MIC2155 datasheet(27/33 Pages) MICREL

27 / 33 page

Micrel, Inc.

MIC2155/2156

May 2009

M9999-052709-A

(408) 944-0800

E/A

Modulator

Filter

VREF = 0.7V

Driver

VIN

RESR

L1 || L2

Figure 24. Voltage Loop and Transfer Functions

For this analysis, the LC filter in the two phase design is

combined into one. The inductances are in parallel and

the output capacitance is the total sum of all Cout. The

ESR is the parallel combination of all ESRs. The output

load is represented by a resistor R.

The output filter contains a complex double pole formed

by the capacitor and inductor and a zero from the output

capacitor and it’s ESR. The transfer function of the filter

is:

)

(

Gfilter

⎟

⎠

⎞

⎜

⎝

⎛

where:

The Modulator Gain is proportional to the input voltage

and inversely proportional to the internal ramp voltage

generated by the oscillator. The MIC2155/6 peak-peak

ramp voltage is 1V.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

RAMP

MOD

The output voltage divider attenuates VOUT and feeds it

back to the error amplifier. The divider gain is:

OUT

REF

The modulator, filter and voltage divider gains can be

multiplied together to show the open loop gain of these

parts.

MOD

FILTER

)

(

)

(

This transfer function is plotted in Figure 25. At low

frequency, the transfer function gain equals the

modulator gain times the voltage divider gain. As the

frequency increases toward the LC filter resonant

frequency, the gain starts to peak. The increase in the

gain’s amplitude equals Q. Just above the resonant

frequency, the gain drops at a -40db/decade rate. The

phase quickly drops from 0° to almost 180° before the

phase boost of the zero brings it back up to -90°. Higher

values of Q will cause the phase to drop quickly. In a

well damped, low Q system the phase will change more

slowly.

-45

-90

-135

-180

FREQUENCY

100

10k 100k

Gain

Phase

Figure 25. GVD Transfer Function

As the frequency approaches the zero frequency (Fz),

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