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Bessel Quasi-Lowpass Filter: QLPFD



QLPFD models represent lumped-element Bessel-Thomson quasi-lowpass filters. They offer simplicity and maximally flat group delay, but suffer from poor selectivity.


Name Description Unit Type Default
ID Element ID Text QLPFD1
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 < 34

  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 a Bessel-Thomson filter:


Where b0 = (2HN-1)!!,i.e, the product of all odd integers less than 2HN.

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

Note that 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).


[1] Rolf Schaumann, Mohammed S. Ghausi, and Kenneth R. Laker, Design of Analog Filters: Passive, Active RC, and Switched Capacitor, (Prentice-Hall, 1990), pp. 51-56.

[2] Louis Weinberg, Network Analysis and Synthesis, (Robert E. Krieger Publishing, 1975), pp. 499-506.

[3] Herman J. Blinchikoff and Anatol I. Zverev, Filtering in the Time and Frequency Domains, (Robert E. Krieger Publishing Co., 1987), pp. 124-127.

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

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