AN937 Datasheet, PDF (23/29 Pages) STMicroelectronics – The L4971 is a 1.5 A monolithic dc-dc converter

AN937
3.7
Error amplifier and compensation blocks
The open loop gain is:
Typical application
A(s)
=
g
m
⋅
------------------------------------------------^R-----^O-----^â‹---⁽---¹----+-----^s-----^â‹---^R----^c----^â‹---^C-----^c--⁾-------------------------------------------------
s² ⋅ R_o ⋅ C_o ⋅ R_c ⋅ C_c + s ⋅ (R_o ⋅ C_c + R_o ⋅ C_o + R_c ⋅ C_c) + 1
where Cout is the parallel between the output and the external capacitance of the Error
Amplifier and Ro the E/A output impedance. Rc and Cc are the compensation values.
3.8
LC filter
A_o(s)
=
-----------¹----+-----^R-----^e---^s--^r----^â‹---^C----^o---^u---^t---^â‹---^s-----------
L ⋅ C_out ⋅ s² + R_esr ⋅ s + 1
3.9
PWM gain
V_-----C---C--
V_ct
=
-^V----^C----^C-----^â‹---⁶---
V_CC – 1
≈
6
where Vct is the peak to peak sawtooth oscillator.
3.10 Voltage divider and leading network
A_o(s)
=
-------^R-----³--------
R₂ + R₃
⋅
-----------¹-----+-----^R----²-----^â‹---^C----⁹------------
1
+
s
⋅
-^R-----²----^â‹---^R-----³--
R₂ + R₃
⋅
C₉
Poles and zeros value are:
F_o
=
-------------------¹-------------------
2 ⋅ πR_esr ⋅ C_out
=
------------------------------¹-------------------------------
2 ⋅ π ⋅ 0.130 ⋅ 150 ⋅ 10^–6
=
8.2KHz
F_p
=
-------------------¹-------------------
2 ⋅ π ⋅ L ⋅ C_out
=
--------------------------------------¹--------------------------------------
2 ⋅ π ⋅ 120 ⋅ 10^–6 ⋅ 150 ⋅ 10^–6
=
1.2kHz
F_ocomp
=
----------------¹-----------------
2 ⋅ π ⋅ R_c ⋅ C_c
=
-------------------------------¹--------------------------------
2 ⋅ π ⋅ 15 ⋅ 10³ ⋅ 22 ⋅ 10^–9
=
492Hz
Doc ID 5655 Rev 15
23/29