Transconductance error amplifier VIPer53 - E
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optocoupler, the internal error amplifier is fully used for regulation). A typical schematic
corresponding to this situation can be seen on Figure 18.
The transfer function of the power cell is represented as G(s) in Figure 24 Iexhibits 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.
The error amplifier has a fixed behavior, similar to the one shown in Figure 23. Its bandwidth
is to avoid injection of high frequency noise in the current mode section. A zero due to the
R
COMP
-C
COMP
network 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 24. For maximum
load (plain line), the load pole is exactly compensated by the zero of the error amplifier, and
the result is a perfect first order decreasing until it reaches the zero of the output capacitor
ESR. The error amplifier cut-off then definitely any further spurious noise or resonance from
disturbing the regulation loop.
The point where the complete transfer function has a unity gain is known as the regulation
bandwidth and has:
– 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 24, 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: As the transfer function above the zero due the capacitor
ESR 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 F
C
and ESR zero.
As the highest bandwidth is obtained with the highest output power (Plain line with R
L2
load
in Figure 24), the above criteria will be checked for this condition and allows to define the
value of R
COMP
, as the error amplifier gain depends only on this value for this frequency
range. The following formula can be derived:
Equation 12
R
COMP
P
OUT2
P
MAX
-----------------
F
BW2
R
L2
C
OUT
⋅⋅
Gm
------------------------------------------------------
⋅=
P
OUT2
V
OUT
2
R
L2
--------------=
P
MAX
1
2
---
L
P
I
LIM
2
F
SW
⋅⋅ ⋅=
With: and:
