TPS54040_16 Datasheet, PDF (27/51 Pages) Texas Instruments – Step Down DC/DC Converter

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Feature Description (continued)
V_O
TPS54040
SLVS918B – MARCH 2009 – REVISED JANUARY 2016
VC
R_ESR
gm_ps
C_OUT
Adc
fp
R_L
fz
Figure 47. Simple Small Signal Model and Frequency Response for Peak Current Mode Control
V_OUT
=
Adc
´
æç₁₊
è
s
2p ´
f_Z
ö
÷
ø
V_C
æ
ç¹⁺
è
s
2p ´
f_P
ö
÷
ø
(14)
Adc = gm_ps ´ R_L
(15)
1
f_P = _{COUT ´ RL ´ 2p}
(16)
1
f_Z = _{COUT ´ RESR ´ 2p}
(17)
7.3.20 Small Signal Model for Frequency Compensation
The TPS54040 uses a transconductance amplifier for the error amplifier and readily supports three of the
commonly-used frequency compensation circuits. Compensation circuits Type 2A, Type 2B, and Type 1 are
shown in Figure 48. Type 2 circuits most likely implemented in high bandwidth power-supply designs using low
ESR output capacitors. The Type 1 circuit is used with power-supply designs with high-ESR aluminum
electrolytic or tantalum capacitors.. Equation 18 and Equation 19 show how to relate the frequency response of
the amplifier to the small signal model in Figure 48. The open-loop gain and bandwidth are modeled using the R_O
and C_O shown in Figure 48. See the application section for a design example using a Type 2A network with a
low ESR output capacitor.
Equation 18 through Equation 27 are provided as a reference for those who prefer to compensate using the
preferred methods. Those who prefer to use prescribed method use the method outlined in the application
section or use switched information.
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