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Gaussian Quasi-Lowpass Filter (Closed Form): QLPFG



QLPFG models represent lumped-element Gaussian quasi-lowpass filters. They offer simplicity, relatively flat group delay, and good time domain performance, but suffer from poor frequency selectivity. Although similar to Bessel-Thomson filters, Gaussian filters offer faster rise times and lower transient overshoots, but have slightly less stopband attenuation and less group delay flatness.


Name Description Unit Type Default
ID Element ID Text QLPFG1
HN Half the number of reactances   3
FL Lower passband edge (when Qu is infinite). Frequency 0.5 GHz
FH Upper passband edge (when Qu is infinite). Frequency 1.5 GHz
AP Maximum passband attenuation (when Qu is infinite). DB 3.0103 dB
*RS Expected source resistance. Resistance 50 ohm
*RL Expected Load resistance Resistance 50 ohm
*QU Average unloaded Q of reactive elements in filter.   1e12

* indicates a secondary Parameter

Parameter Restrictions and Recommendations

  1. 0 < HN < 51

  2. 0 < FL

  3. 0 < FH

  4. 0 < AP Recommend AP greater than or equal to 0.001 dB.

  5. 0 < RS

  6. 0 < RL

  7. 0 < QU. Recommend QU less than or equal to 1e12.

Implementation Details

The model is implemented as a short-circuit admittance matrix,

, whose equivalent transfer function squared magnitude is that of an ideal Gaussian filter. The ideal Gaussian squared magnitude characteristic is:

In the model, the denominator of this ideal Gaussian characteristic is approximated by a truncated Maclaurin series:


and a lowpass-to-quasi-lowpass frequency transformation has been applied:

_FREQ is the variable containing the project frequency, and the admittances are:


This element does not have an assigned layout cell. You can assign artwork cells to any element. See “Assigning Artwork Cells to Layout of Schematic Elements” for details.

Recommendations for Use

This model behaves as if it has ideal impedance transformers at its ports, so there is no attenuation due to mismatched source and load impedances. The model expects that the source impedance will equal RS and that the load impedance will equal RL, but RS need not have any special relationship to RL for ideal transmission (as would normally be the case).

This filter model is non-causal and not usable in transient simulations. An error message is issued if a transient simulation of a circuit containing this model is attempted. (Causality is defined as the response of a circuit following a stimulus--not preceding a stimulus. Non-causal models do not correspond to a physically realizable device.)


[1] Milton Dishal, "Gaussian-Response Filter Design," Electrical Communication, vol. 36, March 1959, pp. 3-26.

[2] Anatol I. Zverev, Handbook of Filter Synthesis, (John Wiley & Sons, 1967), pp. 67, 70, 71, 73, 74, 90, 91.

[3] DeVerl. S. Humpherys, The Analysis, Design, and Synthesis of Electrical Filters, (Prentice-Hall, 1970), pp. 413-417.

[4] Herman J. Blinchikoff and Anatol I. Zverev, Filtering in the Time and Frequency Domains, (Robert E. Krieger Publishing Co., 1987), pp. 130-132.

[5]Max W. Medley, Jr., Microwave and RF Circuits: Analysis, Synthesis and Design, (Artech House, 1993), pp. 312-317.

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