CRYSTAL LADDER FILTER SIMULATION WITH SPICE

For the purposes of this exercise, I’ll assume that the crystal parameters have been measured, and are as follows:

Frequency 4 MHz

Lm (motional inductance) 0.1971 H

Cm (motional capacitance) 8.03554e-15 F

Rm (motional resistance) 48 ohms

Co (static capacitance) 3.5 pF

The filter configuration is as follows:

Calculated capacitor values for this filter are:

C3 = 94 pF

C2 = C4 = 60 pF

C1 = C5 = 14 pF

The terminating resistance is 1200 ohms.

The Pulsonix package I use for PCB design came with Pulsonix SPICE, which I’ll be using here. I created the following schematic for the SPICE analysis:

Each crystal is represented by its equivalent circuit, with its parameters. The five shunt capacitors have been added, and the input resistance (1200R) is in series with the signal source. A 1200R load is placed across the output. The 1G resistors across the shunt capacitors are required by SPICE; it doesn’t like ‘floating’ nodes, and such a high resistance won’t affect the simulation.

Running SPICE gave the following plot:

It appears to be quite a useful filter, with a reasonable shape factor, and a 3 dB bandwidth of about 500 Hz.

Lets see what happens if we change the terminating resistances to 330R:

As you can see, a real mess has been made of the response. The terminating impedance of this type of filter is quite critical.

I've extracted the netlist for this filter from Pulsonix:

With a few minor changes you should be able to use it with any flavour of SPICE.

Here are some free SPICE packages:

SIMetrix is the SPICE used with the Pulsonix package.