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Nexxim Simulator >
Nexxim Component Models >
Nexxim Filters >
Polynomial Filter, Causal

Polynomial Filter, Causal

Netlist Syntax

An instance of a polynomial low pass filter has the following Nexxim netlist syntax:

Axxx n1 n2 FILTER_TYPE=1|2|3|4 [FC=val] [GF=val] [BW=val] NUMER=[a0 a1 ...] DENOM=[b0 b1 ...] COMPONENT=polynomial_filter_causal

n1 and n2 are the nodes connected to the filter. The parameter FILTER_TYPE selects the passband. The entry COMPONENT=polynomial_filter_causal is required.

**Polynomial Low Pass Filter Instance Parameters**
Parameter	Description	Units	Default
FILTER_TYPE	Passband selector: 1=HIGHPASS, 2=LOWPASS, 3=BANDREJECT, 4=BANDPASS	None	None
FC	3dB cutoff frequency	Hz	1e9
GF	Gain factor	None	1.0
BW	3dB Bandwidth	Hz	1e9
a0 ... aN	Coefficients of the numerator polynomial	None	None
b0 ... bD	Coefficients of the denominator polynomial	None	None

Netlist Example

To specify the following transfer function (where coefficient a₁=0):

The netlist would specify:

A22 1 2 FILTER_TYPE=4 FC=80e6 BW=101e4
+ NUMER=[1 0 2] DENOM=[1 1 3]
+ COMPONENT=polynomial_filter_causal

Notes

1. The element is specified using a transfer function given as the ratio of two polynomials in the complex variable s. The bold brackets for the NUMER and DENOM entries are required.

The function of the device is expressed as:

GAIN ´ H(s)

The transfer function H(s) is specified by giving the coefficients:

where F = the analysis frequency and j=sqrt(-1)

2. The first coefficients in both numerator and denominator (a₀ and b₀) are constants, which must be specified even if they are zero. Thus, leading zeros are significant. In addition, intermediate zero-valued coefficients must be explicitly supplied in order to have the non-zero coefficients applied to the correct powers of s.

3. Trailing zeros are not significant, and are automatically removed.

4. Both numerator and denominator must contain at least one non-zero value.

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