DESIGNER’S SERIES

Second-Stage
LC Filter
Design First Inductor

by Dr. Ray Ridley

First Capacitor

P
ower supply output voltages are dropping with each
new generation of Integrated Circuits (ICs).
Anticipated current level reductions have not materi-
alized, and the problem of switching power supply noise is Second Inductor
pervasive. Reducing noise with a conventional single-stage
filter seldom works. The inductor is already large, and drop-
ping the noise an order of magnitude just isn’t feasible.
For this reason, many designers add a second “noise” filter at
Output Capacitor
the output of their power supply. The filter typically consists
of an additional small inductance, and a small, high-quality
capacitor. This seemingly intuitive approach can often lead
to an unstable system. The mistake is in designing with large
components followed by small components.
Designing a single-stage filter is straightforward. The induc- The resonance of a single-stage filter is typically not a criti-
tor is selected to give about 20% current ripple, and the cal concern. It is inside the feedback loop bandwidth (either
capacitor is chosen with sufficiently low ESR to meet the current-mode or voltage-mode control) and its peaking and
output ripple requirements. The output holdup and step-load resonance effects are eliminated by the feedback. Figure 1
requirements also impact the choice of capacitor. shows a typical single-stage filter designed for a point-of-

3.3 V
2.8 mH 20 A 3.3 V
2.8 mH 0.2 mH 20 A
5 mOhm
Switching Power 10 mOhm 5 mOhm
2500 mF Switching Power
Cell 200 kHz 250 mF 2500 mF
Cell 200 kHz

Feedback Feedback
Fig. 1: Point-of-Load Buck Converter with Single-Stage Filter Fig. 2: Point-of-Load Buck Converter with Two-Stage Filter

3.32 3.301

3.31 3.300

3.30 3.299

3.298
3.29 0 5 10 15 20
0 5 10 15 20
Time (ms) Time (ms)
Fig. 1a: Output Voltage Ripple of the Circuit of Fig. 1 Fig. 2a: Output Voltage Ripple of the Circuit of Fig. 2

8 Switching Power Magazine July 2000

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770 640 9024
885 Woodstock Rd.
Suite 430-382
Roswell, GA 30075 USA
 DESIGNER’S SERIES

Figure 3 shows what happens to the filter transfer function

with two stages. It still has a low frequency resonance close
to the single stage resonance, and this will be controlled by
the feedback loop. The second filter resonance for this exam-
ple is at 22 kHz. You can see from the transfer functions that
the additional attenuation is more than 28 dB at the switch-
ing frequency. Furthermore, the additional phase delay (not
shown here) is less than 15 degrees at 10 kHz, so stability is
not significantly affected.

The second filter resonance that you get with a two-stage fil-
ter must be placed very carefully— beyond the control loop
crossover to avoid stability problems, but at a low enough
frequency to attenuate both the switching frequency ripple
and the high frequency noise. This presents a challenge to
the designer. Furthermore, the design of the filter must be
robust and stable under worst case conditions of line, load,
and any extra capacitance the user may add.

Most two-stage filters are designed in as an afterthought. The

converter is finished, but the noise is too high, and there is
only room and time to put some small components on the
board. This works when the converter is tested on the bench,
but when placed in the application, load bypass capacitors
can significantly change the filter characteristics, reducing
the second resonance to a frequency where it causes instabil-
ity. To understand a better way to do it, let’s look at the
analysis of the two-stage filter system.

Analyzing the Filter

It is important to know how the components of the two-stage
filter interact. Recognize that the inductors of the two-stage
load converter, and Figure 1a shows the output voltage rip- filter are very different in size— the first inductor is largest,
ple with this filter. in order to constrain the ripple currents in the power semi-
conductors. Select it on this basis, as you would for a single-
Figure 2 shows a two-stage filter. This is used to reduce the stage design.
ripple without substantially increasing the volume of power
components needed. A two-stage filter is far more effective There are two pairs of poles for this filter. They determine
than a single stage, because components can be smaller for the location and characteristics of the resonant frequencies
the same amount of attenuation. In fact, with this design, shown in Figure 3. These poles are given by:
adding only 10% more capacitance and inductance gives
more than 30 times reduction in output ripple, as shown in
Figure 2a. Notice that the scale of Figure 2a is enlarged— 3
mV full scale, compared to 30 mV full scale for the ripple of
the single-stage filter. There are two resonances— a low frequency resonance, and
a high frequency resonance. The first
20 resonant frequency is calculated
0 from the circuit of Figure 4.
Gain (dB)

-40
where Cp is the parallel combination
-80 of capacitors:
Single-Stage Filter
Two-Stage Filter
-120
0.1 1 10 100 200 1000
Frequency (kHz)

