L6759D Datasheet, PDF (40/51 Pages) STMicroelectronics – Fully configurable through PMBus

System control loop compensation
L6759D
Figure 17. Control loop Bode diagram and fine tuning
dB
dB
C_F
G_LOOP(s)
G_LOOP(s)
K
R_F[dB]
Z_F(s)
K
R_F[dB]
ω_LC = ω_F
ω_ESR
ω
ω_T
ω_LC = ω_F
ω_ESR
Z_F(s)
R_F
ω
ω_T
To obtain the desired shape, an R_F-C_F series network is considered for the Z_F(s)
implementation. A zero at ω_F=1/R_FC_F is then introduced together with an integrator. This
integrator minimizes the static error while placing the zero ω_F in correspondence with the L-
C resonance which assures a simple -20 dB/dec shape of the gain.
In fact, considering the usual value for the output filter, the LC resonance results to be at a
frequency lower than the above reported zero.
The compensation network can be designed as follows:
Equation 22
R_F
=
R_{-----F---B-----}⋅_------∆_----V_{----O----S---C--}
V_IN
⋅
1_----0_--
6
⋅
(^---R^----F-_L^--_LS^----W-+----E^-⋅----S^--L--R^-----)
Equation 23
C_F
=
-----^C----^O-----^â‹------^L--
R_F
11.1
Compensation network guidelines
The compensation network design assures the presence of a system response according to
the crossover frequency selected and to the output filter considered: it is anyway possible to
further fine-tune the compensation network modifying the bandwidth in order to get the best
response of the system, as follows (see Figure 17 ):
● Increase R_F to increase the system bandwidth accordingly
● Decrease R_F to decrease the system bandwidth accordingly
● Increase C_F to move ω_F to low frequencies increasing as a consequence the system
phase margin.
Having the fastest compensation network does not guarantee that the load requirements are
satisfied: the inductor still limits the maximum dI/dt that the system can afford. In fact, when
a load transient is applied, the best that the controller can do is to “saturate” the duty cycle to
its maximum (d_MAX) or minimum (0) value. The output voltage dV/dt is then limited by the
inductor charge / discharge time and by the output capacitance. In particular, the most
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