LM27403 Datasheet, PDF (34/49 Pages) Texas Instruments – Synchronous Buck Controller with Temperature-Compensated, Inductor-DCR-Based Overcurrent Protection and Programmable Thermal Shutdown

LM27403
SNVS896 A – AUGUST 2013 – REVISED SEPTEMBER 2013
www.ti.com
Table 5. Buck Regulator Small-Signal Analysis
PARAMETER
Open-loop transfer function
Duty-cycle-to-output transfer function
Compensator transfer function⁽¹⁾
EXPRESSION
T_v (s)

v^Ö _comp(s)
v^Ö _o(s)
b
v^Ö _o(s)
d^Ö(s)
b
d^Ö(s)
v^Ö _comp(s)

G_c (s)G_vd(s)F_M
G_vd (s)
v^Ö _o (s)
d^Ö(s) v^Ö_in (s) 0
Ö_{i o (s) 0}
1 ^s
V_IN
1
Z_ESR
s

Q_oZ_o
s²
Z _o²
G_c (s)
v^Ö _comp (s)
v^Ö _o (s)
K_mid
§
¨©¹

§
¨¨©1
Z
z1
s
s
Z_p1
·
¸¹
§
¨¹
©

·§
¸¸¹ ¨¨©1 
s
Z_z2
s
Z_p2
·
¸
¹
·
¸¸¹
Modulator transfer function
F_M

d^Ö(s)
vÖ _comp (s)

1
V_RAMP
(1) K_mid = R_C1/R_FB1 is the compensator's mid-band gain. By expressing one of the compensator zeros in inverted zero format, the mid-band
gain is denoted explicitly.
An illustration of the open-loop response gain and phase is given in Figure 40. The poles and zeros of the
system are marked with x and o symbols, respectively, and a + symbol indicates the crossover frequency. When
plotted on a log (dB) scale, the open-loop gain is effectively the sum of the individual gain components from the
modulator, power stage and compensator – this is clear from Figure 41. The open-loop response of the system is
measured experimentally by breaking the loop, injecting a variable-frequency oscillator signal and recording the
ensuing frequency response using a network analyzer setup.
40
Loop
Gain
20
0
Complex
LC Double
Pole
Crossover
-45
Frequency, fc
Loop
Gain 0
(dB)
Loop
Phase
Compensator
Zeros
-20
Compensator
Loop
Poles
-90 ^Phase
(°)
N_M
-135
Output
Capacitor
ESR Zero
-40
-180
1
10
100
1000
Frequency (kHz)
Figure 40. Typical Buck Regulator Loop Gain and Phase with Voltage-Mode Control
If the pole located at ω_p1 cancels the zero located at ω_ESR and the pole at ω_p2 is located well above crossover,
the expression for the loop gain, T_v(s) in Table 5, can be manipulated to yield the simplified expression given as
follows.
T_v (s)
R_C1C_C3
s
Z _o²
V_IN
V_RAMP
(16)
34
Submit Documentation Feedback
Product Folder Links: LM27403
Copyright © 2013, Texas Instruments Incorporated