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Bessel Distributed Lowpass Filter: DLPFD

Symbol

Summary

DLPFD models represent distributed-element Bessel-Thomson lowpass filters. They offer simplicity and maximally flat group delay, but suffer from poor selectivity. They exhibit an initial lowpass characteristic, followed by alternating stopbands and passbands at higher frequencies. The filter's attenuation characteristic is symmetrical about the commensurate frequency, FC. The group delay is maximally flat at zero frequency and at the center of each of the repeating bandpass characteristics.

Parameters

Name Description Unit Type Default
ID Filter ID Text DLPFD1
N Number of ements.in the filter   3
FP Passband corner frequency (when QU is infinite) Frequency 1 GHz
FC Commensurate frequency Frequency 2 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 Uniform unloaded Q of elements   1e12

* indicates a secondary Parameter

Parameter Restrictions and Recommendations

  1. 0 < N < 27

  2. 0 < FP < FC

  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 Richard's transformation has been applied to the frequency variable:

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

The model only takes distributed series inductances and distributed shunt capacitances into account - it does not account for unit elements.

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 equal RL for ideal transmission (as would normally be the case).

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.

References

[1] H. J. Horton and R. J. Wenzel, "Optimum quarter-wave TEM filters," IRE Trans. on MTT, Vol. MTT-13, May 1965, pp. 316-327.

[2] P. I. Richards, "Resistor-transmission-line circuits," Proc. IRE, vol. 36, February 1948, pp. 217-220.

[3] Joseph Helszajn, Synthesis of Lumped Element, Distributed and Planar Filters, (McGraw-Hill, 1990), pp. 160-163, 284-288.

[4] 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.

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

[6] 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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