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One of the areas I wish to modify in any new panadapter design is the crystal filter. The four crystal Gaussian ladder design in the Z90 performs well, but widening the 1 KHz bandpass results in an asymmetrical stopband, as the holder capacitance distorts the response.

There are several approaches to restoring a symmetrical passband. One I've tried with some success is that suggested in Experimental Methods in RF Design by Wes Hayward W7ZOI, et al., canceling the holder capacitance by parallel inductance. The inductance is selected to be resonant with the crystal holder capacitance at the filter center frequency. Since holder capacitance is commonly in the 3 - 5 pF range, the resulting inductance value is often impractical, as the self-resonant frequency of the required inductor is generally below the crystal filter center frequency. The solution to this is to add padding capacitors across the crystals to bring the inductance down to practical values. And, to achieve resonance, either the paralleled inductors must be adjustable or the padding capacitance must include trimmers. Then, each individual LC "neutralizing" networks must be sequentially tuned by shorting out the other networks.

This approach works, but requires a lot of work and, preferably, reasonably sophisticated test equipment, to align. And, the resulting filter is much more complicated, which adds cost.

An alternative approach to a wideband filter is a lattice design, as illustrated below.
 

This circuit should cause you to think that you've seen it before, but in a different context. Perhaps redrawn it will look more familiar.

(I'm not going to use mathematical analysis in this discussion, substituting hand waving, computer simulation and measured results.)

A crystal filter that always gives zero output is not terribly useful, but suppose X1 and X2 are not exactly equal. Suppose, in fact that they have different series resonant frequencies, perhaps two or three KHz different, but are otherwise the same. Assuming the crystals have the same physical holder style, and since the resonant frequencies are so close, the holder capacitance will be essentially identical. At frequencies significantly away from resonance, the response of this circuit should be close to zero, as once we move away from X1 and X2's resonance points, they look similar. Thus the bridge is in balance and point B's voltage equals point A's voltage, and there is no output. Thus, the holder capacitance is effectively cancelled.

As we approach the resonance frequencies, the impedances are no longer equal and the bridge becomes unbalanced and hence an output voltage is developed at point B, proportional to the unbalance. This is exactly how a bandpass filter behaves—maximum output at the center frequency and reduced output outside the passband. 

Andy, G4OEP and M0AYF have done some work with simplified lattice filters that may be seen at http://g4oep.atspace.com/sfxf/sfxf.htm. and http://www.qrss.thersgb.net/QRSS-Band-Pass-Filters.html. Building on their work, I simulated and then built a two-crystal 8 MHz lattice filter.  For information on lattice crystal filter design beyond those two sites, you may with to consult the standard reference on passive filters, Zverev's Handbook of Filter Synthesis. (If you do not already own this book, ask your library to obtain a copy on inter-library loan as the current list price is nearing $300.). Also, Kinsman's Crystal Filters: Design, Manufacture and Application is good on lattice filter design. It is also expensive, at $175 and should be obtained via inter-library loan.  (Zverev works out to about $0.50 per page, but Kinsman's book is closer to $1.00 per page.)

In July, 2007, Brad, AL4T, wrote to say that Zverev is now available in a lower cost paperback edition. Indeed, Amazon carries it for $58, which is only about twice what I paid for the hardbound edition in 1975. To repeat—this book belongs in your personal library if you are interested in filter design.  If you are not an engineer, don't be put off by all the equations. There are plenty of tables and discussions you can use to design filters without delving deeply into the mathematics. But, if you take the time and wade through the math, you will have an even better understanding of filter design.

Since the two crystals should be close in resonant frequency, but not exactly matched, I used an 8 MHz series resonant crystal and an 8 MHz 20 pF parallel resonant frequency crystal. Using an HP 87510A VNA,  I first measured the parameters of these crystals, taking a sample of 10 parallel resonant crystals and using data developed for 65 series resonant crystals when working on the Z90 filters. These are inexpensive crystals used for microprocessor clock oscillators.

The capacitor identified as C3/Cx is a 5-30 pF trimmer. C5 is a 15 pF NP0 ceramic. The two crystals are identified as C1 and C2 because that's the way LTSpice models crystals. The input and output 50 ohm resistors represent the impedance of the test equipment used to measure the filter.

However, we note other changes, in that "wings" develop on the filter at certain capacitance settings, and the ultimate rejection varies considerably with the degree of circuit balance the trimmer is able to achieve.
 

I breadboarded the filter using one of the PCB holders I developed. These are discussed at my Prototyping page. I measured the filter's response using an HP87510A VNA.

Let's see how the filter performs.

All crystals exhibit spurious resonance modes, although some care in crystal production by shaping the blank edges (think increased cost) can reduce their number and intensity. However, spurious responses are not of significant concern for a microcontroller time base oscillator and hence they are not controlled.

One possible fix for at least the far outlying spurious responses would be to back up the crystal lattice with a high quality LC bandpass filter, perhaps 50 KHz wide. This is at the edge of achievable at 8 MHz with powdered iron toroidal inductors. Another fix would be to discard our inexpensive microprocessor crystals and purchase custom designed crystals, intended for crystal filter use. This would increase the filter cost many fold, of course, and would probably still exhibit spurious responses, just not as many as seen with the microprocessor crystals.

We also may ask why these spurious responses show up in the lattice filter but are not present in the Z90's Gaussian ladder filter, which uses the same crystals. As the plot below shows, the Z90's filter is free of spurious signals. (The plot is only 25 KHz span, as I don't have a wider data set at hand. However, the wider studies show similar spurious-free response.)

The answer resides in the filter topology. If we look out 100 or 200 KHz from resonance, where the spurious responses lie, the lattice filter resembles a bridge in balance. Its passband rejection relies upon the two crystals having identical responses, in this case the holder capacitance, plus the padding/trimmer caps. Unless both crystals have identical spurious responses--which is exceedingly unlikely--spurious responses in either crystal result in bridge unbalance and hence output. One might think of the lattice design as placing the spurious responses of the crystals in parallel, i.e., all spurious responses of both crystals appear in the output.

Consider, in contrast, the ladder filter used in the Z90, as presented below.

The crystals are effectively in series. Hence in order for a spurious response seriously compromise the filter, the spurious must be coincident in more than one crystal, which is unlikely as the spurious frequencies depend on more or less random effects in the crystal blank . Otherwise, the selectivity of the remaining three crystals damps out spurious responses of any single crystal. (When building an analog panadapter a few years  ago, I found that a three-crystal ladder had unacceptable spurious problems, as the attenuation of just two series crystals was not enough to control spurious levels. A four-crystal filter performs much better.)

Using AADE Filter Design software, I designed a 50 KHz wide 4th order coupled resonator Butterworth bandpass filter, with the resulting schematic below. I assumed the inductors were wound with 12 turns on a T50-2 core, with a Q of 150. (The actual inductors I wound have measured Q at 7.9 MHz between 230 and 240.)

I'll display the two measured responses side-by-side. Note that the data sweeps have different vertical reference (-70 dB versus -40 dB) and span values (500 KHz versus 1 MHz). The data is taken with an HP8752B vector network analyzer
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