TPS54140 Datasheet, PDF (34/46 Pages) Texas Instruments – 1.5-A, 42V STEP DOWN SWIFT™ DC/DC CONVERTER WITH ECO-MODE™

TPS54140
SLVS889 – OCTOBER 2008 .............................................................................................................................................................................................. www.ti.com
To compensate the TPS54140 using this method, first calculate the modulator pole and zero using the following
equations:
¦p mod =
Ioutmax
2 × p × Vout × Cout
(41)
Where Ioutmax is the maximum output current, Cout is the output capacitance and Vout is the nominal output
voltage.
1
¦z mod =
2 ´ p ´ Resr × Cout
(42)
For the example design, the modulator pole is located at 1.5 kHz and the ESR zero is located at 338 kHz.
Next, the designer needs to select a crossover frequency which will determine the bandwidth of the control loop.
The cross over frequency must be located at a frequency at least five times higher than the modulator pole. The
cross over frequency must also be selected so that the available gain of the error amplifier at the cross over
frequency is high enough to allow for proper compensation.
Equation 47 is used to calculate the maximum cross over frequency when the ESR zero is located at a frequency
that is higher than the desired cross over frequency. This will usually be the case for ceramic or low ESR
tantalum capacitors. Aluminum Electrolytic and Tantalum capacitors will typically produce a modulator zero at a
low frequency due to their high ESR.
The example application is using a low ESR ceramic capacitor with 10mΩ of ESR making the zero at 338 kHz.
This value is much higher than typical crossover frequencies so the maximum crossover frequency is calculated
using both Equation 43 and Equation 46.
Using Equation 46 gives a minimum crossover frequency of 7.6 kHz and Equation 43 gives a maximum
crossover frequency of 45.3 kHz.
A crossover frequency of 45 kHz is arbitrarily selected from this range.
F_{c max} £ 2100
F_{pmod for ceramic capacitors.}
V_out
(43)
51442
F_{c max} £ _Vout for Tantalum or Aluminum capacitors.
(44)
F_{c max}
£
F_sw
5
for all cases
.
(45)
F_{c min} ³ 5 ´F_pmod for all cases.
(46)
Once a cross over frequency, Fc, has been selected, the gain of the modulator at the cross over frequency is
calculated. The gain of the modulator at the cross over frequency is calculated using Equation 47 .
G_{mod ¦c} =
6.6 ´ R_load ´ (2p ´ F_C ´ C_out ´ R_esr +1)
éë2p ´ F_C ´ C_{out (}´ R_load + R_{esr )}+1ùû
(47)
For the example problem, the gain of the modulator at the cross over frequency is 0.542. Next, the compensation
components are calculated. A resistor in series with a capacitor is used to create a compensating zero. A
capacitor in parallel to these two components forms the compensating pole. However, calculating the values of
these components varies depending on if the ESR zero is located above or below the cross over frequency. For
ceramic or low ESR tantalum output capacitors, the zero will usually be located above the cross over frequency.
For aluminum electrolytic and tantalum capacitors, the modulator zero is usually located lower in frequency than
the cross over frequency. For cases where the modulator zero is higher than the cross over frequency (ceramic
capacitors).
34
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