On Sat, 22 Feb 2003, Russell McMahon wrote:

> > I need to design a filter with the following spec.
> > Im not sure about the cutoff but it needs to maintain the following
> > figures up to 70kHz:
> >
> > amplitude flatness to within 0.01%
> > phase flatness to within 0.01%
> >
> > and be around 40dB down by 700kHz.
>
> 70 to 700 = 1 decade.
> You get 20 dB per decade per pole so you want at least two poles.
> You can get 2 poles with RC alone but almost certainly not to meet your
> spec.

Yeah, but 0.01% flatness in the passband and 40 dB attenuation over one
decade is extremely hard (actually impossible) to achieve with just 2
poles!

>
> While you can do this with LC the normal method would be to use an active
> filter UNLESS there are good reasons to go passive. Using an active filter
> you would probably use 4 poles to relieve design constraints. Some versions
> can be built with a dual opamp.
>
> I think you'll find that the phase and gain flatness are a real challenge.
> Chebychev is definitely out. Butterworth is maximally flat but Bessel has
> best phase flatness.

Bessel is definitely cool in that it's monotonic in phase and amplitude.
Unfortunately, its cutoff knee is so soft that in my opinion it's really
just useful as an antialiasing filter that has more attenuation a
single-pole RC filter.

To achieve 0.01% flatness and 40dB attenuation at 700kHz will require
either a Chebychev II or an elliptic filter. The Chebychev type II filters
are monotonic in the passband as opposed to Chebychev type I filters
(which what most people simply call Chebychev filters) which are monotonic
in the stop band.

The elliptic filters have ripple in the pass and stop bands. However,
these have the greates flexibility and can be designed to meet the
constraints of this problem. Unfortunately, it may be impossible to
actually build the filter. The reason is that the component tolerances
(specifically the 1% tolerance of the capacitors) will limit the accuracy
of the poles. A 1% shift on pole locations of an 8'th order elliptic
filter could have a catastrophic effect on the transfer function!

BTW, you can minimize the component tolerance issues by using "GIC" analog
filters. GIC is either "Gyrating Impedance Converters" or "General
Impedance Circuit" depending on who is doing the talking. (But, I believe
that the term gyrating goes back to the tube days...) These filters can
transform an LC analog filter into a circuit consisting only of resistors,
capacitors and Opamps. For each pair of poles, there are two Capacitors,
two opamps, and 4 or 5 resistors. In addition, all of the capacitors can
be designed to be the same value. Thus you can purchase an array of
matching, equal-valued capacitors.

>
> There are any number of free opamp design programs around - most IC
> manufacturers provide them including Linear Technology, NatSemi, Burr Brown
> (now TI), Microchip and more.

The IC's are Switched Capacitor filters. These are *much* easier to design
with.

>
> Here's Microchip's offering
>
>         http://www.microchip.com/1010/pline/tools/analog/software/flab/
>
> Don't pay money for any such software - lots of free versions around.

I agree. I use Octave, and pen and paper.

Scott

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