NBPFG models represent lumped-element Gaussian bandpass filters. The applicability of this filter type is not limited to narrow bandwidths, as the name seems to imply. The group delay is flatter than that of a "regular" Gaussian bandpass filter of the same bandwidth, especially for wideband filters. Also, the passband magnitude displays arithmetic, rather than geometric, symmetry. NBPFG models approximate the ideal Gaussian magnitude response and offer simplicity, relatively flat group delay, and good time domain performance, but suffer from poor frequency selectivity. Although similar to Bessel-Thomson filters, Gaussian filters offer faster rise times and lower transient overshoots, but have slightly less stopband attenuation and less group delay flatness.
Name | Description | Unit Type | Default |
---|---|---|---|
ID | Element ID | Text | NBPFG1 |
N | Number of resonators in the filter | 3 | |
FP1 | Passband lower band-edge frequency (when Qu is infinite). | Frequency | 0.5 GHz |
FP2 | Passband upper band-edge frequency (when Qu is infinite). | Frequency | 1.5 GHz |
AP | Maximum 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 filter resonators | 1e12 |
* indicates a secondary parameter
0 < N < 51
0 < FP1
0 < FP2
0 < AP Recommend AP greater than or equal to 0.001 dB.
0 < RS
0 < RL
0 < QU. Recommend QU less than or equal to 1e12.
This model is implemented as a short-circuit admittance matrix,
, whose equivalent transfer function squared magnitude is that of an ideal Gaussian filter. The ideal Gaussian squared magnitude characteristic is:
In the model, the denominator of this ideal Gaussian characteristic is approximated by a truncated Maclaurin series:
where
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.
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).
This filter model is non-causal and not usable in transient simulations. An error
message is issued if a transient simulation of a circuit containing this model is
attempted. (Causality is defined as the response of a circuit
following
a stimulus--not preceding
a
stimulus. Non-causal models do not correspond to a physically realizable device.)
[1] Milton Dishal, "Gaussian-Response Filter Design," Electrical Communication, vol. 36, March 1959, pp. 3-26.
[2] Anatol I. Zverev, Handbook of Filter Synthesis, (John Wiley & Sons, 1967), pp. 67, 70, 71, 73, 74, 90, 91.
[3] DeVerl. S. Humpherys, The Analysis, Design, and Synthesis of Electrical Filters, (Prentice-Hall, 1970), pp. 413-417.
[4] Herman J. Blinchikoff and Anatol I. Zverev, Filtering in the Time and Frequency Domains, (Robert E. Krieger Publishing Co., 1987), pp. 130-132.
[5] H. Blinchikoff, "A note on wide-band group delay," IEEE Trans. Circuit Theory, pp. 577-578, Sept. 1971.