EMRFD Message Archive 7203

Message Date From Subject
7203 2012-01-28 14:24:50 g3wie Ultra-spherical lpf - sums don't seem to work out
Hello All,

I'm trying to design an ultra-spherical lpf as per pp3.4 to 3.6 of EMRFD. The application is for an output filter on the LO chain of a transverter for the 70MHz band. The design should be able to use 42 or 49MHz xtals for 21 or 28MHz if and the u-sph filter looked to me a good candidate as it would cover both with no component change, and I get the improved attenuation compared to standard Chebyshev

Using equations 3.1 and 3.2 and the g(n) values from table 3.2 [corrected as per the errata] I set out to design an N=5 wide ultra-spherical lpf with Fc = 52MHz and Zo = 50ohm, on the expectation that the wide/flat part of the response just below Fc would cover 42/49MHz.

I put a spreadsheet together to do the sums, and my component values work out as 108pF, 108nH, 206pF, 108nH, 108pF. I put these into the gpla program and Fc is a long way from the design goal. A screen capture is in the G3WIE folder as ultra-sph1.


I was very suspicious that the C and L values turn out the same in pF/nH (the medium u-s coefficients do the same). As a check, I put the Butterworth coefficients into my spreadsheet, and the values it calculated are the same as the lowhi08 program, so I guess it's ok.

As a bodger of long standing, I tried setting Fc to 40MHz. That gave me a response more like what I'm seeking - see ultra-sph2.

Any ideas on why the response isn't as expected?


Chris G3WIE

ps A search on the web hasn't revealed any useful info on how to calculate the coefficients for different flavours of ultra-spherical Does anyone know of anything?
7206 2012-01-28 20:52:47 Wes Re: Ultra-spherical lpf - sums don't seem to work out
Hi Chris and group,

Very interesting problem. I'm glad that the obscure ultraspherical filter has a practical application yor you.

I went through your numbers and they are fine. I had not noticed the way the L value in nH equals the end cap value in pF. That was a quirk, but your calculations were correct.

Probably the place where you got in trouble was in trying to pick a design frequency on the basis of a cutoff. These ultraspherical filters are designed on the basis of a peak frequency. Moreover, for the wide case, "Wide U.Sp.", the frequency to use is the center of the upper passband. I took the geometric mean of 42 and 49 as a viable center. This was used for a design at 45.4 MHz, coming up with 123 pF, 123 nH, 235 pF, 123 nH, and 123 pF. A plot with GPLA then shows that you have a viable filter. It looks like you might be able to even drop the center down a little without any problems. These values gave an attenuation of 0.22 dB at 42 and 0.42 dB at 49 MHz. The 2nd harmonics were well attenuated.

I don't know of any tables. These filtes need an extra parameter that defines the nature of the filter beyond the familiar Chebyshev ripple. You also have to look at the bandwidth related to the
upper peak. So there are a very large number of possible filters that fit the polynomials described in that paper by Johnson and Johnson that's referenced in EMRFD.

I originally got interested in these filters back in the late 70s or early 80s. (Too long ago!) I had noticed that a 5th order low pass could be viewed as either the intended frequency filter, or it could be an impedance transforming network at a single frequency. I was investigating some matching structures. But then the question came up: "So, what do these things look like as filters?" I told some colleagues at Tektronix about these quests. One of them (Gordon Long) discovered the Johnson and Johns
7208 2012-01-29 05:41:41 g3wie Re: Ultra-spherical lpf - sums don't seem to work out
Thanks Wes, that's a great help.

I've tweaked the component values in gpla to get some preferred values and I'll build one and try it out, hopefully I get to talk to a network analyser tomorrow and I will look at the u-s filter as well as the top-coupled (mixed form) examples I'm evaluating.

I'll see if I can find the original paper, my searches to date have turned up lots of stuff about ultra-spherical windows for digital filter design.

Chris G3WIE

7221 2012-01-31 11:14:30 g3wie Re: Ultra-spherical lpf - results on a network analyser
7223 2012-01-31 15:15:27 Wes Re: Ultra-spherical lpf - results on a network analyser
Hi Chris,

Very interesting. It appears that the new filter does the job, although it might be a hard circuit to adjust.

I have not used the -17 toroid mix, so can't comment on the spread to expect when winding. My experience with the -6, -2, and -10 cores is that when winding just a few turns, the final L can be a strong function of the spacing of the turns. The permeability of the -17 material is even lower than the -6 that I usually use and, as such, would be even more dependent up