PRM48AH480T200A00 Datasheet, PDF (36/44 Pages) Vicor Corporation – PRM™ Regulator

Control Loop Compensation Requirements (Remote
Sense operation)
In order to properly compensate the control loop, all
components which contribute to the closed loop frequency
response should be identified and understood. Figure 24
shows the AC small signal model for the module. Modulator
DC gain G_CN and powertrain equivalent resistance r_{EQ_OUT} are
shown. These modeling parameters will support a design cut-
off frequency up to 50kHz.
Standard Bode analysis should be used for calculating the
error amplifier compensation and analyzing the closed loop
stability. The recommended stability criteria are as follows:
1) Phase Margin > 45º : for the closed loop response, the
phase should be greater than 45º where the gain crosses 0dB.
2) Gain Margin > 10dB : The closed loop gain should be lower
than -10dB where the phase crosses 0º.
3) Gain Slope = -20dB/decade : The closed loop gain should
have a slope of -20dB/decade at the crossover frequency.
The compensation characteristics must be selected to meet
these stability criteria. Refer to Figure 37 for a local sense,
voltage-mode control example based on the configuration in
Figure 36. In this example, it is assumed that the maximum
crossover frequency (F_CMAX) has been selected to occur
between B and C. Type-2 compensation (Curve IJKL) is
sufficient in this case.
The following data must be gathered in order to proceed:
 Modulator Gain G_CN: See Figures 18, 19, 20
 Powertrain equivalent resistance r_EQ: See Figures 18,
19, 20
 Internal output capacitance: see Figure 13
 External output capacitance value
In the case of ceramic capacitors, the ESR can be considered
low enough to push the associated zero well above the
frequency of interest. Applications with high ESR capacitor
may require a different type of compensation, or cascade
control.
PRM48AH480 X 200A00
The system poles and zeros of the closed loop can then be
defined as follows:
 Powertrain pole, assuming the external capacitor
ESR is negligible:
R  _{rr } ^RR _{COUT _ EXT}
EQ _ OUT
EQ _ OUT
LOAD
LOAD
 Main pole frequency:
  ^FP

2 π
r_{EQ _ OUT}  R_LOAD
r_{EQ _ OUT}  R_LOAD
1

C  C _{OUT _ INT}
OUT _ EXT
 Compensation Mid‐Band Gain:
G _MB

20 log
R₃
R₁
(8)
 Compensation Zero:
F_Z1

2
1
π R ₃ C₁
(9)
 Compensation Pole:
F_{P 2}

2 π
1
R₃  C₁
 C₂
C₁  C₂
and for F_P2>>F_Z1 (C₁ + C₂ ≈ C₁):
F_{P 2}

2

1
R₃
 C₂
(10)
- 36 -
Rev. 1.1
11/2012