Bandpass filter tutorial (was K3 Filters)

[Alan Bloom]

The amount of ringing of a bandpass filter depends on the bandwidth of the
individual poles (crystals or tuned circuits) that make up the filter.
One way to make a bandpass filter is to cascade a bunch of 1-pole
(single-crystal) filters with isolation amps so they don't interact.  You
select the pole bandwidths and space the pole frequencies across the
passband so as to obtain an equal-ripple response.

Filters are rarely constructed that way because of dynamic range
limitations, but a crystal-lattice or ladder filter achieves much the same
result.  The bandwidth of the narrowest poles (the ones towards the band
edges) determines the amount of ringing.

To get steeper filter skirts (smaller shape factor) you can:
1. Use more poles (with narrower bandwidths)
2. Increase the passband ripple (by narrowing the pole bandwidths)
Either method increases the ringing.

So the amount of ringing depends on the filter bandwidth and the steepness
of the filter skirts.  The narrower the bandwidth and the steeper the
skirts, the more ringing.

The above is true for both digital and analog filters.  Digital FIR
filters do have several advantages however:
1. You can trade off stop-band rejection to reduce the ringing.
2. It is easy and cheap to use many more poles for better shape factor and
stop-band rejection.
3. They have inherently flat group delay.

Al N1AL

> Any filter will produce "ringing" when the bandwidth is too small.
>
> Ringing is a function of the bandwidth and only affected by the type of
> filter. In some filter designs it's possible for some elements of the
> filter
> to have such a high Q they ring even though the overall filter bandpass is
> not that small, but that's a aberration in the filter design.
>
> Ringing typically occurs when the bandwidth at either the transmitter or
> receiver is restricted too much to allow the CW sidebands to pass through.
>
> Of course, the sidebands on a CW signal are the frequencies represented by
> the rise and fall of each CW element. If the bandwidth isn't sufficient to
> pass them, the element is stretched out in time as the amplitude decays,
> just like the amplitude of a bell decays after the bell was stuck. That's
> what we call "ringing".
>
> Ron AC7AC
>
> -----Original Message-----
> From: [hidden email]
> [mailto:[hidden email]] On Behalf Of Alan Bloom
> Sent: Friday, November 30, 2007 1:47 PM
> To: Darwin, Keith
> Cc: [hidden email]
> Subject: RE: [Elecraft] K3 filters
>
>
> For the same passband ripple and bandwidth I think more poles pretty much
> invariably means more ringing.
>
> By the way, many people think that DSP-based filters don't ring.
> Actually, a digital filter's impulse response, measured at say the
> half-power point, is pretty comparable to an analog (e.g. cyrstal) filter
> with the same ripple and bandwidth.  However, the ringing from a digital
> FIR (finite impulse response) filter eventually drops all the way to
> zero, while an IIR (e.g. analog) filter theoretically rings forever.
> Since human sound perception tends to be logarithmic, the ringing
> _sounds_ longer with the analog filter.
>
> Al N1AL

>


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