Note: This crystal filter requires very high precision components. We strongly recommend changing the "Digits right of decimal" in Options from the Tools menu to 6. You may want to change it back after you are done with this example.
A 4th order Chebyshev filter with a center frequency of 9.001 MHz, a bandwidth of 3 KHz and 300 ohms terminating impedance is designed using a crystal with the following parameters:
Rs = 31 ohms
Lm = 24.54 millihenries (24.54E6 nH)
Co = 4.18 pF
Cm = 0.0127429 pF, which resonates with Lm at the crystal series frequency
FILTER was used to design the shunt-C coupled bandpass, specifying 24.54E6 nH for the inductor, and then writing the Genesys file. The shunt-C coupled bandpass filter topology is similar to ladder crystal bandpass filters. Since the shunt-C filter allows specifying the series inductance, designing ladder crystal filters is straightforward. Each series inductor-capacitor pair is converted to a crystal XTL model as shown in the circuit above. The response is shown in the figures below.
The 2.4 pF crystal parallel capacitance causes the high side selectivity to be greater. This places an upper limit on the bandwidth of this type of ladder crystal filter. Placing an inductor in parallel with the crystal to resonate out Co may allow a wider bandwidth.