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Gaussian Narrowband Bandpass Filter (Closed Form): NBPFG



NBPFG models represent lumped-element Gaussian bandpass filters. The applicability of this filter type is not limited to narrow bandwidths, as the name seems to imply. The group delay is flatter than that of a "regular" Gaussian bandpass filter of the same bandwidth, especially for wideband filters. Also, the passband magnitude displays arithmetic, rather than geometric, symmetry. NBPFG models approximate the ideal Gaussian magnitude response and 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 NBPFG1
N Number of resonators in the filter   3
FP1 Passband lower band-edge frequency (when Qu is infinite). Frequency 0.5 GHz
FP2 Passband upper band-edge frequency (when Qu is infinite). Frequency 1.5 GHz
AP Maximum Passband corner 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 filter resonators   1e12

* indicates a secondary parameter

Parameter Restrictions and Recommendations

  1. 0 < N < 51

  2. 0 < FP1

  3. 0 < FP2

  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

This 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-narrowband-bandpass frequency transformation has been applied:

This frequency transformation has good delay preserving properties for wide band filters and produces passband amplitudes with arithmetic symmetry. _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 equal 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] H. Blinchikoff, "A note on wide-band group delay," IEEE Trans. Circuit Theory, pp. 577-578, Sept. 1971.

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