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Error Amplifier Pole-Zero Selection
A
PS(fcc)
+ A
MOD
* 40 LOG
ǒ
F
CO
F
RES
Ǔ
(26)
F
P2(max)
+
F
SW
A
MID(band)
(27)
TPS40040 , TPS40041
SLUS700D – MARCH 2006 – REVISED DECEMBER 2007
Place two zeros at 80% and 125% of the resonance frequency to keep the actual resonance frequency between
the two zeros over the L and C tolerance. For F
RES
= 11.3 kHz, F
Z1
= 9.0 kHz and F
Z2
= 14 kHz. Selecting the
cross-over frequency (F
CO
) of the control loop between 3 times the LC filter resonance and 1/5th the switching
frequency. For most applications 1/10th the switching frequency provides a good balance between ease of
design and fast transient response.
If F
ESR
< F
CO
; F
P1
= F
CO
and F
P2
= 2x F
CO
.
If F
ESR
> 2x F
CO
; F
P1
= F
CO
and F
P2
= 4x F
CO
.
For this design with F
SW
= 600 kHz, F
RES
= 11.3 kHz and F
ESR
= 318 kHz.
F
CO
= 60 kHz and since F
ESR
> 2x F
CO
, F
P1
= F
CO
and F
P2
= 4x F
CO
.
Since F
CO
< F
ESR
the power stage gain at the desired cross-over can be approximated by:
A
PS
(F
CO
) = -11.7 dB, so the error amplifier gain between the two poles should be 10
(11.7/20)
= 3.84.
If the error amplifier gain is greater than 0 dB at F
SW
, the converter can achieve a stable bi-modal operation with
duty cycles alternating between two stable values, and the output regulated with a output ripple component at
F
SW
. To prevent this effect, check F
P2
by the equation:
Since F
P2
> F
P2(max)
, it is possible for this control loop to obtain bi-modal operation. To prevent this bi-modal
operation, reduce F
CO
and re-calculate A
PC
(F
CO
), F
P1
, and F
P2(max)
.
Now, F
CO
= 50 kHz, A
MID-BAND
= 2.67, F
P1
= 50 kHz and F
P2
= 200 kHz.
The table below summarizes the error amplifier compensation network design criteria.
Error Amplifier Compensation Network
PARAMETER SYMBOL VALUE UNITS
First zero frequency F
Z1
9 kHz
Second zero frequency F
Z2
14
First pole frequency F
P1
50
Second pole frequency F
P2
200
Mid-band gain A
MID-BAND
2.67 V/V
Copyright © 2006 – 2007, Texas Instruments Incorporated 25
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