CW Filter Shape Factors

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Has anyone with a signal generator measured the CW filter shape factors by measuring the -6/-60 dB points. It may be a little tough to do with the 10 hz frequency step and the S-meter not being calibrated in decibel level, but has anyone attempted this. I'm only asking because, after years and years of using 1.4:1 shape factor crystal filters, I'm not hearing what I expect to hear from "brick wall" digital filters. By using the term "brick wall" filters, I am assuming that this definition implies a much better approximation to the 1:1 shape factor of a "perfect" filter than is possible with analog filters. This is why I would like to know if anyone has measured this using the 6500 narrow CW filters.
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Charles - K5UA

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Posted 6 years ago

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Charles - K5UA

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The comment by Stan,VA7NF, about the way shape factor is determined has stuck in my head ever since I read it. After a few calculations with the measured values by Paul on the 100, 250, and 2700 filters, it appears that Stan has a valid point. On Paul's three measurements, the distance between the -6 and -60 db points on all filers was about 33 hz. This is a slope of about 1.6 db per hz for all three filters. When applied to a 2700 hz filter, the shape factor comes out to be 1.02. Wow! Brick wall, right? Why can't we create a 100 hz filter with skirts like that?

Well, they did! Paul's measurements show the same 33 hz distance between the -6 and -60 db points on the 100 hz filter. Only this time, the formula for shape factor gives a value of 1.6. So we hang our heads in sorrow that the 100 hz filter does not have as steep a skirt as the 2700 hz filter. BUT IT DOES!!! If you were a downhill skier looking over the edge of a 100 hz filter or a 2700 hz filter, you would see the same "steepness" of the slope...... a fall of 54 db in 33 hz, or 1.6 db per hz. When the edge of that 100 hz filter is applied against an unwanted signal, it is going to attenuate that unwanted signal just as effectively as that 2700 hz filter. From these three measurements by Paul, I am inclined to believe that all these digital filters are going to have the same slope factor of 1.6 db per hz. When drawn out to scale, it makes a 2700 hz filter appear to have virtually vertical sides. When drawn to scale, it makes a 50 hz filter look fair, and a 25 hz filter downright pathetic. But we must remember, it is the wall of the filter that is applied to the undesired signal, and a 54 db attenuation over a span of 33 hz is remarkable. For me, Stan's post is an epiphany because I finally understand that shape factor is a mathematical enigma. As filter width decreases, shape factor gets worse even though the slope of the skirts remain constant. The following list of filter width versus shape factor assumes a constant filter slope of 1.6 db per hz.

25 hz filter ----- 3.64 shape factor
50 hz filter ----- 2.30 shape factor
100 hz filter ----- 1.66 shape factor
250 hz filter ----- 1.26 shape factor
400 hz filter ----- 1.16 shape factor
600 hz filter ----- 1.11 shape factor
800 hz filter ----- 1.08 shape factor
1600 hz filter ----- 1.04 shape factor
3200 hz filter ----- 1.02 shape factor

Take comfort in the fact that all these filters have the same "brick wall" slope of 54db per 33 hz (1.6 db per hz).

Thanks Stan, you nailed it.
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Paul Christensen, W9AC, Elmer

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Good analysis, Charles.  What you've shown also applies to crystal filters, but unlike the mathematical perfection attained in DSP, as the crystal filter's bandwidth decreases, even slight slope imperfections have an impact on shape factor and symmetry from center. 

Putting this into perspective, look at the shape factor of the best INRAD crystal filters.  Due to manufacturing cost and inability to attain repeatable tolerance, I don't believe they offer one under 250 Hz. Their typical 250 Hz filter (at 8 MHz) has a shape factor of 2.2.

In addition to nearly perfect control of the slope, the DSP filters are providing much better ultimate filtering well beyond the -60dB point where crystal filters are subject to degradation due to I/O isolation and other blow-by effects that limit ultimate filtering performance.  Thru-loss also escalates as a crystal filter becomes narrow.  Look at the schemes developed by competing manufacturers to compensate for that loss.

It would be interesting to plot an overlay of the Flex's filters on top of a comparable INRAD crystal filter. 


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Ken - NM9P

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NN4ZZ will probably have that graphic by tomorrow!  He is really good at that stuff. [gauntlet dropped....grin]

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