LC +
1
2p
L
OUT
C2
^ Z1
(17)
C2 ^
1
4p2
2
Z1
L
OUT
(18)
P(ESR) +
1
2pR
(C2ESR)
C5
+ Z2
(19)
CO +
1.125
10*
3
P(ESR)
LC
(20)
Capacitor ESR and Output Ripple
www.ti.com ....................................................................................................................................................... SLVS684A – JANUARY 2007 – REVISED JULY 2009
The TPS54356 contains a compensation network with the following nominal characteristics:
INT = 1.7 kHz
Z1 = 2.5 kHz
Z2 = 4.8 kHz
P1 = 95 kHz
P2 = 125 kHz
For a stable design, the closed-loop crossover frequency should be set less than one-fifth of the switching
frequency, and the phase margin at crossover must be greater than 45 degrees. The general procedure outlined
here produces results consistent with these requirements, without going into great detail about the theory of loop
compensation.
In this case, the output filter LC corner frequency should be selected to be near the first compensation zero
frequency, as described by equation 17:
Placement of the LC corner frequency at fZ1 is not critical; it only needs to be close. For the design example,
fLC = 2 kHz.
Solving for C2 using equation 18:
The desired value for C2 is calculated as 184
F. A close standard value of 330 F is chosen, with a resulting
LC corner frequency of 1.9 kHz. As shown, this value is not critical as long as it results in a corner frequency in
the vicinity of fZ1.
Next, when using a large ceramic capacitor in parallel with a high-ESR electrolytic capacitor, there is a pole in
the output filter that should be at fZ2, as shown in equation 19:
Now, the actual C2 capacitor must be selected based on the ESR and the value of capacitor C5, so that the
above equation is satisfied. In this example, the R(C2ESR)C5 product should be 3.18 × 10
–5. From the available
capacitors, by choosing a Panasonic EEVFKOJ331XP aluminum electrolytic capacitor with a nominal ESR of
0.34
yields a calculated value for C5 of 98
F. The closest standard value is 100 F. As the actual ESR of the
capacitor can vary by a large amount, this value also is not critical.
The closed-loop crossover frequency should be greater than fLC and less than one-fifth of the switching
frequency. Also, the crossover frequency should not exceed 70 kHz, as the error amplifier may not provide the
desired gain. As stated previously, closed loop-crossover frequencies between 5 and 15 times fLC work well. For
this design, the crossover frequency can be estimated by:
This simplified equation is valid for this design because the output filter capacitors are mixed technology.
Compare this result to the actual measured loop response plot of
Figure 5. The measured closed-loop crossover
frequency of 19.95 kHz differs from the calculated value because the actual output filter capacitor component
parameters differed slightly from the specified data-sheet values.
The amount of output ripple voltage, as specified in the initial design parameters, is determined by the maximum
ESR of the output capacitor and the input ripple current. The output ripple voltage is the inductor ripple current
times the ESR of the output filter, so the maximum specified ESR as listed in the capacitor data sheet is given by
equation 21:
Copyright 2007–2009, Texas Instruments Incorporated
21