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Bessel Highpass Filter: HPFD

Symbol

Summary

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

Parameters

Name Description Unit Type Default
ID Element ID Text HPFD1
N Number of reactive 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 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 < N < 32

  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 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

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

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. 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.

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