response

The open-loop response for the MIC2159 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 and 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.

Figure 9. Open-Loop Gain Margin

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