Ladder Crystal Filter Design

John Hardcastle, G3JIR, described an interesting ladder filter design technique in 1980 that appears to have been forgotten. I've extracted the relevant information from John's article and presented it, somewhat simplified, in 'cookbook' form.

Basically, G3JIR's technique involves measuring the bandwidth of a simple two-pole filter, modifying it for the desired bandwidth, and then calculating the shunt capacitors required for a filter of the same bandwidth, but with more crystals to improve the shape factor.

The following test rig needs to be constructed. I just wired it up on a scrap of PCB material. Since the input and output impedance should be equal I used a dual pot. Separate ten-turn pots might make the settings easier if you want to get the resistance settings 'spot-on'. They aren't all that critical.

1. Using

               R1 = 0.613*1E6/(2*PI*f*C1) 

calculate the test impedance (Ohms).

2. Set the filter input and output impedance on the test rig to this value, measuring between A-B and C-D using a DVM.

3. Sweep the signal generator across the filter pass-band. The ripple should be about 1 dB with two peaks. If it isn't you've either got the calculation wrong, or set the pots incorrectly.

4. Measure the 3 dB bandwidth (BW1).

5. Calculate C for the desired bandwidth (BW2), using

               C2 = C1*(BW1/BW2)^2. 

6. Calculate the new impedance using

               R2 = 0.613*1E6/(2*PI*f*C2) 

7. Change the coupling capacitors to C2, and set the input and output impedance to R2.

8. Measure the new bandwidth. It should now be BW2.

To be continued ...

References:

Hardcastle, J.A. Ladder Crystal Filter Design. QST. November 1980. Pages 20-23.