AN2644 datasheet(44/64 Pages) STMICROELECTRONICS

44 / 64 page

The LLC resonant half-bridge converter

AN2644

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gets higher at low impedance). In fact, the low frequency pole is not determined by the load

resistor alone but by the output impedance of the tank circuit as well.

2.8.2

Operation below resonance (fR2 < f < fR1, R>Rcrit)

In this operating mode the converter's dynamics changes considerably. In the left half-plane,

there are three poles and one zero but no beat frequency double pole. The pole distribution

is quite insensitive to switching frequency as compared to that in the above resonance

operation. The pole that in the above resonance operation was moving to higher frequency

when switching frequency was approaching resonance here moves back to lower

frequencies as switching frequency is further reduced going away from resonance. Its

position, however does not change much. The low-frequency double pole is minimally

affected too.

A Right Half Plane Zero (RHPZ) can be observed that moves with switching frequency but,

fortunately, it stays typically away from the low frequency region of interest in the design of

the feedback loop.

Approaching capacitive region, beat frequency dynamics tends to appear again. The phase

has an abrupt 180º shift just beyond the capacitive region threshold (feedback from negative

turns into positive).

Starting from heavy load conditions, at first the Q associated to the low frequency double

pole decreases. The RHPZ shifts to higher frequencies and leaves the stage. Further

reducing the load, the Q of the low frequency double pole increases. At very light load the

low frequency double pole splits, one moves to higher frequencies and the other to lower

frequencies. Again, at very light load the converter can be regarded as a single-pole system.

Unlike in the above resonance operation, in this case the parallel inductor Lp has a

considerable impact on the DC gain of the converter. Additionally, it affects the RHPZ as

well. Larger values for Lp tends to shift it to lower frequencies. As far as the impedance of

the resonant tank is concerned, the effect is the same as in the above resonance operation.

2.8.3

Operation at resonance (f = fR1)

Operation at resonance can be regarded as the borderline between the two previously

considered operating modes. The behavior will not be different from that seen just above

(and just below) resonance: two low-frequency poles, one high-frequency pole and the ESR

zero. The same behavior can be seen as far as load dependence is concerned.

The compensation of the error amplifier must consider the different types of small-signal

behavior that the converter can exhibit, especially if it is designed to operate both above and

below resonance. The challenge comes essentially from its second-order behavior exhibited

in its operation close to resonance frequency due to the low frequency double pole. To

properly compensate that, the best option is a type 3 amplifier, i.e. a compensator with one

pole at the origin plus two poles and two zeros at finite frequencies. The pole at the origin

gives excellent load and line regulation characteristics. The two zeros are placed at low

frequency to compensate the double pole of the control-to-output transfer function, by

counteracting their phase lag. The poles are placed to compensate the ESR zero and

provide more attenuation at switching frequency. A practical implementation of this

compensator is shown in Figure 28 along with the relationship between the component

values and its transfer function.

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