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Kirt Blattenberger - RF Cafe Webmaster

Copyright: 1996 - 2024
Webmaster:
    Kirt Blattenberger,

    BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while typing up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived...

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Gaussian Lowpass Filter Poles
(to 6 dB & to 12 dB)

Filter Gaussian to 12 dB (Analog Devices) - RF Cafe

Click here for the Analog Devices (Fig. 10) document containing the graph.

A Gaussian filter is a filter whose impulse response is a Gaussian function. Gaussian filters are designed to give no overshoot to a step function input while minimizing the rise and fall time. This behavior is closely connected to the fact that the Gaussian filter has the minimum possible group delay. Mathematically, a Gaussian filter modifies the input signal by convolution with a Gaussian function; this transformation is also known as the Weierstrass transform. - Wikipedia

See the online filter calculators and plotters here.

Here are the lowpass prototype poles for a Gaussian filter to 6 dB and to 12 dB. Lowpass prototype inductor and capacitor values are here.


Gaussian to 6 dB, Gaussian to 12 dB Copyright © 2006 The McGraw-Hill CompaniesNote*: The values given in the two tables below have been edited to agree with those in Table XI and Table XII in "AN-649: Using the Analog Devices Active Filter Design Tool." Even it contains an extraneous number in the 3rd-order Gaussian to 12 dB table. The values given in Chapter 8 of Analog Device's Design Handbook for both the Gaussian to 6 dB and Gaussian to 12 dB appear to be wrong (they are what I originally used). Always be sure to verify critical references.

Gaussian to 6 dB
Order (N) Re Part (-σ) Im Part (±jω)
3 0.9622
0.9776
1.2214
4 0.7940
0.6304
0.5029
1.5407
5 0.6190
0.3559
0.6650
0.8254
1.5688
6 0.5433
0.4672
0.2204
0.3431
0.9991
1.5067
7 0.4580
0.3649
0.1522
0.4828
0.5932
1.1286
1.4938
8 0.4222
0.3833
0.2878
0.1122
0.2640
0.7716
1.2066
1.4798
9 0.3700
0.3230
0.2309
0.08604
0.3842
0.4704
0.9068
1.2634
1.4740
10 0.3384
0.3164
0.2677
0.1849
0.06706
0.2101
0.6180
0.9852
1.2745
1.4389
Gaussian to 12 dB
Order (N) Re Part (-σ) Im Part (±jω)
3 0.9360
0.9360
1.2168
4 0.9278
0.9192
1.6995
0.5560
5 0.8075
0.7153
0.8131
0.9973
2.0532
6 0.7019
0.6667
0.4479
0.4322
1.2931
2.1363
7 0.6155
0.5486
0.2905
0.6291
0.7703
1.5154
2.1468
8 0.5441
0.5175
0.4328
0.1978
0.3358
0.9962
1.6100
2.0703
9 0.4961
0.4568
0.3592
0.1489
0.5065
0.6192
1.2145
1.7429
2.1003
10 0.4535
0.4352
0.3886
0.2908
0.1136
0.2794
0.8289
1.3448
1.7837
2.0599

* Thanks to RF Cafe visitor Tim C. for pointing out the errors.

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