AN2644 datasheet(43/64 Pages) STMICROELECTRONICS

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AN2644

The LLC resonant half-bridge converter

43/64

operation, here only a qualitative description will be given, which is the result of a

characterization by simulation [7] (refer to Section 4).

As stated many times, the operating frequency is the parameter that allows regulation of the

input-to-output energy flow. The control-to-output transfer function G(j

ω) that characterizes

the small-signal behavior of the LLC resonant converter will then be defined as:

Equation 17

In the overall converter's dynamics it is convenient to separate the contribution of the

"inverter" part and that of the rectifying and filtering block that transforms the inverter in a

converter. This is quite a useful concept of superposition because it gives considerable

physical insight. Regardless of the operating mode of the inverter and, then, of its

contribution to converter's dynamics, the rectifying and filtering block always introduces a

low frequency pole associated to the output capacitor, the load resistance and the open-

loop output impedance Zo0 of the resonant tank, plus a zero due to the output capacitor and

its ESR (equivalent series resistor). This pole moves with the load (frequency is higher at

heavy load, lower at light load) because of the changes in Zo0, while the zero is at an

essentially fixed frequency, exactly like in PWM converters.

Different types of dynamic behavior, corresponding to different pole distributions of G(j

ω),

can be observed depending on the operating mode. Again we will consider operation at,

above and below resonance.

2.8.1

Operation above resonance (f > fR1)

In this operating mode the converter features a special characteristic typical of resonant

converters, the so-called "beat frequency double pole", i.e. two complex and conjugate

poles having their imaginary part at the difference between the switching frequency f and

the resonant frequency fR1. In addition to this double pole, contributed by the inverter part,

there is the pole-zero pair associated to the output filter. If f is significantly higher than fR1,

the system can be regarded as a single-pole system.

As switching frequency moves close to resonant frequency, the beat frequency double pole

will move to lower frequency. When the switching frequency is very close to resonant

frequency, the beat frequency double pole will eventually split and become two real poles.

One moves to higher frequencies and the other moves to lower frequencies as switching

frequency gets closer and closer to resonant frequency. Finally, the split pole moving to low

frequency will merge with the low frequency pole caused by the output filter and form a

double pole. This type of characteristic is very similar to that of the conventional series LC

converter.

Provided the converter is not operating too close to resonance, as long as it runs in CCM,

the pole distribution tends not to change significantly. In DCM operation, instead, the beat

frequency double pole will more pronouncedly move to higher frequencies and the low

frequency pole to lower frequencies. At light load, the converter can then be regarded as a

single-pole system.

Concerning how the resonant tank characteristics affect the small-signal behavior, the

parallel inductor Lp has no practical effect. Conversely, increasing the impedance of the

resonant tank (i.e. increasing Ls and reducing Cr while keeping the same fR1), the DC gain

will increase. Also the low frequency pole changes with the resonant tank impedance (it

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