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Butterworth Highpass Filter: HPFB

Symbol

Summary

HPFB models represent lumped-element Butterworth highpass filters. They offer simplicity and a compromise between high selectivity and flat group delay. The insertion loss is maximally flat at infinite frequency and the stopband attenuation increases monotonically with decreasing frequency at an asymptotic rate of 6N dB per octave.

Parameters

Name Description Unit Type Default
ID Element ID Text HPFB1
N Number of elements in the filter   3
FP Passband corner frequency (when Qu is infinite). Frequency 1 GHz
*AP Passband corner 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 of elements   1e12

* indicates a secondary parameter

Parameter Restrictions and Recommendations

  1. 0 < N < 29

  2. 0 < FP

  3. 0 < AP Recommend AP greater than or equal to 0.001 dB.

  4. 0 < RS

  5. 0 < RL

  6. 0 < QU. Recommend QU less than or equal to 1012.

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

and a lowpass-to-highpass 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

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).

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.

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

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