MIC2155YML datasheet(30/35 Pages) MICREL

30 / 35 page

Micrel, Inc.

MIC2155/2156

November 2009

M9999-111209-B

. R2

()

C2 C1

. R3

20 log

⋅

Figure 26. Type III Error Amplifier Gain/Phase

Error Amplifier Design Procedure

Step 1: Decide on the crossover frequency

To maximize transient response, the open loop

bandwidth should be made reasonably high. Initially, the

bandwidth can be selected to be 1/10 of the output

switching frequency. This may be improved once the

design is built and measurements are made. An initial

bandwidth of 100kHz for the 2155 and 60kHz for the

2156 are good choices.

Step 2: Determine the gain required at the crossover

frequency

GBoost is how much gain boost is needed so the open

loop transfer function crosses 0dB at the pre-determined

crossover frequency. This can be measured by plotting

the GVD(s) transfer function or can be estimated with the

following formula:

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

Boost

Where: fo = LC filter resonant frequency

fc= open loop bandwidth chosen in Step 1

fz = zero formed by COUT and its ESR

H = voltage divider attenuation

VM=amplitude of the internal sawtooth ramp (VM=1)

VIN= Input voltage to the power supply

Step 3: Determine the gain boost needed at the

crossover frequency (fc)

Typically, 50° of phase margin can be used for most

applications. This is a good tradeoff between an

overdamped system (slower response to transients) and

an underdamped system (overshoot or unstable

response to transients). It also allows some margin for

component tolerances and variations due to ambient

temperature changes. The phase margin at the

crossover frequency (fc) can be determined by plotting

the GVD(s) phase on a bode plot or can be estimated

with the following formula:

⎥⎦

⎤

⎢⎣

⎡

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−

tan

The additional phase boost required from the error

amplifier is:

Boost

−

Step 4: Determine the frequencies fz2 and fp1

The frequencies for the zero and pole (fz2 and fp1) are

calculated for the desired amount of phase boost at the

crossover frequency (fc):

[]

Boost

sin

−

Step 5: Determine the frequency for fz1

The low-frequency zero, fz1, is initially set to one-fifth of

the LC resonant frequency. If it is set too low, it will force

the low frequency gain to be low and impact transient

response. If set too high, it will not add enough phase

boost at the LC resonant frequency. This could cause

conditional stability, which when the phase drops below -

180° before the gain crosses 0dB. If the DC gain should

drop in this situation, this may lead to an unstable

system.

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