## Crystal ladder filter calculator

This crystal ladder filter calculator is a simple tool for dimensioning crystal bandpass filters composed by 2 to 8 identical quartz crystals and some capacitors. Quartzes are used in their fundamental mode (even if they are overtone) in their series resonance (even if they were designed for parallel mode operation).
The series and parallel resonance of the crystals must be precisely known, as well as the crystal's series capacitance Cs. Those values cannot be found on datasheets with the necessary accuracy and need to be manually measured with the method described before. It's also important to select crystals with very similar characteristics (the resonance frequencies should be within 100 Hz).
If no bandpass ripple is allowed the filter will be of Butterworth type and the transitions between pass-band and stop-band will not be very fast and the ultimate attenuation (horizontal asymptote) will be poor. If some bandpass ripple is allowed the filter will be of Chebytheff type with much better stop-band characteristics.
The number of poles of the filter equals the number of crystals and depends on how many identical crystals one happens to have.
The target bandwidth is the bandwidth the filter should pass: the maximum possible bandwidth depends on all the data entered and is usually only a few kHz.
Hitting the "Calculate" button will start the simulation.

Crystal series resonance frequency: | fs3 = |  | MHz
Crystal parallel resonance frequency: | fp = |  | MHz
Crystal series capacitance: | Cs = |  | fF
Filter bandpass ripple: | RPPB = |  | dB (0..3dB)
Number of poles: | N = | 2 3 4 6 8
Target bandwidth: | BW = |  | kHz @ -3 dB

Calculation result:

Not computed yet.

After hitting the "Calculate" button the characteristics of the filter are shown. First there is a summary of the data entered for the calculation (for easier cut & paste), than there is the maximum possible bandwidth with the current settings (but the filter is calculated for the target bandwidth).
Finally the parameters of the filter are shown: the center frequency (the frequency in the middle of the pass-band), the ultimate attenuation (horizontal asymptote well describing the filter for frequency well above or below the pass-band), the impedance (which needs to be precisely matched in order to achieve the desired bandwidth and pass-band ripple) and the values of all the capacitors.

Filter schematic:

This is the circuit diagram of the filter. This is updated according to the number of poles (crystals) when the "Calculate" button is pressed.

Filter response:

Not computed yet.

This is the simulation of the response of the filter. Crystal ladder filters are not symetrical. For filters with series crystal (as simulated here) the transition between the ultimate attenuation and the pass-band is slower on the left side (below the pass-band). This is shown in column A where the frequency offset from the filter center frequency is given for several values of attenuation (every 5 dB).
On the right side (above the pass-band) the transistion is much more sharp and the attenuation increases to infinity a few kHz above the pass-band (because of the parallel resonance of the crystals) and this part of the response is shown in column B (see drawing below).
For higher frequencies the attenuation decreases approching the ultimate attenuation again and this is shown in column C.
Column BW shows the bandwidth of the filter for different attenuations and usually the ratio between the bandwidth at -60 dB and the bandwidth at -3 dB (target bandwidth) is used to describe the sharpness of a filter.

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