Regulation Loop Stability VIPer53EDIP - E / VIPer53ESP - E
16/31
The complete converter open loop transfer function can be built from both power cell and the feedback network transfer functions. A theoretical example can be seen in
Figure 11 on page 22 for a discontinuous mode flyback loaded by a simple resistor.
A typical schematic corresponding to this situation can be seen on
Figure 3 on page 8 . The
transfer function of the power cell is represented as G(s) in .
Figure 11 on page 22
It exhibits a pole which depends on the output load and on the output capacitor value. As the load of a converter may change, two curves are shown for two different values of output resistance value, R
L1
and R
L2
. A zero at higher frequency values then appears, due to the output capacitor ESR. Note: The overall transfer function does not depend on the input voltage because of the current mode control. A typical regulation loop is shown on
Figure 3 on page 8
and has a fixed behavior represented by F(s) on Figure 11 on page 22
. A double zero due to the R
1
-C
1
network on the COMP pin and to the integrator built around the TL431 and R
2
-C
2
is set at the same value as the maximum load R
L2
pole.
The total transfer function is shown as F(s). G(s) at the bottom of
Figure 11 on page 22
. For maximum load (plain line), the load pole begins exactly where the zeros of the COMP pin and the TL431 stop, and this results in a first order decreasing slope until it reaches the zero of the output capacitor ESR. The point where the complete transfer function has a unity gain is known as the regulation bandwidth and has a double interest:
– The higher it is, the faster the reaction will be to an eventual load change, and the smaller the output voltage change will be.
– The phase shift in the complete system at this point has to be less than 135° to ensure good stability. Generally, a first-order slope gives 90° of phase shift, and a second-order gives 180°.
In Figure 3 on page 8
, the unity gain is reached in a first order slope, so the stability is ensured.
The dynamic load regulation is improved by increasing the regulation bandwidth, but some limitations have to be respected:
1. As the transfer function above zero due the ESR capacitor is not reliable (the ESR itself is not well specified, and other parasitic effects may take place), the bandwidth should always be lower than the minimum of FC and ESR zero
2. As the highest bandwidth is obtained with the highest output power (plain line with RL2
load in Figure 3
, the above criteria will be checked for this condition and allows the value of R4 if R1 is set to a fixed value (e.g., (2.2k
Ω ).
As the highest bandwidth is obtained with the highest output power (Plain line with R
L2
load in
Figure 3 ), the above criteria will be checked for this condition and allows to define the
value of R
4
, if R1 is set fixed (2.2k
Ω , for instance). The following formula can be derived:
R
4
=
P
MA X
---------------------
P
O UT2
⋅
F
BW 2
G
⋅
O
R
⋅ R
L2
⋅
1
C
OUT with: P
O UT2
=
V
2
OUT
-----------------
R
L2 and:
P
MA X
=
1
2
⋅ L
P
⋅
2
I
LIM
⋅ F
SW
Go is the current transfer ratio of the optocoupler.
DocRev1
VIPer53EDIP - E / VIPer53ESP - E Regulation Loop Stability
The lowest load gives another condition for stability: The frequency F
BW1
must not encounter the third order slope generated by the load pole, the R1-C1 network on the
COMP pin and the R2-C2 network at the level of the TL431 on secondary side. This condition can be met by adjusting both C
1
and C2 values:
C
1
>
R
L 1
6.3
⋅
⋅ C
OUT
G
O
R
4
⋅
2
--------R
1
⋅
P
---------------------
P
MAX
R
C
2
>
6.3
⋅
L 1
G
R
⋅
O
4
C
⋅
OUT
R
1
⋅
R
2
⋅
P
---------------------
P
MAX with: P
OUT1
=
V
2
OUT
R
L1
The above formula gives a minimum value for C1. It can be then increased to provide a natural soft start function as this capacitor is charged by the current I
COMP
at start-up.
DocRev1 17/31
