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Chebyshev Distributed Lowpass Filter: DLPFC

Symbol

Summary

DLPFC models represent distributed-element Chebyshev lowpass filters. They offer simplicity and good selectivity. They exhibit an initial lowpass characteristic, followed by alternating stopbands and passbands at higher frequencies. The insertion loss ripples between zero and a specified maximum in the passband. The stopband attenuation increases rapidly beyond the passband edge towards FC. The attenuation characteristic is symmetrical about the commensurate frequency, FC.

Parameters

Name Description Unit Type Default
ID Filter ID Text DLPFC1
N Number of elements in the filter   3
FP Passband corner frequency (when QU is infinite) Frequency 1 GHz
FC Commensurate frequency ( Frequency 2 GHz
*AP Maximum passband insertion loss (when QU is infinite) DB 0.1 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 Chebyshev filter:

where Cn is the Chebyshev polynomial of the first kind, and

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.

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 equal RL for ideal transmission (as would normally be the case for odd-order Chebyshev filters).

References

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

[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. 44-48.

[5] Louis Weinberg, Network Analysis and Synthesis, (Robert E. Krieger Publishing, 1975), pp. 507-529.

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