TPS40200 Datasheet, PDF (27/39 Pages) Texas Instruments – WIDE INPUT RANGE NON-SYNCHRONOUS VOLTAGE MODE CONTROLLER

TPS40200
www.ti.com
SLUS659 – FEBRUARY 2006
In order to properly compensate this system, it is necessary to know the frequencies of its Poles and Zeros.
Step 1
The break frequency of the output capacitor is given by:
1
F_esr = _2pResrC
where
• L= 33 µH
• C= 221 µF
Because of the ESR of the output capacitor, this output filter has a single-pole response above the 1.8-kHz break
frequency of the output capacitor and its ESR. This simplifies compensation since the system becomes
essentially a single pole system.
Step 2
The first zero is place well below the 1.8-kHz break frequency of the output capacitor and its ESR. Phase boost
from this zero is shown in Figure 42.
1
f_Z1 = _2pR8C8
where:
• R8 =100 kΩ
• C8= 1500 pF
• F_Z1= 354 Hz
Step 3
From a minimum Gain bandwidth product of 1.5 MHz, and knowing it has a 20dB/decade roll off, the the gain of
the error amplifier is 33 dB at 35 kHz. This approximate frequency is chosen for a crossover frequency to keep
the amplifier gain contribution to the overall system gain small.
Step 4
The second zero is placed well above the 35 kHz cross over frequency.
f_P3
=
2p ´ C₇
1
´ C₈
´ R₈
´ (C₇
+
C₈ )
where:
• R₈ = 300 kΩ
• C₇ = 10 pF
• C₈ 1500 pF
• f_P3 = 53 kHz
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