Fig. 3: Output Filter Transfer Functions

July 2000 Switching Power Magazine 9

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885 Woodstock Rd.
Suite 430-382
Roswell, GA 30075 USA

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DESIGNER’S SERIES

In other would allow us to damp the two-stage filter without sacrificing

2.8 mH words, we add attenuation, but this increases the dissipation of the filter. For
the capacitor the filter design of Figure 2, the ESRs of all three reactive ele-
10 mOhm 5 mOhm values togeth- ments contribute to the filter damping.
250 mF 2500 mF er to get the
With this analysis, it’s easy to design the second filter. The
first resonance
smaller capacitor has to be carefully selected to carry the full
formed with
ripple current from the inductor. In some power supplies, this
the big
Fig. 4: Low-frequency circuit for calculating first resonance inductor. entails using a different type of capacitor. Even though it is
ten times smaller in capacitance for the example in this arti-
This resonant frequency won’t move much with capacitive
cle, the ESR has to be a similar value to the output capacitor.
loading. There is usually sufficient capacitance in the filter that
For commercial applications, this often leads to film capaci-
any load capacitance won’t significantly change the value.
tors for the first stage, and electrolytic or tantalum capacitors
Even with a 2:1 change, the filter resonance would only move
on the output.
by 40%, and stability will not be a problem.
The Q of the first resonance is not very interesting. We’ll Industry Application
close a control loop around it, and use the feedback to cancel Since this filter technique was first developed, many compa-
the filter peaking effects. nies have adopted it as the standard way to design. This is the
The second filter frequency is given by the circuit of Figure 5. technique used by IBM in the design of all load regulators for
their mainframes described in this magazine. The photograph
in this article shows three 2-kW converters. Two of them are
0.2 mH 5 mOhm mounted next to each other, and the third is shown on its side to
reveal the hidden components. The main inductor is a large EE
10 mOhm 5 mOhm core, with a single bus bar through each window. These bus bars
250 mF 2500 mF where Cs is the series mount to the first capacitor, which is a low-ESR film type.
combination of capacitors A second, smaller EE core is clamped around the bus bars to
given by: form the second inductor, and the output of this feeds a bank
Fig. 5: High-frequency circuit for
calculating second resonance of electrolytic capacitors. The EE core construction with bus
bars forms a very low-capacitance inductor for each of the
filter stages, and helps with both differential-mode, and com-
this expression is dominated by the mon-mode filtering.
smaller of the two capacitors. This
creates an interesting design choice. If your power supply is too noisy, but there is not much space
to increase filter components, a two-stage filter is the only
If the output capacitor, C2 is smaller, the second resonance practical solution. Follow the design rules in this article and
is very sensitive to any capacitive loading by the application. you can have it all— low noise output, small filter components,
In fact, load capacitance can make the system unstable. stable operation, and immunity from capacitive loading.
If the first capacitor, C1 , is smaller, the second resonance is
insensitive to capacitive loading, and system stability can be
maintained with significant load capacitance. This is the Design Rule #1:Don't think of the filter as “Main filter fol-
proper way to design two-stage filters. lowed by Noise filter”, that can get your design in trouble.
It's an integral filter which you won't separate that way when
In most applications the second filter resonance is placed you design it properly.
beyond the crossover frequency of the feedback loop. (We’ll
examine in a future issue of Switching Power Magazine Design Rule #2: Make the first capacitor the smaller of the
whether that can be changed for some converters— an inter- two. Then you'll have a second filter resonance which is fixed—
esting possibility brought up recently by one of our readers.) it won't be affected by capacitive loading. Typically, the first
We must control this resonance very careful, by fixing the capacitor will be 2-20 times smaller than the output capacitor
resonant frequency, and then by controlling the peaking with
damping elements. This is similar to input filter design. We Design Rule #3: Make the second inductor much smaller than
don’t directly damp the resonances with a control loop, so the first— typically about 10% of the main inductor value.
we must damp them with resistive components.
The Q of the second filter is given by: Design Rule #4: Put the second filter resonance about 3
times higher than the loop crossover frequency.

Design Rule #5: Damp the second filter resonance properly.

That means carefully choosing the ESR of the second induc-
For good design, the Q of the second stage filter should be one tor and the filter capacitors.
or less. It is usually necessary to compromise the attenuation of
the filter to achieve this. Increasing the inductor resistance, R3 ,

10 Switching Power Magazine July 2000

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Ridley Engineering
www.ridleyengineering.com
770 640 9024
885 Woodstock Rd.
Suite 430-382
Roswell, GA 30075 USA