SXFERR - S-domain Transfer Function (Differential IO)

Model Kind

General

Model Sub-Kind

Generic Editor

SPICE Prefix

A

Model Name

S_XFER

SPICE Netlist Template Format

@DESIGNATOR %%vd(%1,%2) %%vd(%3,%4) @"DESIGNATOR"SXFER
.MODEL @"DESIGNATOR"SXFER s_xfer (?in_offset|in_offset=@in_offset| ?gain|gain=@gain| num_coeff=[@num_coeff] den_coeff=[@den_coeff] ?int_ic|int_ic=[@int_ic]| ?denormalized_freq|denormalized_freq=@denormalized_freq|)

Parameters (definable at component level)

The following component-level parameters are definable for this model type and are listed on the Parameters tab of the Sim Model dialog. To access this dialog, simply double-click on the entry for the simulation model link in the Models region of the Component Properties dialog.

Notes

This model provides a single input, single output transfer function in the Laplace transform variable, s. This function enables you to modulate the frequency-domain characteristics of a signal.
The s-domain transfer function you define must adhere to the following two restrictions:

• The degree of the numerator polynomial cannot exceed that of the denominator polynomial.
• All polynomial coefficients must be stated explicitly, even if a coefficient is zero.

The model takes the differential input signal, applies any offset and gain specified by the in_offset and gain parameters and then multiplies the result by the transfer function determined by the polynomial coefficient entered in the respective num_coeff and den_coeff parameters.

When specifying the coefficients for numerator and denominator, the highest powered term coefficient must be entered first, followed by those coefficients for subsequent decreasing power terms.

There are no limits on the internal signal values, or on the output of the transfer function. Care should therefore be taken when specifying coefficients and gain, so that excessively large output values do not result.

In AC Small Signal analysis, the output of the function is equal to the real and imaginary components of the total s-domain transfer function at each frequency of interest.

The int_ic parameter is an array that must be the same size as the array of values specified for the den_coeff parameter. For example, if there are three coefficient entries defined in the den_coeff parameter, then the int_ic parameter must also have three entries, using spaces as separators. By default, this parameter has the value 0. The size of the array is not initialized by default. This means that if the den_coeff parameter has more than one coefficient, the int_ic parameter will still only have the single entry, 0, if used in its default mode. The mismatch in array sizes will cause errors when trying to run the simulation. If you intend to use the default value for int_ic, you must enter this value the required number of times, such that the number of entries match the number of coefficient entries in den_coeff. For example, if den_coeff had the entries:

1.9087 1.4325 0.28783

and you wished to use the default value (0) for int_ic, then you would need to enter the following for the int_ic parameter value:

0 0 0

The provision of the denormalized_freq parameter allows you the freedom to either:

• specify the transfer function for a normalized (1 rad/s) filter and then enter the frequency of interest - effectively scaling the filter after the normalized coefficients have been defined. The frequency must be entered in radians/second.
• specify the transfer function and related coefficients directly for the frequency of interest. In this case, the denormalization_freq parameter can be left blank as the default value of 1 rad/s will be used.
  Truncation error checking is an inherent part of the model. If truncation errors become excessive, the model uses smaller time increments between simulation data points, therefore providing for a more accurate simulation.

Examples

Consider the s-domain transfer function in the above image, with the following characteristics:

• Pin1 (positive input) is connected to net In1
• Pin2 (negative input) is connected to net In2
• Pin3 (positive output) is connected to net Out
• Pin4 (negative output) is connected to net GND
• Designator is U1
• num_coeff = 1
• den_coeff = 1 2.6131 3.4142 2.6131 1
• int_ic = 0 0 0 0 0
• denormalized_freq = 18849.5559 rads/s (3kHz)
• All other model parameters are left at their inherent default values

The transfer function represented by the model is that of a normalized 4th order Butterworth lowpass filter. The value entered in the denormalized_freq parameter will move the corner frequency to 3kHz (from the normalized 1 rad/s, or 159mHz).

The normalized transfer function for the filter is:

                           1
G(s) =  ------------------------------------------
          1s4 + 2.6131s3 + 3.4142s2 + 2.6131s + 1

The entry in the SPICE netlist would be:

*Schematic Netlist:
AU1 %vd(IN1,IN2) %vd(OUT,0) AU1SXFER
.MODEL AU1SXFER s_xfer (  num_coeff=[1] den_coeff=[1 2.6131 3.4142 2.6131 1]
+ int_ic=[0 0 0 0 0] denormalized_freq=18849.5559)

The effect of the function can be seen in the resultant waveforms obtained by running an AC Small Signal analysis of the circuit.

In this example, the following analysis parameters on the AC Small Signal Analysis page of the Analyses Setup dialog have been used:

• Start Frequency - set to 10.00
• Stop Frequency - set to 100.0k
• Sweep Type - set to Decade
• Test Points - set to 500

By plotting the magnitude response in dBs, the corner frequency can be seen more clearly.