DF06M View Datasheet(PDF) - STMicroelectronics
Part Name
Description
MFG CO.
'DF06M' PDF : 42 Pages View PDF
AN1262 APPLICATION NOTE
The transfer function G2(jω) 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(jω) 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-
loop gain crosses the 0 dB axis only once at f= fc (crossover frequency), stability will be ensured if the gain phase
shift (besides the 180° due to negative feedback) is less than 180° at f = fc. This is the well-known Nyquist's
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" Φm should never go below 20 or 30°. Typically, Φm = 45° in nominal condi-
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.
Although Nyquist's criterion allows the phase shift to be over 180° at a frequency below fc, this is not recom-
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
get close to 180° at any frequency below fc.
Optimum dynamic performance requires a large gain bandwidth, that is the crossover frequency fc to be pushed
as high as possible (≤ fsw/4). When optimum dynamic performance is not a concern, fc will be typically chosen
equal to fsw/10.
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(jω) in order to select an appropriate structure for G1(jω).
The transfer function G2(jω) of the plant is described in Tab. 15, while its asymptotic Bode plot is illustrated in
Fig.10.
In G20 definition the ratio Dmax/Vs is the PWM modulator gain, while Dmax = 0.7 is the maximum duty cycle and
Vs = (3.5-1.5) = 2 V is the oscillator peak-to-valley swing (see the relevant section). Rout = Vout/Iout is the equiv-
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(jω), which comprises a pole at the origin and a zero-pole pair, is defined as:
G1 (jω) = -G--j--ω-1---0- ⋅ -11----++-------ωω-jj------ωω------PZ---
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(jω)) in the neighborhood of the crossover frequency.
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