AN1059 datasheet(6/20 Pages) STMICROELECTRONICS

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This function, shown in fig. 4a for different values of Kv, is a periodic even function, at twice line fre-

quency, not negative because of the bridge rectifier. Conversely, the current drawn from the mains will

be the "odd counterpart" of (6), at line frequency, as shown in fig. 4b).

Actually, it is realistic to think that a filtering action eliminates the switching frequency component of the

current upstream the rectifier bridge, so that the mains "can see" only the average value. This current

would be sinusoidal for Kv = 0 but will be distorted from an ideal sinusoid so much as Kv increases.

Since Kv cannot be zero (which would require the reflected voltage to tend to infinity), flyback topology

does not permit unity power factor even in the ideal case, unlike boost topology.

In order to simplify the following calculations, it is possible to eliminate the absolute value from | sin (

θ)|

by considering

θ ∈ [0 , π] and assuming the various functions to be either even or odd by definition, de-

pending on their physical role.

The input power Pin will be calculated by averaging the product Vin(

θ) • Iin(θ) over a line half-cycle:

= Vin (θ) ⋅ Iin (θ)

____________

⋅ VPK ⋅ IPKp ⋅

sin

(θ)

+ Kv ⋅ sin (θ)

(7).

It is now advantageous to introduce the following function:

(x) =

sin

(θ)

+ x ⋅ sin (θ)

⋅

∫

sin

(θ)

+ x ⋅ sin (θ)

θ (8),

whose diagram as a function of the variable x is shown in fig. 5.

Although a closed form exists for the integral in (8),

it is not so handy, thus for practical use it is more

convenient to provide a "best fit" approximation:

(x) ≈

0.5

+ 1.4 ⋅ 10−3 ⋅ x

+ 0.815 ⋅ x

From (7), taking (8) into account, it is possible to

calculate IPKp:

IPKp

⋅ Pin

VPK

⋅ F2(Kv)

which will assume its maximum value at minimum

mains voltage.

The total RMS value of the primary current, useful for power loss estimate on the primary side, is calcu-

lated considering the RMS value of each triangle of Ip(t) and averaging over a line half-cycle:

IRMSp

√

⋅ Ipkp

(θ) ⋅ D = IPKp ⋅

√

⋅

sin

(θ)

+ Kv ⋅ sin(θ)

= IPKp ⋅

√

(Kv)

(9).

The DC component of the primary current, useful to discriminate DC and AC losses in the transformer, is

the average value of Iin(

θ) over a line half-cycle:

IDCp

= Iin(θ)

_____

⋅ IPKp ⋅

sin

(θ)

+ Kv ⋅ sin(θ)

(10).

Considering the following function:

(x) =

sin

(θ)

+ x ⋅ sin (θ)

⋅

∫

sin

(θ)

+ x ⋅ sin (θ)

θ,

0123

456

789

0.1

0.2

0.3

0.4

0.5

F2( )

Figure 5. High-PF Flyback characteristic

functions: F2(x) diagram

AN1059 APPLICATION NOTE

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