MIC2131 datasheet(17/20 Pages) MICREL

17 / 20 page

Micrel, Inc.

MIC2130/1

April 2008

M9999-042108-C

Example:

VIN = 24V; VOUT = 3.3V; IOUT = 10A; L = 7.3µH; COUT =

660µF; Resr = 40mΩ; Fsw = 150KHz

The gain and phase of the modulator and filter is:

GMod(s) x Gflt(s)

This is the gain

comp

OUT

(s) in Figure 12

A computer generated plot of GMod(s) x Gflt(s) is shown in

Figure 12.

Figure 12. Modulator Transfer Function

There is a -180° phase change near F0. At frequencies

greater then F0 the phase increases towards -90° due to

the zero of Fesr. The phase effects of poles and zeros

start a decade below and finish a decade above the

frequency of a pole or zero. Therefore, at the frequency

of a pole or zero the phase effect is only half of the final

value. At the complex pole 2.3kHz the phase is -90 and

would be -180 at 23kHz if not for the +90 phase lead of

the zero at around 6kHz due to the esr of the filter

capacitors. (Actually, the phase gain plots reach their

final values asymptotically).

By inspecting Figure 12 the DC and low frequency gain

of GMod = 20Log(0.85 x 24) = 26.2db; F0 = 2.3kHz; Fesr =

6kHz and Q is 13.6db.

The peak Gain equals the low freq gain plus the Q =

26.2 + 13.6 = 39.9db.

It is desired that T(s) (the open loop transfer function)

have a cross over frequency (Fco) of 1/10 the Switching

frequency at 15kHz. It is require that

πFco)

T(j2

∠

(the

phase of T(s) at Fco), to be greater than -180° by at

least the phase margin. By inspecting the Gain plot of

GMod(s) at 15kHz, GMod(s) has a gain of about 3.9db.

Therefore, to make T(j2πFco) = 1→ 0db;

T(s) = Gea(s) x GMod(s) x Hfb(s) = 1 at Fco

Hfb = Vref/Vout = 0.7/3.3 = 0.212 → -13.5db

|Gea|db = |T|db - |GMod|db -|Hfb|db = 0-3.9db – (-13.5db) =

9.6db ═>3.02 The error amp needs 9db of gain at Fco.

Therefore gm x ZComp = 3.02 at 15kHz.

The location of the error amp’s zero and poles are

selected in order to achieve the desired phase margin of

T(s). For the maximum phase boost at the cross over

Frequency (Fco), place the first Zero1 of the EA at

Fco/10 since the effect of its phase boost will be at the

maximum at Fco. Likewise, place the pole of the EA at

least 10 x Fco so the effects of its phase lag will be at a

minimum at Fco. Therefore, use R1 = 2k; C1 = 0.068µF;

C2 = 470pF.

gm Error Amplifier

Usually, it is undesirable to have high error amplifier gain

at high frequencies otherwise high frequency noise

spikes at large amplitude would be present at the output.

Hence, 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 for the internal gm error amplifier

with R1, C1, and C2 at the comp pin is given by the

following equation:

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

⋅

)

(

)

(

The above equation can be simplified by assuming

C2<C1,

()⎥⎦

⎤

⎢

⎣

⎡

⋅

)

(

)

(

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:

Fzero1= 1/2 π × R1 × C1 Fpole1 = 1/2 π × C2 × R1

Fpole@origin = 1/2 π × C1

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