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Simplify Your Filter Design
By William D. Kimmel, P.E.
and Daryl D. Gerke, P.E.
Many EMC problems enter or exit via the power line, so we
get a lot of opportunities to work on the filter. Increasingly,
we are seeing filters implemented on the circuit board level,
whether the power is external AC or DC or DC from inside the
box.
The power line filter companies have this problem under control
– if you are using a commercially produced power line
filter, it is pretty likely to work as expected. But if you
are doing the job yourself on the circuit board, you will
probably run into some difficulties, the reason being that
you haven’t paid attention to the “hidden schematic.”
Let’s investigate this issue.
The Problem
We aren’t going to discuss filter theory – we’re
going to discuss why filters don’t work as intended.
The major reason is failure to account for the parasitic circuit
elements within the component itself and to the coupling between
adjacent circuit elements.
We’ll start by looking at the basic filter elements,
the capacitor and inductor. Figure 1 shows an ideal, or textbook,
inductor and capacitor and its real world equivalent circuit.
Basically, all capacitors have some series inductance, resulting
in a series resonant circuit; and all inductors have some
parallel capacitance, resulting in a parallel resonant circuit.
Below resonance, the component performs pretty much as basic
circuit theory predicts. Above resonance, the capacitor turns
into an inductor and the inductor turns into a capacitor,
a notable reversal of roles.
At and above resonance, the published component value ceases
to have any meaning. But resonance is the interesting aspect
of this article – funny things happen at resonance, and
here is where EMI problems, both emissions and immunity, tend
to surface.
To get an idea of where these resonances occur, let’s
take a look at some typical circuit parameters. Ceramic capacitors
are pretty good performers – most of the series inductance
occurs due to the external lead length. In the case of surface
mount capacitors, the inductance is primarily in the vias,
which is about one nH per via, or two nH per capacitor mount.
Calculating the resonance frequency from fr = 1/2*pi*sqrt(LC),
we find that a 100nF capacitor self-resonates at about 11MHz
and a 1nF capacitor at about 110MHz. Above the resonance frequency
the capacitors become inductive. That is not to say the capacitor
stops working above resonance, but the impedance is definitely
on the rise, and the capacitor becomes increasingly ineffective.
For a wound inductor, we like to use the empirical relationship
fr = 200/sqrt(L), where L is in uH and fr is in MHz. Thus
100uH inductor resonates at about 20MHz and a 10mH inductor
resonates at about 2MHz. Again, above resonance, the inductor
looks like a capacitor.
If this is your first real look at resonances, you may be
surprised at how low a frequency the resonances occur.
Combining Filter Elements
Now let’s look at what happens when we start stacking
up filter elements. A common practice is to employ various
component values to get a wider useful frequency range. For
example, we might put a high frequency ceramic capacitor with
an electrolytic capacitor. This is pretty much a necessity
– the electrolytic capacitor is nearly useless above
a few MHz.
This practice has been extended to the higher frequency ranges
– chip houses often recommend paralleling, say, a 1nF
capacitor with a 100nF capacitor to get a wider frequency
range of effective decoupling. But look what happens when
you do this. Figure 2 shows the two capacitors stacked in
parallel, along with the inductance of each leg. From the
above paragraphs, we know that the two capacitors will resonate
at about 11 and 110MHz. Certainly, we have spread out the
resonant frequencies, but in between these two frequencies
is a parallel resonance, occurring at about 80 MHz, where
the impedance of the network goes to infinity. In short, at
80MHz, we have no decoupling or filtering. If you add more
parallel capacitors, you add more parallel resonances.
A similar situation occurs with series inductances. Each inductor
will resonate at its self-resonant frequencies, and in between,
there will be a series resonance where the effective series
impedance drops to zero, negating the desired high series
impedance.
The plot becomes more interesting when we stack up filter
elements. The parasitic filter elements muultiply. Add more
filter elements and the possible number of resonant frequencies
increases accordingly. It is this situation that leads to
unexpected problem frequencies.
In addition to the parasitic components, you need to consider
the impedances of the driver and receiver and, at higher frequencies,
the inter-component coupling paths and the path inductance.
What to Do
The first order of business is to minimize the number of
possible resonances. The common practice of paralleling two
different capacitor sizes creates the undesired parallel resonance
mentioned above. If you are using ceramic capacitors, we recommend
using one large capacitor alone, throwing out the small value
capacitor. This argument does not apply to electrolytics –
they always need high frequency bypassing. Similarly, alternating
inductors and capacitors create additional resonances. Our
observation is the fewer filter elements you use, the more
reliable the filtering.
Second, you need to account for the parasitics in your filter
elements as a minimum. Capacitors and inductors resonate at
a surprisingly low frequency, almost assuredly low in your
frequency range of interest. Ditto for transformers. Select
filter elements that are working in your frequency range of
interest.
Third is to soften the resonances. You can’t get rid
of them, but the effects can be minimized with use of low
Q filter elements. The most common is the ferrite – it
does resonate, but is lossy at resonance, and does not contribute
significantly to the stray resonance issue. Electrolytic capacitors
are also low Q and contribute but little to stray resonances.
Wound inductors are generally high Q and are to be avoided
if possible. Unfortunately, ferrites do not have enough inductance
for low frequency filtering, making a wound inductor a necessity.
But you can insert a loss factor (usually, a high value parallel
resistor – small series resistance will work, too, but
is usually not permitted in power filtering).
Fourth, mount your capacitors for minimum lead inductance.
Avoid spacing between via and solder pad. You can reduce the
lead inductance further by dropping two vias per capacitor,
by using reverse aspect capacitors (e.g. 0306 instead of 0603)
or by using a low inductance mount, such as X2Y® capacitors.
Fifth, beware of cross coupling in the circuit board layout.
Filters that work well when breadboarded in-line often fail
to perform up to expectations when mounted in the circuit
board. We have added some additional parasitic elements. This
is true with any circuit board filter layout, but is particularly
noticeable in power supplies where components tend to be large
and protrude well above the circuit board ground plane.
Summary
The major reason for filter failure is failure to account
for parasitic parameters, resulting in unanticipated resonances.
Designs need to minimize the occurrence of resonances, push
the resonant frequencies as high as possible and soften those
resonances that cannot be eliminated. Simple filters with
well chosen and carefully placed components usually work out
best.
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