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Chebyshev Narrowband Bandpass Filter (Closed Form): NBPFC



NBPFC models represent lumped-element Chebyshev bandpass filters. The applicability of this filter type is not limited to narrow bandwidths, as the name would appear to imply. The group delay is flatter than that of a "regular" Chebychev bandpass filter of the same bandwidth, especially for wideband filters. And the passband magnitude displays arithmetic, rather than geometric, symmetry. The insertion loss ripples between zero and a specified maximum in the passband. The stopband attenuation increases rapidly and monotonically beyond the passband edges. This filter type offers simplicity and good selectivity.


Name Description Unit Type Default
ID Element ID Text NBPFC1
N Number of resonators in the filter   3
FP1 Lower frequency edge of passband (when Qu is infinite). Frequency 0.5 GHz
FP2 Upper frequency edge of passband (when Qu is infinite). Frequency 1.5 GHz
AP Maximum passband attenuation (when Qu is infinite). DB 0.1 dB
*RS Expected source resistance. Resistance 50 ohm
*RL Expected load resistance Resistance 50 ohm
*QU Average unloaded Q of filter resonators   1e12

* indicates a secondary parameter

Parameter Restrictions and Recommendations

  1. 0 < N < 27

  2. 0 < FP1

  3. 0 < FP2

  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 Chebyshev filter:

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

and a lowpass-to-narrowband-bandpass frequency transformation has been applied:

This frequency transformation has good delay preserving properties for wide band filters and produces passband amplitudes with arithmetic symmetry. _FREQ is the variable containing the project frequency, and the admittances are:


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).


[1] 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.

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

[3] H. Blinchikoff, "A note on wide-band group delay," IEEE Trans. Circuit Theory, pp. 577-578, Sept. 1971.

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