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How not to design analog filters!

Posted by Chris Francis+ on Friday, July 11, 2014 · Leave a
Comment

By Chris Francis

I thought I would share some of the crimes against filters that I have seen
people commit over the years.

2+2=4?

So, you have designed a 2 pole Butterworth filter for example and want a 4
pole one so you put two of them together. You have a four pole filter? Yes, but
not a Butterworth filter! The schematics of a 4 pole filter and a cascade of two
2 pole filters might look identical but the component values will be different.
This can be illustrated below

The design of the various filter types such as Butterworth, Chebyshev, Bessel
etc creates a certain characteristic which is not based on simply repeating
identical stages but selecting the Q of stages to give the desired cut-off
characteristic. While the basic filter types will have 20dB/decade per pole it
is the way that they get there that is important, as well as the corresponding
transient response and/or group delay and phase response.

The situation is worse with a passive filter if you don’t remember the fact
that a simple 2 pole LC needs a source and load impedance. If you cascade two
passive LC filters, not only will you not get the desired response due to the
fact that a 4 pole filter isn’t a simple cascade of two identical 4 pole
designs, you will also see the effects of the interaction of the two stages.

Below is shown the effect of cascading two identical LC 2 pole filters and
also showing the effect of a buffer with a gain of 2 (with source/load
resistors) between the two stages. Even that is not a good filter design but
avoids the peaking caused by mismatching the source and loads of the two
stages.

Variable Gain

The commonly used Sallen & Key filter is a unity gain version of the
“single amplifier biquad” (SAB). With a SAB filter you can have some gain.
However, once you have designed the filter and chosen the component values you
cannot use it as a variable gain stage. At best it will be the wrong response,
at worst it will be an oscillator. While it may seem obvious, I have seen people
make this mistake on more than one occasion.

Don’t forget about opamp bandwidth

While the Sallen & Key and SAB filters are commonly used, you must
remember that the bandwidth requirement of the opamps can get very high as the
number of poles increases. The free software from Texas Instruments – FilterPro
– shows this bandwidth requirement and it shouldn’t be ignored otherwise you
will not get the filter response you want, nor will you get the cut-off
frequency you want. As an example, a 6 pole Chebyshev 1dB ripple filter with
1kHz cut-off needs a 51MHz opamp bandwidth if you use a Sallen & Key filter.
By contrast, the “Multiple Feedback” design needs 800kHz. That is one of the
reasons that the Sallen & Key filter, while popular, is not always the best
choice for higher numbers of poles.

Remember Component Tolerances

The first problem after designing a filter is finding the nearest component
value to the one you need and making sure that it doesn’t affect the filter
design significantly. If you have some cost constraints then you will be
avoiding very expensive capacitors and probably avoiding E192 0.1% resistors.
Some filter topologies are more sensitive to component tolerances than others.
Whichever topology you use, you must remember to check the effect of component
tolerances. Below is a 4 pole 0.5dB Chebyshev with a nominal cut-off of 11kHz
(green trace) and the results of 100 Monte Carlo runs to look at the likely
effect of component tolerances.

As you can see, it is not a 0.5dB ripple Chebyshev any more. The real
situation could be worse because a Monte Carlo analysis is not a “worst case”.
The filter design software from Nuhertz will give a sensitivity analysis for
each component so you can see the effect on gain, phase and group delay. There
is a free version of the Nuhertz software but it is limited and doesn’t have the
sensitivity analysis.

Source/Load Impedances

Depending on the filter design you may not have a problem with source/load
impedances but most filters don’t have an infinite input impedance so if your
signal source hasn’t a very low impedance relative to the filter impedance it
will need buffering first. If you are designing a passive LC filter, don’t
forget to check the effect of the series resistance of the inductors.

Category: Tools · Tags: commentary

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