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Butterworth Quasi-Lowpass Filter: QLPFB

Symbol

Summary

QLPFB models represent lumped-element Butterworth quasi-lowpass filters. They offer simplicity and a compromise between high selectivity and flat group delay. The insertion loss is maximally flat at the passband's geometric center and the upper stopband attenuation increases monotonically.

Parameters

Name Description Unit Type Default
ID Element ID Text QLPFB1
HN Half the number of reactances.   3
FL Lower frequency edge of passband (when Qu is infinite). Frequency 0.5 GHz
FH Upper frequency edge of passband (when Qu is infinite). Frequency 1.5 GHz
*AP Maximum passband attenuation (when Qu is infinite). DB 3.0103 dB
*RS Source resistance. Resistance 50 ohm
*RL Load resistance Resistance 50 ohm
*QU Uniform unloaded Q reactive element in the filter   1e12

* indicates a secondary parameter

Parameter Restrictions and Recommendations

  1. 0 < HN < 29

  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 Butterworth filter:

where

where

where

where

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

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

Layout

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).

References

[1] Rolf Schaumann, Mohammed S. Ghausi, and Kenneth R. Laker, Design of Analog Filters: Passive, Active RC, and Switched Capacitor, (Prentice-Hall, 1990), pp. 40-44.

[2] Louis Weinberg, Network Analysis and Synthesis, (Robert E. Krieger Publishing, 1975), pp. 493-498.

[3] Adel S. Sedra and Peter O. Brackett, Filter Theory and Design: Active and Passive, (Matrix Publishers, 1978), pp. 105-111.

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

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