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System control loop compensation
L6711
42/50
●
is the PWM transfer function where
VOSC is the oscillator ramp
amplitude and has a typical value of 3V
Removing the dependence from the Error Amplifier gain, so assuming this gain high
enough, the control loop gain results:
With further simplifications, it results:
Considering now that in the application of interest it can be assumed that Ro>>RL;
ESR<<Ro and RDROOP<<Ro, it results:
The ACM control loop gain is designed to obtain a high DC gain to minimize static error and
cross the 0dB axes with a constant -20dB/dec slope with the desired crossover frequency
ωT. Neglecting the effect of ZF(s), the transfer function has one zero and two poles.
Both the poles are fixed once the output filter is designed and the zero is fixed by ESR and
the Droop resistance.
To obtain the desired shape an RF-CF series network is considered for the ZF(s)
implementation. A zero at
ωF =1/RFCF is then introduced together with an integrator. This
integrator minimizes the static error while placing the zero in correspondence with the L-C
resonance a simple -20dB/dec shape of the gain is assured).
In fact, considering the usual value for the output filter, the LC resonance results to be at
frequency lower than the above reported zero.
Compensation network can be simply designed placing
ωZ=ωLC and imposing the cross-
over frequency
ωT as desired obtaining:
PWM
4
5
---
V
IN
V
osc
---------------
=
G
L OOP s
()
4
5
---
V
IN
V
OSC
------------------
Z
F s
()
Z
P s
() Z
L s
()
+
------------------------------------
Rs
Rg
--------
Z
P s
()
R
FB
---------------
+
–
=
G
L OOP s
()
4
5
---
V
IN
V
OSC
------------------
Z
F s
()
R
FB
--------------
Ro
R
DROOP
+
Ro
R
L
3
-------
+
-------------------------------------
1s Co
R
DROOP//Ro
ESR
+
()
+
s
2
Co
L
3
---
s
L
3Ro
---------------
Co ESR
Co
+
R
L
3
-------
+
1
+
+
---------------------------------------------------------------------------------------------------------------------------------
–
=
G
L OOP s
()
4
5
---
V
IN
V
OSC
------------------
Z
F s
()
R
FB
--------------
1s Co
R
D ROOP
ESR
+
()
+
s
2
Co
L
3
---
s
L
3Ro
---------------
Co ESR
Co
+
R
L
3
-------
+
1
+
+
---------------------------------------------------------------------------------------------------------------------------------
–
=
R
F
R
FB
V
OSC
V
IN
----------------------------------
5
4
---
ω
T
L
3R
DROOP
ESR
+
()
-------------------------------------------------------
=
C
F
Co
L
3
---
R
F
--------------------
=