Figure 8-1 shows the current loop block diagram of each phase in buck mode. VHV is the
input while VLV is the output.
The inner current loop should be designed
first. The average current-mode control loop of buck mode can be modeled as:Figure 8-2
The buck power plant transfer function from
the duty cycle (d) to the channel inductor current (iLm) is determined by the
following:
Equation 23.
where
Equation 24.
Equation 25.
Equation 26.
Equation 27.
- Lm is the power inductor,
- RCS is the current sense resistor,
- RS is the equivalent total resistance along the current path excluding
RCS,
- COUT_BK is the output capacitance for each phase in buck mode. For a
system with np phases, COUT_BK is 1/np times the total
capacitance.
- RESR_BK is the output capacitor equivalent series resistance (ESR) for each
phase in buck mode. For np phase system, RESR_BK is np
times total system output capacitor ESR.
Figure 8-3 shows the current loop
block diagram in boost mode. VLV is the input while VHV is the
output.
The average current-mode control loop of boost mode is the same as buck as shown in Figure 8-2. But the transfer
function of the boost power stage Gid(s) and Gvd(s) is different from
that of buck power stage.
The boost power plant transfer function from the duty cycle (d) to the channel inductor
current (iLm) is determined by the following:
Equation 28.
where
Equation 29.
Equation 30.
Equation 31.
Equation 32.
Equation 33.
- COUT_BST is the output capacitance for each phase in boost mode. For a system
with np phases , COUT_BST is 1/np times the total
capacitance.
- RESR_BST is the output capacitor equivalent series resistance (ESR) for each
phase in boost mode. For a system with np phases, RESR_BST is
np times total system output capacitor ESR.
When we select the current loop cross over
frequency at 1/6 of switching frequency, Gid_BK(s) can be simplified. For the
numerator, s×ROUT_BK×COUT_BK dominates. And for the denominator,
s2/ω0_BK2 dominates. Equation 23 can be simplified as:
Equation 34.
Similarly, Equation 28 can be simplified as:
Equation 35.
It can be observed that the same duty cycle
(d) to channel inductor current (iLm) transfer function is shared by both buck
and boost mode:
Equation 36.
So compensator for buck current loop and
boost current loop can also be shared.