[Elecraft] K3S DSP Filter Plots

[charles at k5ua.com]

Hi Bill,

Thanks so much for the data for the two filter configurations.  This 
will give me a pretty good idea of the shape factor of the 200hz DSP 
filter.

I just ordered a K3S, and the technician that helped me with some of my 
questions said that no one has ever asked him about the shape factor of 
the DSP filters.  So I guess we are breaking new ground with this 
thread.  The definition of a filter's shape factor is the width of the 
filter between its -6 dB points and it's -60 dB points.  Since we are 
using an S-meter to determine signal strength as we move away from the 
signal's center frequency, it is a rough approximation of true signal 
strength.  We are also going to assume that the K3 S-meter is 6 dB per 
S-unit all the way from S5 to S9+40dB.  I am also assuming that these 
reading would be symmetrical if you had measured the lower side of the 
filter skirts.  Given those assumptions and their limitations, let's see 
if we can determine the shape factor of the two filter scenario's you 
measured.

Data Set 1. Cascading the DSP 400hz filter with the 400hz roofing filter 
gave a -6 dB point approximately 140hz higher than the center frequency 
(extrapolating 1 dB down from the -5 dB frequency of +134hz).  That 
would make the width of the filter at the -6 dB points approx 280 hz.  
The S6 level would represent a drop of 58 dB from the center of the 
filter (+40 dB + 18dB), so the -60 dB frequency would occur at approx 
+216hz from the center frequency.  That would make the -60 dB width of 
the filter (216hz + 216hz) = 432hz.  So the shape factor of this 
cascaded 400hz roofing filter and 400 hz DSP filter would be 432hz/280hz 
= 1.52.  Notice that this is a better shape factor than the roofing 
filter alone which has a Elecraft documented shape factor of 2.1.

Data Set 2.  The DSP filter has been narrowed to 200 hz in this scenario 
and still cascaded with the 400hz roofing filter.  This should give the 
opportunity to dtermine the shape factor of the DSP filter itself since 
it is entirely contained within the passband of the wider 400hz roofing 
filter.  The -6 dB point of the DSP filter is approx +70 from the center 
frequency ( extrapolating again 1 dB down from the -5 dB frequency of 
+68hz).  That would make the filter width at the -6 dB points (70hz + 
70hz) = 140hz.  As in the first scenario, the S6 level would represent a 
drop of 58 dB from the center of the filter (+40 dB + 18dB), so the -60 
dB frequency would occur at approx +146hz from the center frequency. 
That would make the -60 dB width of the filter (146hz + 146hz) = 292hz.  
So the shape factor of the 200hz DSP filter is 292hz/140hz = 2.08.

Based upon the data provided, the shape factor of the DSP filter is 
virtually identical to the shape factor of the roofing filter.  I'm not 
surprised that cascading two 400hz filters with identical shape factors 
create a resultant filter with a better shape factor than either filter 
alone.

I ordered the XG3 with my K3S, so I will obtain data for the 50, 100, 
and 150 hz DSP filters inside of the 400hz roofing filters.  I will also 
obtain data for the 200hz DSP filter inside of the 2800hz SSB filter.  
The data should be identical to the 200hz filter inside of the 400hz 
roofing filter.

Thanks to all that replied to my inquiry.

Charles   K5UA