AN1059 datasheet(14/20 Pages) STMICROELECTRONICS

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The pole is placed at a very low frequency so that the gain at twice line frequency is quite less than

unity, while the zero boosts the phase in the neighbourhood of the open-loop crossover frequency so as

to provide phase margin.

A variation

∆VCOMP, due to a line and/or load change, modifies the amplitude Vcx of the rectified sinusoid

at the output of the multiplier. This considering, the transfer function of the multiplier block will be:

∆Vcx

∆VCOMP

= KM ⋅ KP ⋅ VPK

where KM is the gain of the multiplier (= 0.75 max.).

The gain of the PWM modulator, which includes the current loop, is simply:

∆IPKp

∆Vcx

where Rs is the sense resistor.

Small-Signal analysis shows that the gain G4(s) of the power stage is:

(s) =

∆Vout

∆IPKp

⋅ Kv ⋅ F2(Kv)

Γ(Kv) + 1

⋅

+ s ⋅ (Co ⋅ ESR)

+ s ⋅ (Co ⋅

Γ(Kv) + 1

)

where the function

Γ(x) is defined as follows:

Γ(x) = 1 +

(x)

⋅

dF2

(x)

≈

+ 0.01 ⋅ x

+ 0.8 ⋅ x

The feedback network can have different configurations, depending on the requirements on the toler-

ance and on the regulation of the output voltage.

In this context a popular configuration (see fig. 15) will be taken into consideration. It uses an optocou-

pler for galvanic isolation between primary and secondary and a TL431, a cheap voltage reference/op-

amp housed in a three pin package.

The gain, H(s), at twice line frequency must be low. In fact, being the output voltage ripple quite high, a

high gain could saturate the dynamics of the TL431 and/or of the optocoupler, besides complicating

things in getting a narrow overall bandwidth.

Referring to fig. 15, it is possible to write:

(s) =

∆VE

∆Vout

⋅

⋅ R6

+ R6

⋅ CTR ⋅

+ s ⋅ C1 ⋅ (R1 + R3)

⋅ (C1 ⋅ R1)

where CTR is the Current Transfer Ratio of the optocoupler.

When designing the control loop, first select the operating current of optocoupler’s transistor (IC). It is ad-

vantageous to selects a low IC value (e.g. 1 mA): this will not only extend the lifetime of the device but, in

the present case, will also help keep low the gain of the feedback network at twice line frequency.

Since in closed-loop operation the quiescent value of VE will be in the neighbourhood of 2.5V (internal

reference of the L6561 E/A), R5 will be:

2.5

R4 will be selected so as to maintain VK voltage above 2.5V for a correct functionality of the TL431 even

in the worst case, that is when the optocoupler exhibits its minimum CTR, because of the statistical

spread of this parameter.

AN1059 APPLICATION NOTE

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