SIMPLIS Parts

2nd Order Discrete Time Filter

The 2nd Order Discrete Time Filter models a second order z-domain transfer function. The transfer function in the z-domain from the input I(z) to the output O(z) for the 2nd order discrete filter is shown below:

The difference equation representing this transfer function is:

To achieve various the two-pole discrete filters, follow these guidelines:

For a two-pole discrete filter without any zero, set both N1 and N2 to zero.
For a a two-pole discrete filter with a single zero, set N2 to zero and N1 to a non-zero value.
For a two-pole, two-zero discrete filter, set both N1 and N2 to non-zero values.

Related topics:

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Editing the 2nd Order Discrete Time Filter
Examples
Waveforms
Subcircuit Parameters

Model Name:	2nd Order Discrete Time Filter
Simulator:		This device is compatible with the SIMPLIS simulator.
Parts Selector Menu Location:	Digital Functions \| Discrete Time Filters
Symbol Library:	None - the symbol is automatically generated when placed or edited.
Model File:	None - the device model is generated before simulation.
Subcircuit Name:	SIMPLIS_DIGI1_D_DF_2POLE_Y
Symbols:
Multiple Selections:	Only one device at a time can be edited.

Editing the 2nd Order Discrete Time Filter

To configure the 2nd order discrete time filter, follow these steps:

Double click the symbol on the schematic to open the editing dialog to the Parameters tab.
Make the appropriate changes to the fields described in the table below the image.

Label	Parameter Description
N2	Numerator constant term
N1	Numerator coefficient for z^-1 term
N0	Numerator coefficient for z^-2 term
Acquisition Time	Filter acquisition time in seconds
D1	Denominator coefficient for z^-1 term
D0	Denominator coefficient for z^-2 term
Initial Condition	Initial condition of the filter output

Examples

The test circuit used to generate the waveform examples in the next section can be downloaded here: simplis_033_2ndordfilter_example.sxsch.

Waveforms

The POP waveforms below show that the DC input voltage to the filter is 0.5V and the DC output voltage is 2.5V, confirming that the DC gain of the 2nd order discrete time filter is 5.

The following AC waveforms confirm that the DC gain is 13.98dB and the pole is approximately 1kHz.

Subcircuit Parameters

Because this 2nd order discrete time filter model is generated by a template script when the simulation is executed, a fixed model cannot be inserted into a netlist. The template script for this device is simplis_make_digital_filter_model.sxscr, which you, as a licensed user, can download in a zip archive of all built-in scripts.

To download this zip file, follow these steps:

Note: You will be prompted to log in with the user name and password given to you when you registered.

Click here to go to the product-installation page on the SIMetrix website.
Click Download Links in the first paragraph of the product-installation web page.
Scroll down to the Built-in Scripts section.
Right click on Download and select Save target as..., and then navigate to a location on your computer to save the zip file.