AN1262 APPLICATION NOTE

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The transfer function G2(j

ω) of the plant is defined by the control method (voltage mode), the topology of the

converter (flyback) and its operating mode (DCM in the specific case). The task of the control loop design is then

to determine the transfer function G1(j

ω) of the error amplifier and define the relevant frequency compensation

network. The objective of the design is to ensure that the resulting closed-loop system will be stable and well

performing in terms of dynamic response, line and load regulation.

The characteristics of the closed-loop system can be inferred from its open-loop properties. Provided the open-

stability criterion.

Anyway, adequate margin to this boundary condition must be provided to prevent instability due to parameter

variations and to optimize the dynamic response that would be severely underdamped otherwise. Under worst

case condition this "phase margin"

tions is used as a design guideline: this ensures fast transient response with very little ringing. Sometimes a

higher margin (up to 60° or 75°) is required to account for very large spreads in line, load and temperature

changes as well as manufacturing tolerances.

mended because it would result in a conditionally stable system. A reduction of the gain (which may temporarily

happen during large load transients) would cause the system to oscillate, therefore the phase shift should not

as high as possible (

Good load and line regulation implies a high DC gain, thus the open loop gain should have a pole at the origin.

In this way the theoretical DC gain would tend to infinity, whereas the real-world one will be limited by the low-

frequency gain of the Error Amplifier. Since voltage mode control has poor open-loop line regulation, the overall

gain should be still high also at frequencies around 100-120 Hz to maximize rejection of the input voltage ripple.

This is related to phase margin: a higher phase margin leads to a lower low-frequency gain.

Once the goal of the design has been established in terms of crossover frequency and phase margin, the next

step is to determine the transfer function of the plant G2(j

ω) in order to select an appropriate structure for G1(jω).

The transfer function G2(j

ω) of the plant is described in Tab. 15, while its asymptotic Bode plot is illustrated in

Fig.10.

alent load resistor.

This kind of plant will be stabilized in closed-loop operation by what is commonly known as a Type 2 amplifier.

Its transfer function G1(j

ω), which comprises a pole at the origin and a zero-pole pair, is defined as:

Its asymptotic Bode plot is illustrated in Fig. 11.

The main task of this correction is to boost the phase of the overall loop (actually, to reduce the phase lag of

G2(j

ω)) in the neighborhood of the crossover frequency.

G1 j

ω

()

G1

0

j

ω

-----------

1

j

ω

ω

Z

-------

+

1

j

ω

ω

P

-------

+

-----------------

⋅

=