[sdiy] Filter terminology question

[Don Tillman]

   > Date: Wed, 19 Nov 2003 19:35:48 -0800
   > From: Tom Arnold <xyzzy at sysabend.org>
   > 
   > When talking about a filter, what is the difference between Poles
   > and Order?

Typically not much.  (That's a serious answer.)

The order of a filter is the number of devices with state (devices
that store energy, such as capacitors or inductors) which
independantly contribute to the filter's transfer function.  Or for a
mechanical filter, that would be masses and springs.

When we work out the transfer function of a filter, we normalize it to
a single fraction, with a polynomial for the numerator and another
polynomial for the denominator.  Like this:

          as^2 + bs + c
   F(s) = -------------
          ds^2 + es + f

Where a..f are constants from parameters of the circuit.

Polynomials have 'roots', values of s where the value of the
polynomial is zero.  An nth order polynomial will have n roots.

The roots of the numerator polynomial are called the 'zeros'.
The roots of the denominator polynomial  are called the 'poles'.

And the order of the filter is the greater of the number of poles and
the number of zeros.

The number of zeros will usually be less than or equal to the number
of poles. It's possible to have additional zeros, zeros without poles,
but such a filter would have a gain that goes up with frequency, and
infinite gain at infinite frequency.  That's not real practical.

So typically the order of the filter will be the number of poles.

  -- Don

-- 
Don Tillman
Palo Alto, California
don at till.com
http://www.till.com