[Elecraft] Up-conversion.

[Jack Smith]

> Can really good CW filters be made for VHF? By "really good", I mean, 
> say, 400 Hz bandwidth, less than 6 dB loss, 6:60 dB shape factor less 
> than 3 to 1?
>
> What about stability over the temperature range?
>
>
>   
Going to be difficult.

 From filter theory (see, e.g., Zverev) we know that the crystal Q and 
the filter fractional bandwidth are  related by the equation:

qx = (delta fs/f0)*Qx

where:
qx is the normalized Q in Zverev's prototype low pass filter table
delta fs is the flter bandwidth
f0 is the filter center frequency
Qx is the individual crystal Q needed to construct the filter.


I'll leave the details to the interested reader, but I plugged in these 
requirements (6 dB loss, 400 Hz bandwidth and 3:1 or better shape 
factor) into the equations and tables for a few typical designs, all at 
45 MHz, a common IF frequency. (Go higher and the problem is 
proportionally worse; and you can't go much lower and still have an 
up-converting design for a maximum receiver frequency of 30 MHz.)

The results call for crystal Qs in the order of 1.5 million to 2.5 
million, depending on the number of filter sections and design type.

I've measured quite a few crystals in the process of building and 
testing about 20 crystal filters for my pandapter design. The highest Q 
crystals I've found (these are all HC-49 case microprocessor crystals of 
the inexpensive variety) run around 100K to 110K, and a more typical 
value is 80K to 90K. I've also measured about 10% of a batch of 
microprocessor crystals as having Qs in the 30-40K range. Still 
perfectly OK for an oscillator but not so good for a low loss crystal 
filter. (If you go to a crystal manufacturer and purchase custom 
crystals for filter purposes, I believe you may see Qs closer to 200K if 
you are willing to pay for them.)

Now those Q values are perfectly adequate for a decent filter at 8 MHz, 
but are an order of magnitude or more short of adequate for a 45 MHz 
narrow band filter.

Crystals with Qs in the 106 range are possible and have been built, but 
the are not cheap and I don't know if they are available in the desired 
frequency range.

I have also not looked at issues related to the ratio of holder 
capacitance to motional capacitance and some other design 
considerations, as the minimum Qx seems to be a show stopper.

There are some many practical problems with the holder capacitance, 
stray capacitance and the like that would make such a filter 
challenging, even if someone were to deliver a box of 45 MHz crystals 
with measured Qs of 2 million to my doorstep. And if  the box of 
crystals arrive, to obtain frequency stability might require stabilizing 
the filter assembly in a temperature controlled oven.

The typical roofing filters at 45 MHz have a bandwidth of 20 KHz or so. 
Thus the fractional bandwidth is 50 times larger and the Qx is down into 
the 100K range, making these filters relatively easy to realize.


Jack K8ZOA
www.cliftonlaboratories.com

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